TSTP Solution File: SYN758-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN758-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:57:13 EDT 2022
% Result : Unsatisfiable 1.88s 1.44s
% Output : Proof 2.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN758-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 06:27:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 1.88/1.44 % SZS status Unsatisfiable
% 1.88/1.44 % SZS output start Proof
% 1.88/1.44 tff(ssPv4_type, type, (
% 1.88/1.44 ssPv4: $i > $o)).
% 1.88/1.44 tff(skf1_type, type, (
% 1.88/1.44 skf1: $i > $i)).
% 1.88/1.44 tff(elem_0_type, type, (
% 1.88/1.44 elem_0: $i)).
% 1.88/1.44 tff(ssPv3_type, type, (
% 1.88/1.44 ssPv3: $i > $o)).
% 1.88/1.44 tff(ssPv1_type, type, (
% 1.88/1.44 ssPv1: $i > $o)).
% 1.88/1.44 tff(ssPv2_type, type, (
% 1.88/1.44 ssPv2: $i > $o)).
% 1.88/1.44 tff(ssRr_type, type, (
% 1.88/1.44 ssRr: ( $i * $i ) > $o)).
% 1.88/1.44 tff(1,assumption,(~ssPv3(skf1(skf1(elem!0)))), introduced(assumption)).
% 1.88/1.44 tff(2,assumption,(~ssPv1(skf1(skf1(elem!0)))), introduced(assumption)).
% 1.88/1.44 tff(3,assumption,(~ssPv4(skf1(skf1(elem!0)))), introduced(assumption)).
% 1.88/1.44 tff(4,assumption,(~ssPv2(skf1(skf1(elem!0)))), introduced(assumption)).
% 1.88/1.44 tff(5,assumption,(~ssPv3(skf1(elem!0))), introduced(assumption)).
% 1.88/1.44 tff(6,plain,
% 1.88/1.44 (^[U: $i] : refl(ssRr(U, skf1(U)) <=> ssRr(U, skf1(U)))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(7,plain,
% 1.88/1.44 (![U: $i] : ssRr(U, skf1(U)) <=> ![U: $i] : ssRr(U, skf1(U))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[6])).
% 1.88/1.44 tff(8,plain,
% 1.88/1.44 (![U: $i] : ssRr(U, skf1(U)) <=> ![U: $i] : ssRr(U, skf1(U))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(9,axiom,(![U: $i] : ssRr(U, skf1(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.88/1.44 tff(10,plain,
% 1.88/1.44 (![U: $i] : ssRr(U, skf1(U))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.88/1.44 tff(11,plain,(
% 1.88/1.44 ![U: $i] : ssRr(U, skf1(U))),
% 1.88/1.44 inference(skolemize,[status(sab)],[10])).
% 1.88/1.44 tff(12,plain,
% 1.88/1.44 (![U: $i] : ssRr(U, skf1(U))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[11, 7])).
% 1.88/1.44 tff(13,plain,
% 1.88/1.44 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(elem!0), skf1(skf1(elem!0)))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(14,plain,
% 1.88/1.44 (ssRr(skf1(elem!0), skf1(skf1(elem!0)))),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[13, 12])).
% 1.88/1.44 tff(15,plain,
% 1.88/1.44 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(elem!0, skf1(elem!0))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(16,plain,
% 1.88/1.44 (ssRr(elem!0, skf1(elem!0))),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[15, 12])).
% 1.88/1.44 tff(17,plain,
% 1.88/1.44 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(18,plain,
% 1.88/1.44 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[17])).
% 1.88/1.44 tff(19,plain,
% 1.88/1.44 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(20,plain,
% 1.88/1.44 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) <=> (((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(V)))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) <=> ((ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(Y)))), rewrite(((ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(Y)) <=> (ssPv1(Y) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) <=> (ssPv1(Y) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) | ssPv3(Z)) <=> ((ssPv1(Y) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Z)))), rewrite(((ssPv1(Y) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Z)) <=> (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) | ssPv3(Z)) <=> (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) | ssPv3(Z)) | ssPv1(W)) <=> ((ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)))), rewrite(((ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)) <=> (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) | ssPv3(Z)) | ssPv1(W)) <=> (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(21,plain,
% 1.88/1.44 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) | ssPv3(Z)) | ssPv1(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[20])).
% 1.88/1.44 tff(22,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(V)) | ssPv1(Y)) | ssPv3(Z)) | ssPv1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.88/1.44 tff(23,plain,
% 1.88/1.44 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.88/1.44 tff(24,plain,
% 1.88/1.44 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[23, 19])).
% 1.88/1.44 tff(25,plain,(
% 1.88/1.44 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(skolemize,[status(sab)],[24])).
% 1.88/1.44 tff(26,plain,
% 1.88/1.44 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[25, 18])).
% 1.88/1.44 tff(27,plain,
% 1.88/1.44 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(28,plain,
% 1.88/1.44 ((ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(29,plain,
% 1.88/1.44 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))))),
% 1.88/1.44 inference(monotonicity,[status(thm)],[28])).
% 1.88/1.44 tff(30,plain,
% 1.88/1.44 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))))),
% 1.88/1.44 inference(transitivity,[status(thm)],[29, 27])).
% 1.88/1.44 tff(31,plain,
% 1.88/1.44 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(32,plain,
% 1.88/1.45 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.88/1.45 tff(33,plain,
% 1.88/1.45 (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[32, 26, 16, 14])).
% 1.88/1.45 tff(34,plain,
% 1.88/1.45 (ssPv1(elem!0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[33, 2, 5, 3])).
% 1.88/1.45 tff(35,plain,
% 1.88/1.45 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W))) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(36,plain,
% 1.88/1.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[35])).
% 1.88/1.45 tff(37,plain,
% 1.88/1.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(38,plain,
% 1.88/1.45 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv4(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv4(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv4(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W))) | ssPv4(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv4(V)) | ssPv3(X)) <=> ((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W))) | ssPv3(X)))), rewrite(((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(W))) | ssPv3(X)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv4(V)) | ssPv3(X)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(39,plain,
% 1.88/1.45 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv4(V)) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[38])).
% 1.88/1.45 tff(40,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv4(V)) | ssPv3(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause11')).
% 1.88/1.45 tff(41,plain,
% 1.88/1.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.88/1.45 tff(42,plain,
% 1.88/1.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.88/1.45 tff(43,plain,(
% 1.88/1.45 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[42])).
% 1.88/1.45 tff(44,plain,
% 1.88/1.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[43, 36])).
% 1.88/1.45 tff(45,plain,
% 1.88/1.45 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(46,plain,
% 1.88/1.45 ((ssPv4(skf1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))) <=> (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(47,plain,
% 1.88/1.45 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[46])).
% 1.88/1.45 tff(48,plain,
% 1.88/1.45 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[47, 45])).
% 1.88/1.45 tff(49,plain,
% 1.88/1.45 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(50,plain,
% 1.88/1.45 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.88/1.45 tff(51,plain,
% 1.88/1.45 (ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[50, 44, 16, 14])).
% 1.88/1.45 tff(52,plain,
% 1.88/1.45 (~ssPv4(elem!0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[51, 34, 5, 3])).
% 1.88/1.45 tff(53,plain,
% 1.88/1.45 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : refl((ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(54,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[53])).
% 1.88/1.45 tff(55,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(56,plain,
% 1.88/1.45 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) <=> (((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(Z, X1))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(Z, X1))) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) <=> (((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) <=> (((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) <=> (((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)))), rewrite((((~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) <=> ((~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) | ssPv2(Y)) <=> (((~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(Y)))), rewrite((((~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) | ssPv2(Y)) | ssPv1(X1)) <=> ((ssPv2(Y) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(X1)))), rewrite(((ssPv2(Y) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(X1)) <=> (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) | ssPv2(Y)) | ssPv1(X1)) <=> (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(57,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) | ssPv2(Y)) | ssPv1(X1)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[56])).
% 1.88/1.45 tff(58,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssRr(W, Z))) | (~ssPv1(W))) | ssPv3(V)) | ssPv2(Y)) | ssPv1(X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.88/1.45 tff(59,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.88/1.45 tff(60,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.88/1.45 tff(61,plain,(
% 1.88/1.45 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[60])).
% 1.88/1.45 tff(62,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[61, 54])).
% 1.88/1.45 tff(63,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(64,plain,
% 1.88/1.45 ((ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(65,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[64])).
% 1.88/1.45 tff(66,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[65, 63])).
% 1.88/1.45 tff(67,plain,
% 1.88/1.45 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(68,plain,
% 1.88/1.45 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.88/1.45 tff(69,plain,
% 1.88/1.45 (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(elem!0))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[68, 62, 16, 14])).
% 1.88/1.45 tff(70,plain,
% 1.88/1.45 (ssPv3(skf1(skf1(elem!0)))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[69, 34, 4, 2])).
% 1.88/1.45 tff(71,plain,
% 1.88/1.45 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(72,plain,
% 1.88/1.45 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[71])).
% 1.88/1.45 tff(73,plain,
% 1.88/1.45 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(74,plain,
% 1.88/1.45 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(Y)) <=> (((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv1(Y)))), rewrite((((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(Y)) | ssPv4(W)) <=> ((ssPv1(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(W)))), rewrite(((ssPv1(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(W)) <=> (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(Y)) | ssPv4(W)) <=> (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(75,plain,
% 1.88/1.45 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(Y)) | ssPv4(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[74])).
% 1.88/1.45 tff(76,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(Y)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause29')).
% 1.88/1.45 tff(77,plain,
% 1.88/1.45 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.88/1.45 tff(78,plain,
% 1.88/1.45 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[77, 73])).
% 1.88/1.45 tff(79,plain,(
% 1.88/1.45 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[78])).
% 1.88/1.45 tff(80,plain,
% 1.88/1.45 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.88/1.45 tff(81,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(82,plain,
% 1.88/1.45 ((ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(83,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[82])).
% 1.88/1.45 tff(84,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[83, 81])).
% 1.88/1.45 tff(85,plain,
% 1.88/1.45 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(86,plain,
% 1.88/1.45 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.88/1.45 tff(87,plain,
% 1.88/1.45 ((~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv1(elem!0))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[86, 80, 16, 14])).
% 1.88/1.45 tff(88,plain,
% 1.88/1.45 ($false),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[87, 70, 52, 34, 2])).
% 1.88/1.45 tff(89,plain,(ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.45 tff(90,plain,
% 1.88/1.45 (ssPv4(skf1(skf1(elem!0)))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[89, 2, 5, 4])).
% 1.88/1.45 tff(91,assumption,(ssPv4(skf1(skf1(elem!0)))), introduced(assumption)).
% 1.88/1.45 tff(92,plain,
% 1.88/1.45 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(93,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[92])).
% 1.88/1.45 tff(94,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(95,plain,
% 1.88/1.45 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) <=> (((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)) <=> ((~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) <=> ((~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) <=> (((~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(Y)))), rewrite((((~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) | ssPv3(Z)) <=> ((ssPv2(Y) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Z)))), rewrite(((ssPv2(Y) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Z)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) | ssPv3(Z)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W)) <=> ((ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)))), rewrite(((ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(96,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[95])).
% 1.88/1.45 tff(97,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv3(V)) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.88/1.45 tff(98,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.88/1.45 tff(99,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.88/1.45 tff(100,plain,(
% 1.88/1.45 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[99])).
% 1.88/1.45 tff(101,plain,
% 1.88/1.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[100, 93])).
% 1.88/1.45 tff(102,plain,
% 1.88/1.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(103,plain,
% 1.88/1.45 ((ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(104,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[103])).
% 1.88/1.46 tff(105,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(transitivity,[status(thm)],[104, 102])).
% 1.88/1.46 tff(106,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(107,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.88/1.46 tff(108,plain,
% 1.88/1.46 (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[107, 101, 16, 14])).
% 1.88/1.46 tff(109,plain,
% 1.88/1.46 (ssPv1(elem!0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[108, 1, 4, 5])).
% 1.88/1.46 tff(110,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[69, 109, 1, 4, 2])).
% 1.88/1.46 tff(111,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(112,plain,
% 1.88/1.46 (ssPv3(skf1(skf1(elem!0)))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[111, 2, 4, 5])).
% 1.88/1.46 tff(113,plain,
% 1.88/1.46 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(114,plain,
% 1.88/1.46 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[113])).
% 1.88/1.46 tff(115,plain,
% 1.88/1.46 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(116,plain,
% 1.88/1.46 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(Y)))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) | ssPv3(Z)) <=> ((ssPv2(Y) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Z)))), rewrite(((ssPv2(Y) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Z)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) | ssPv3(Z)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W)) <=> ((ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)))), rewrite(((ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W)) <=> (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(117,plain,
% 1.88/1.46 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[116])).
% 1.88/1.46 tff(118,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv2(Y)) | ssPv3(Z)) | ssPv1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.88/1.46 tff(119,plain,
% 1.88/1.46 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.88/1.46 tff(120,plain,
% 1.88/1.46 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[119, 115])).
% 1.88/1.46 tff(121,plain,(
% 1.88/1.46 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[120])).
% 1.88/1.46 tff(122,plain,
% 1.88/1.46 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[121, 114])).
% 1.88/1.46 tff(123,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(124,plain,
% 1.88/1.46 ((ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(125,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[124])).
% 1.88/1.46 tff(126,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(transitivity,[status(thm)],[125, 123])).
% 1.88/1.46 tff(127,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(128,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.88/1.46 tff(129,plain,
% 1.88/1.46 (ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[128, 122, 16, 14])).
% 1.88/1.46 tff(130,plain,
% 1.88/1.46 (ssPv1(elem!0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[129, 112, 4, 5])).
% 1.88/1.46 tff(131,plain,
% 1.88/1.46 (ssPv4(elem!0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[87, 112, 2, 130])).
% 1.88/1.46 tff(132,plain,
% 1.88/1.46 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(133,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[132])).
% 1.88/1.46 tff(134,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(135,plain,
% 1.88/1.46 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv4(W))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv4(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(Y)) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))) | ssPv2(Y)))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(136,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[135])).
% 1.88/1.46 tff(137,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.88/1.46 tff(138,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.88/1.46 tff(139,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.88/1.46 tff(140,plain,(
% 1.88/1.46 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[139])).
% 1.88/1.46 tff(141,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.88/1.46 tff(142,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(143,plain,
% 1.88/1.46 ((ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(144,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[143])).
% 1.88/1.46 tff(145,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[144, 142])).
% 1.88/1.46 tff(146,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(147,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.88/1.46 tff(148,plain,
% 1.88/1.46 (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv1(elem!0))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[147, 141, 16, 14])).
% 1.88/1.46 tff(149,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[148, 131, 130, 4, 91])).
% 1.88/1.46 tff(150,plain,(ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(151,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[150, 90, 2, 4, 5])).
% 1.88/1.46 tff(152,plain,(ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(153,plain,
% 1.88/1.46 (ssPv3(skf1(elem!0))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[152, 4, 2])).
% 1.88/1.46 tff(154,plain,
% 1.88/1.46 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(155,plain,
% 1.88/1.46 (ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[154, 12])).
% 1.88/1.46 tff(156,plain,
% 1.88/1.46 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) <=> (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(157,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[156])).
% 1.88/1.46 tff(158,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(159,plain,
% 1.88/1.46 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | (~ssPv3(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) | ssPv3(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) | ssPv4(X)) <=> ((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) | ssPv4(X)))), rewrite(((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) | ssPv4(X)) <=> (ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) | ssPv4(X)) <=> (ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) | ssPv4(X)) | ssPv2(Y)) <=> ((ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) | ssPv2(Y)))), rewrite(((ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W))) | ssPv2(Y)) <=> (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) | ssPv4(X)) | ssPv2(Y)) <=> (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(160,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) | ssPv4(X)) | ssPv2(Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[159])).
% 1.88/1.46 tff(161,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | (~ssPv3(W))) | ssPv3(V)) | ssPv4(X)) | ssPv2(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause23')).
% 1.88/1.46 tff(162,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.88/1.46 tff(163,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[162, 158])).
% 1.88/1.46 tff(164,plain,(
% 1.88/1.46 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[163])).
% 1.88/1.46 tff(165,plain,
% 1.88/1.46 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[164, 157])).
% 1.88/1.46 tff(166,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(167,plain,
% 1.88/1.46 ((ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0)))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(168,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[167])).
% 1.88/1.46 tff(169,plain,
% 1.88/1.46 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.46 inference(transitivity,[status(thm)],[168, 166])).
% 1.88/1.46 tff(170,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(171,plain,
% 1.88/1.46 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.88/1.46 tff(172,plain,
% 1.88/1.46 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[171, 165, 14, 155])).
% 1.88/1.46 tff(173,plain,
% 1.88/1.46 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[172, 3, 4, 153])).
% 1.88/1.46 tff(174,assumption,(ssPv1(skf1(elem!0))), introduced(assumption)).
% 1.88/1.46 tff(175,assumption,(ssPv3(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 1.88/1.46 tff(176,plain,
% 1.88/1.46 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) <=> (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(177,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[176])).
% 1.88/1.46 tff(178,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(179,plain,
% 1.88/1.46 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, X))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv1(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv1(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(X)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv1(X)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv1(X)) <=> (ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(X)) <=> (ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(X)) | ssPv4(W)) <=> ((ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv4(W)))), rewrite(((ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv4(W)) <=> (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(X)) | ssPv4(W)) <=> (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(180,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(X)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[179])).
% 1.88/1.46 tff(181,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv1(X)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause14')).
% 1.88/1.47 tff(182,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.88/1.47 tff(183,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[182, 178])).
% 1.88/1.47 tff(184,plain,(
% 1.88/1.47 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.47 inference(skolemize,[status(sab)],[183])).
% 1.88/1.47 tff(185,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[184, 177])).
% 1.88/1.47 tff(186,plain,
% 1.88/1.47 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(187,plain,
% 1.88/1.47 ((ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(188,plain,
% 1.88/1.47 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[187])).
% 1.88/1.47 tff(189,plain,
% 1.88/1.47 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[188, 186])).
% 1.88/1.47 tff(190,plain,
% 1.88/1.47 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(191,plain,
% 1.88/1.47 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.88/1.47 tff(192,plain,
% 1.88/1.47 (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[191, 185, 14, 155])).
% 1.88/1.47 tff(193,plain,
% 1.88/1.47 (ssPv4(skf1(elem!0))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[192, 174, 2, 175])).
% 1.88/1.47 tff(194,assumption,(ssPv3(skf1(elem!0))), introduced(assumption)).
% 1.88/1.47 tff(195,plain,
% 1.88/1.47 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl(((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(196,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[195])).
% 1.88/1.47 tff(197,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(198,plain,
% 1.88/1.47 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) <=> (((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(Y))))), rewrite((((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(Y))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) <=> (((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> (((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(W))))), rewrite((((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(W))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(199,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[198])).
% 1.88/1.47 tff(200,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv1(Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.88/1.47 tff(201,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.88/1.47 tff(202,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[201, 197])).
% 1.88/1.47 tff(203,plain,(
% 1.88/1.47 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(skolemize,[status(sab)],[202])).
% 1.88/1.47 tff(204,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[203, 196])).
% 1.88/1.47 tff(205,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(206,plain,
% 1.88/1.47 (((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(207,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[206])).
% 1.88/1.47 tff(208,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[207, 205])).
% 1.88/1.47 tff(209,plain,
% 1.88/1.47 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(210,plain,
% 1.88/1.47 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.88/1.47 tff(211,plain,
% 1.88/1.47 ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[210, 204, 14, 155])).
% 1.88/1.47 tff(212,plain,
% 1.88/1.47 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[211, 174, 194, 175])).
% 1.88/1.47 tff(213,plain,
% 1.88/1.47 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(214,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[213])).
% 1.88/1.47 tff(215,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(216,plain,
% 1.88/1.47 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(W))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv1(Y)) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) | ssPv1(Y)))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(217,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv1(Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[216])).
% 1.88/1.47 tff(218,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv1(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.88/1.47 tff(219,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[218, 217])).
% 1.88/1.47 tff(220,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[219, 215])).
% 1.88/1.47 tff(221,plain,(
% 1.88/1.47 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(skolemize,[status(sab)],[220])).
% 1.88/1.47 tff(222,plain,
% 1.88/1.47 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[221, 214])).
% 1.88/1.47 tff(223,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(224,plain,
% 1.88/1.47 ((ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(225,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[224])).
% 1.88/1.47 tff(226,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[225, 223])).
% 1.88/1.47 tff(227,plain,
% 1.88/1.47 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(228,plain,
% 1.88/1.47 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.88/1.47 tff(229,plain,
% 1.88/1.47 ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[228, 222, 14, 155])).
% 1.88/1.47 tff(230,plain,
% 1.88/1.47 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[229, 212, 194, 174])).
% 1.88/1.47 tff(231,plain,
% 1.88/1.47 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(232,plain,
% 1.88/1.47 ((ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(233,plain,
% 1.88/1.47 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[232])).
% 1.88/1.47 tff(234,plain,
% 1.88/1.47 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[233, 231])).
% 1.88/1.47 tff(235,plain,
% 1.88/1.47 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(236,plain,
% 1.88/1.47 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.88/1.47 tff(237,plain,
% 1.88/1.47 (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[236, 44, 14, 155])).
% 1.88/1.47 tff(238,plain,
% 1.88/1.47 ($false),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[237, 230, 193, 1, 174])).
% 1.88/1.47 tff(239,plain,((~ssPv1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.47 tff(240,plain,
% 1.88/1.47 (~ssPv1(skf1(elem!0))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[239, 173, 153, 2, 1])).
% 1.88/1.47 tff(241,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(242,plain,
% 1.88/1.47 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(243,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[242])).
% 1.88/1.47 tff(244,plain,
% 1.88/1.47 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[243, 241])).
% 1.88/1.47 tff(245,plain,
% 1.88/1.47 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(246,plain,
% 1.88/1.47 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.88/1.47 tff(247,plain,
% 1.88/1.47 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[246, 122, 14, 155])).
% 1.88/1.47 tff(248,plain,
% 1.88/1.47 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[247, 240, 1, 173])).
% 1.88/1.47 tff(249,assumption,(ssPv2(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 1.88/1.47 tff(250,assumption,(~ssPv1(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 1.88/1.47 tff(251,plain,
% 1.88/1.47 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(252,plain,
% 1.88/1.47 (ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[251, 12])).
% 1.88/1.47 tff(253,plain,
% 1.88/1.47 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(254,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[253])).
% 1.88/1.47 tff(255,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(256,plain,
% 1.88/1.47 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) <=> ((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(X)))), rewrite(((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(X)) <=> (ssPv3(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) <=> (ssPv3(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) | ssPv2(W)) <=> ((ssPv3(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(W)))), rewrite(((ssPv3(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(W)) <=> (ssPv3(V) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) | ssPv2(W)) <=> (ssPv3(V) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) | ssPv2(W)) | ssPv4(W)) <=> ((ssPv3(V) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(W)))), rewrite(((ssPv3(V) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(W)) <=> (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) | ssPv2(W)) | ssPv4(W)) <=> (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(257,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) | ssPv2(W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[256])).
% 1.88/1.47 tff(258,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv3(V)) | ssPv1(X)) | ssPv2(W)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 1.88/1.47 tff(259,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.88/1.47 tff(260,plain,
% 1.88/1.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[259, 255])).
% 1.88/1.48 tff(261,plain,(
% 1.88/1.48 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.48 inference(skolemize,[status(sab)],[260])).
% 1.88/1.48 tff(262,plain,
% 1.88/1.48 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[261, 254])).
% 1.88/1.48 tff(263,plain,
% 1.88/1.48 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(264,plain,
% 1.88/1.48 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(265,plain,
% 1.88/1.48 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[264])).
% 1.88/1.48 tff(266,plain,
% 1.88/1.48 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(transitivity,[status(thm)],[265, 263])).
% 1.88/1.48 tff(267,plain,
% 1.88/1.48 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(quant_inst,[status(thm)],[])).
% 1.88/1.48 tff(268,plain,
% 1.88/1.48 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.88/1.48 tff(269,plain,
% 1.88/1.48 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[268, 262, 155, 252])).
% 1.88/1.48 tff(270,plain,
% 1.88/1.48 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[269, 250, 4, 3])).
% 1.88/1.48 tff(271,plain,
% 1.88/1.48 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(272,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[271])).
% 1.88/1.48 tff(273,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(274,plain,
% 1.88/1.48 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) <=> (((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(X))))), rewrite((((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(X))) <=> ((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) <=> ((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) <=> (((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))))), rewrite((((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))) <=> ((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) <=> ((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(Y)) <=> (((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv1(Y)))), rewrite((((~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(Y)) | ssPv2(W)) <=> ((ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)))), rewrite(((ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(Y)) | ssPv2(W)) <=> (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(275,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(Y)) | ssPv2(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[274])).
% 1.88/1.48 tff(276,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(Y)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 1.88/1.48 tff(277,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.88/1.48 tff(278,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[277, 273])).
% 1.88/1.48 tff(279,plain,(
% 1.88/1.48 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(skolemize,[status(sab)],[278])).
% 1.88/1.48 tff(280,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[279, 272])).
% 1.88/1.48 tff(281,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(282,plain,
% 1.88/1.48 ((ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(283,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[282])).
% 1.88/1.48 tff(284,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(transitivity,[status(thm)],[283, 281])).
% 1.88/1.48 tff(285,plain,
% 1.88/1.48 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(quant_inst,[status(thm)],[])).
% 1.88/1.48 tff(286,plain,
% 1.88/1.48 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.88/1.48 tff(287,plain,
% 1.88/1.48 (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[286, 280, 155, 252])).
% 1.88/1.48 tff(288,plain,
% 1.88/1.48 ($false),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[287, 270, 250, 4, 249])).
% 1.88/1.48 tff(289,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.48 tff(290,plain,
% 1.88/1.48 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[289, 248, 4, 3])).
% 1.88/1.48 tff(291,plain,
% 1.88/1.48 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(292,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[291])).
% 1.88/1.48 tff(293,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(294,plain,
% 1.88/1.48 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) <=> (((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))))), rewrite((((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) <=> (((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv4(X)))), rewrite((((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) | ssPv2(Y)) <=> ((ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(Y)))), rewrite(((ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(Y)) <=> (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) | ssPv2(Y)) <=> (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) | ssPv2(Y)) | ssPv2(W)) <=> ((ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)))), rewrite(((ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)) <=> (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) | ssPv2(Y)) | ssPv2(W)) <=> (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(295,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) | ssPv2(Y)) | ssPv2(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[294])).
% 1.88/1.48 tff(296,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssRr(W, Y))) | ssPv4(X)) | ssPv2(Y)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 1.88/1.48 tff(297,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.88/1.48 tff(298,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[297, 293])).
% 1.88/1.48 tff(299,plain,(
% 1.88/1.48 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(skolemize,[status(sab)],[298])).
% 1.88/1.48 tff(300,plain,
% 1.88/1.48 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[299, 292])).
% 1.88/1.48 tff(301,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(302,plain,
% 1.88/1.48 ((ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(303,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[302])).
% 1.88/1.48 tff(304,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(transitivity,[status(thm)],[303, 301])).
% 1.88/1.48 tff(305,plain,
% 1.88/1.48 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 1.88/1.48 inference(quant_inst,[status(thm)],[])).
% 1.88/1.48 tff(306,plain,
% 1.88/1.48 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.88/1.48 tff(307,plain,
% 1.88/1.48 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[306, 300, 14, 155])).
% 1.88/1.48 tff(308,plain,
% 1.88/1.48 (ssPv2(skf1(elem!0))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[307, 290, 4, 3])).
% 1.88/1.48 tff(309,plain,
% 1.88/1.48 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : refl(((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(310,plain,
% 1.88/1.48 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[309])).
% 1.88/1.48 tff(311,plain,
% 1.88/1.48 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(312,plain,
% 1.88/1.48 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) <=> (((~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(Y))))), rewrite((((~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(Y))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) <=> (((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) <=> (((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(Z, X1))))), rewrite((((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(Z, X1))) <=> ((~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) <=> ((~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) <=> (((~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X1))))), rewrite((((~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X1))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) | (~ssRr(W, Z))) <=> (((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) | (~ssRr(W, Z))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) | (~ssRr(W, Z))) | (~ssPv2(W))) <=> (((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(W))))), rewrite((((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(W))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))), (((((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) | (~ssRr(W, Z))) | (~ssPv2(W))) <=> ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(313,plain,
% 1.88/1.48 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) | (~ssRr(W, Z))) | (~ssPv2(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[312])).
% 1.88/1.48 tff(314,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(Z, X1))) | (~ssPv1(X1))) | (~ssRr(W, Z))) | (~ssPv2(W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.88/1.48 tff(315,plain,
% 1.88/1.48 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.88/1.48 tff(316,plain,
% 1.88/1.48 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[315, 311])).
% 1.88/1.48 tff(317,plain,(
% 1.88/1.48 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(skolemize,[status(sab)],[316])).
% 1.88/1.48 tff(318,plain,
% 1.88/1.48 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[317, 310])).
% 1.88/1.48 tff(319,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(320,plain,
% 1.88/1.48 (((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(321,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[320])).
% 1.88/1.48 tff(322,plain,
% 1.88/1.48 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.48 inference(transitivity,[status(thm)],[321, 319])).
% 1.88/1.48 tff(323,plain,
% 1.88/1.48 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(324,plain,
% 1.88/1.49 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[323, 322])).
% 1.88/1.49 tff(325,plain,
% 1.88/1.49 ((~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[324, 318, 14, 155])).
% 1.88/1.49 tff(326,plain,
% 1.88/1.49 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[325, 308, 290, 248])).
% 1.88/1.49 tff(327,plain,
% 1.88/1.49 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X)))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(328,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[327])).
% 1.88/1.49 tff(329,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(330,plain,
% 1.88/1.49 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(X)))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(X)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X)) | ssPv1(W)))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X)) | ssPv1(W)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W)) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X)) | ssPv3(W)))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X)) | ssPv3(W)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W)) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(331,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[330])).
% 1.88/1.49 tff(332,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause9')).
% 1.88/1.49 tff(333,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.88/1.49 tff(334,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[333, 329])).
% 1.88/1.49 tff(335,plain,(
% 1.88/1.49 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(skolemize,[status(sab)],[334])).
% 1.88/1.49 tff(336,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[335, 328])).
% 1.88/1.49 tff(337,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(338,plain,
% 1.88/1.49 (((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(339,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[338])).
% 1.88/1.49 tff(340,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(transitivity,[status(thm)],[339, 337])).
% 1.88/1.49 tff(341,plain,
% 1.88/1.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(342,plain,
% 1.88/1.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.88/1.49 tff(343,plain,
% 1.88/1.49 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[342, 336, 155, 252])).
% 1.88/1.49 tff(344,plain,
% 1.88/1.49 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[343, 326, 2, 1])).
% 1.88/1.49 tff(345,plain,
% 1.88/1.49 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(346,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[345])).
% 1.88/1.49 tff(347,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(348,plain,
% 1.88/1.49 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, X))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | ssPv4(X)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V))) | ssPv4(X)) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X) | (~ssPv3(V))) | ssPv1(W)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv4(X) | (~ssPv3(V))) | ssPv1(W)) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X) | (~ssPv3(V))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X) | (~ssPv3(V))) | ssPv3(W)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv4(X) | (~ssPv3(V))) | ssPv3(W)) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W)) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(349,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[348])).
% 1.88/1.49 tff(350,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(X)) | ssPv1(W)) | ssPv3(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 1.88/1.49 tff(351,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.88/1.49 tff(352,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[351, 347])).
% 1.88/1.49 tff(353,plain,(
% 1.88/1.49 ![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(skolemize,[status(sab)],[352])).
% 1.88/1.49 tff(354,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[353, 346])).
% 1.88/1.49 tff(355,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(356,plain,
% 1.88/1.49 (((~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(357,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[356])).
% 1.88/1.49 tff(358,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(transitivity,[status(thm)],[357, 355])).
% 1.88/1.49 tff(359,plain,
% 1.88/1.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(360,plain,
% 1.88/1.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.88/1.49 tff(361,plain,
% 1.88/1.49 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[360, 354, 155, 252])).
% 1.88/1.49 tff(362,plain,
% 1.88/1.49 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[361, 326, 2, 1])).
% 1.88/1.49 tff(363,plain,
% 1.88/1.49 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) <=> (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(364,plain,
% 1.88/1.49 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[363])).
% 1.88/1.49 tff(365,plain,
% 1.88/1.49 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(366,plain,
% 1.88/1.49 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv4(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Y)))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) | ssPv1(W)) <=> ((ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)))), rewrite(((ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)) <=> (ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) | ssPv1(W)) <=> (ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) | ssPv1(W)) | ssPv2(W)) <=> ((ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) | ssPv2(W)))), rewrite(((ssPv3(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) | ssPv2(W)) <=> (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) | ssPv1(W)) | ssPv2(W)) <=> (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(367,plain,
% 1.88/1.49 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) | ssPv1(W)) | ssPv2(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[366])).
% 1.88/1.49 tff(368,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv3(Y)) | ssPv1(W)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause26')).
% 1.88/1.49 tff(369,plain,
% 1.88/1.49 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.88/1.49 tff(370,plain,
% 1.88/1.49 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[369, 365])).
% 1.88/1.49 tff(371,plain,(
% 1.88/1.49 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(skolemize,[status(sab)],[370])).
% 1.88/1.49 tff(372,plain,
% 1.88/1.49 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[371, 364])).
% 1.88/1.49 tff(373,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(374,plain,
% 1.88/1.49 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0)))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(375,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[374])).
% 1.88/1.49 tff(376,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(transitivity,[status(thm)],[375, 373])).
% 1.88/1.49 tff(377,plain,
% 1.88/1.49 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(378,plain,
% 1.88/1.49 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.88/1.49 tff(379,plain,
% 1.88/1.49 (ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[378, 372, 155, 252])).
% 1.88/1.49 tff(380,plain,
% 1.88/1.49 (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[379, 362, 2, 4])).
% 1.88/1.49 tff(381,plain,
% 1.88/1.49 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(382,plain,
% 1.88/1.49 (ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[381, 12])).
% 1.88/1.49 tff(383,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(384,plain,
% 1.88/1.49 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(385,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[384])).
% 1.88/1.49 tff(386,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.49 inference(transitivity,[status(thm)],[385, 383])).
% 1.88/1.49 tff(387,plain,
% 1.88/1.49 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(388,plain,
% 1.88/1.49 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.88/1.49 tff(389,plain,
% 1.88/1.49 ((~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[388, 165, 252, 382])).
% 1.88/1.49 tff(390,plain,
% 1.88/1.49 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[389, 380, 173, 344])).
% 1.88/1.49 tff(391,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(392,plain,
% 1.88/1.49 (((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(393,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[392])).
% 1.88/1.49 tff(394,plain,
% 1.88/1.49 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.50 inference(transitivity,[status(thm)],[393, 391])).
% 1.88/1.50 tff(395,plain,
% 1.88/1.50 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.50 inference(quant_inst,[status(thm)],[])).
% 1.88/1.50 tff(396,plain,
% 1.88/1.50 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[395, 394])).
% 1.88/1.50 tff(397,plain,
% 1.88/1.50 ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[396, 204, 252, 382])).
% 1.88/1.50 tff(398,plain,
% 1.88/1.50 (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[397, 390, 173, 290])).
% 1.88/1.50 tff(399,plain,
% 1.88/1.50 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(400,plain,
% 1.88/1.50 ((ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(401,plain,
% 1.88/1.50 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.88/1.50 inference(monotonicity,[status(thm)],[400])).
% 1.88/1.50 tff(402,plain,
% 1.88/1.50 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.88/1.50 inference(transitivity,[status(thm)],[401, 399])).
% 1.88/1.50 tff(403,plain,
% 1.88/1.50 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.88/1.50 inference(quant_inst,[status(thm)],[])).
% 1.88/1.50 tff(404,plain,
% 1.88/1.50 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.88/1.50 tff(405,plain,
% 1.88/1.50 (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[404, 80, 252, 382])).
% 1.88/1.50 tff(406,plain,
% 1.88/1.50 ($false),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[405, 398, 390, 290, 326])).
% 1.94/1.50 tff(407,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.50 tff(408,plain,
% 1.94/1.50 (ssPv4(skf1(skf1(elem!0)))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[407, 1, 4, 2])).
% 1.94/1.50 tff(409,plain,
% 1.94/1.50 (~ssPv1(elem!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[69, 1, 2, 4])).
% 1.94/1.50 tff(410,plain,
% 1.94/1.50 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(411,plain,
% 1.94/1.50 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0)) <=> (ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(412,plain,
% 1.94/1.50 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0)))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[411])).
% 1.94/1.50 tff(413,plain,
% 1.94/1.50 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0))),
% 1.94/1.50 inference(transitivity,[status(thm)],[412, 410])).
% 1.94/1.50 tff(414,plain,
% 1.94/1.50 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(415,plain,
% 1.94/1.50 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv1(elem!0) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0)),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.94/1.50 tff(416,plain,
% 1.94/1.50 (ssPv1(elem!0) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(elem!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[415, 372, 16, 14])).
% 1.94/1.50 tff(417,plain,
% 1.94/1.50 (ssPv2(elem!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[416, 408, 409, 1])).
% 1.94/1.50 tff(418,plain,
% 1.94/1.50 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))) <=> ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))))),
% 1.94/1.50 inference(bind,[status(th)],[])).
% 1.94/1.50 tff(419,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(quant_intro,[status(thm)],[418])).
% 1.94/1.50 tff(420,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(421,plain,
% 1.94/1.50 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(X))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(X)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(X))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) | (~ssPv2(W))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(X))) | (~ssPv2(W))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(X))) | (~ssPv2(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) | (~ssPv2(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) | (~ssPv2(W))) | ssPv4(W)) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))) | ssPv4(W)))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X))) | ssPv4(W)) <=> ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) | (~ssPv2(W))) | ssPv4(W)) <=> ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))))),
% 1.94/1.50 inference(bind,[status(th)],[])).
% 1.94/1.50 tff(422,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) | (~ssPv2(W))) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(quant_intro,[status(thm)],[421])).
% 1.94/1.50 tff(423,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(X))) | (~ssPv2(W))) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause17')).
% 1.94/1.50 tff(424,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[423, 422])).
% 1.94/1.50 tff(425,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[424, 420])).
% 1.94/1.50 tff(426,plain,(
% 1.94/1.50 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(skolemize,[status(sab)],[425])).
% 1.94/1.50 tff(427,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[426, 419])).
% 1.94/1.50 tff(428,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0)))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(429,plain,
% 1.94/1.50 (((~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0)))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(430,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0))))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[429])).
% 1.94/1.50 tff(431,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0)))),
% 1.94/1.50 inference(transitivity,[status(thm)],[430, 428])).
% 1.94/1.50 tff(432,plain,
% 1.94/1.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(433,plain,
% 1.94/1.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[432, 431])).
% 1.94/1.50 tff(434,plain,
% 1.94/1.50 ((~ssPv4(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv3(skf1(elem!0))) | (~ssPv2(elem!0))),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[433, 427, 16, 14])).
% 1.94/1.50 tff(435,plain,
% 1.94/1.50 (ssPv4(elem!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[434, 417, 153, 408])).
% 1.94/1.50 tff(436,plain,
% 1.94/1.50 (^[W: $i, V: $i, U: $i] : refl((ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))))),
% 1.94/1.50 inference(bind,[status(th)],[])).
% 1.94/1.50 tff(437,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(quant_intro,[status(thm)],[436])).
% 1.94/1.50 tff(438,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(439,plain,
% 1.94/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) <=> ((~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) <=> (((~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(W))))), rewrite((((~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(W))) <=> ((~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) <=> ((~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) | ssPv3(V)) <=> (((~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)))), rewrite((((~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) | ssPv3(V)) <=> (ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W)) <=> ((ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(W)))), rewrite(((ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(W)) <=> (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W)) <=> (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))))),
% 1.94/1.50 inference(bind,[status(th)],[])).
% 1.94/1.50 tff(440,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(quant_intro,[status(thm)],[439])).
% 1.94/1.50 tff(441,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssPv2(W))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.94/1.50 tff(442,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.94/1.50 tff(443,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[442, 438])).
% 1.94/1.50 tff(444,plain,(
% 1.94/1.50 ![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(skolemize,[status(sab)],[443])).
% 1.94/1.50 tff(445,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[444, 437])).
% 1.94/1.50 tff(446,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(447,plain,
% 1.94/1.50 ((ssPv3(elem!0) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(448,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0)))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[447])).
% 1.94/1.50 tff(449,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0))),
% 1.94/1.50 inference(transitivity,[status(thm)],[448, 446])).
% 1.94/1.50 tff(450,plain,
% 1.94/1.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 1.94/1.50 inference(quant_inst,[status(thm)],[])).
% 1.94/1.50 tff(451,plain,
% 1.94/1.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0)),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.94/1.50 tff(452,plain,
% 1.94/1.50 (ssPv3(skf1(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | ssPv3(elem!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[451, 445, 16, 14])).
% 1.94/1.50 tff(453,plain,
% 1.94/1.50 (ssPv3(elem!0)),
% 1.94/1.50 inference(unit_resolution,[status(thm)],[452, 417, 1, 435])).
% 1.94/1.50 tff(454,plain,
% 1.94/1.50 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) <=> ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))))),
% 1.94/1.50 inference(bind,[status(th)],[])).
% 1.94/1.50 tff(455,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(quant_intro,[status(thm)],[454])).
% 1.94/1.50 tff(456,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(457,plain,
% 1.94/1.50 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) <=> (((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(W))))), rewrite((((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(W))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) | ssPv1(X)) <=> (((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) | ssPv1(X)))), rewrite((((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) | ssPv1(X)) <=> ((~ssPv1(V)) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) | ssPv1(X)) <=> ((~ssPv1(V)) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) | ssPv1(X)) | ssPv2(W)) <=> (((~ssPv1(V)) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) | ssPv2(W)))), rewrite((((~ssPv1(V)) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) | ssPv2(W)) <=> ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) | ssPv1(X)) | ssPv2(W)) <=> ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))))),
% 1.94/1.50 inference(bind,[status(th)],[])).
% 1.94/1.50 tff(458,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) | ssPv1(X)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(quant_intro,[status(thm)],[457])).
% 1.94/1.50 tff(459,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(W))) | ssPv1(X)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause16')).
% 1.94/1.50 tff(460,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.94/1.50 tff(461,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[460, 456])).
% 1.94/1.50 tff(462,plain,(
% 1.94/1.50 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(skolemize,[status(sab)],[461])).
% 1.94/1.50 tff(463,plain,
% 1.94/1.50 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 1.94/1.50 inference(modus_ponens,[status(thm)],[462, 455])).
% 1.94/1.50 tff(464,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(465,plain,
% 1.94/1.50 (((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.50 inference(rewrite,[status(thm)],[])).
% 1.94/1.50 tff(466,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.50 inference(monotonicity,[status(thm)],[465])).
% 1.94/1.50 tff(467,plain,
% 1.94/1.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.50 inference(transitivity,[status(thm)],[466, 464])).
% 1.94/1.50 tff(468,plain,
% 1.94/1.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(469,plain,
% 1.94/1.51 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.94/1.51 tff(470,plain,
% 1.94/1.51 (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[469, 463, 155, 252])).
% 1.94/1.51 tff(471,plain,
% 1.94/1.51 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[470, 250, 4, 408])).
% 1.94/1.51 tff(472,assumption,(~ssPv3(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 1.94/1.51 tff(473,assumption,(~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 1.94/1.51 tff(474,plain,
% 1.94/1.51 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))),
% 1.94/1.51 inference(bind,[status(th)],[])).
% 1.94/1.51 tff(475,plain,
% 1.94/1.51 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(quant_intro,[status(thm)],[474])).
% 1.94/1.51 tff(476,plain,
% 1.94/1.51 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(477,plain,
% 1.94/1.51 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(X))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(X))) <=> ((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) <=> ((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) <=> (((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))))), rewrite((((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))) <=> ((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) <=> ((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) <=> (((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv1(V)))), rewrite((((~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv1(V)) <=> (ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) <=> (ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) | ssPv3(Y)) <=> ((ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv3(Y)))), rewrite(((ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv3(Y)) <=> (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) | ssPv3(Y)) <=> (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) | ssPv3(Y)) | ssPv2(W)) <=> ((ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)))), rewrite(((ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)) <=> (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) | ssPv3(Y)) | ssPv2(W)) <=> (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))))),
% 1.94/1.51 inference(bind,[status(th)],[])).
% 1.94/1.51 tff(478,plain,
% 1.94/1.51 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) | ssPv3(Y)) | ssPv2(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(quant_intro,[status(thm)],[477])).
% 1.94/1.51 tff(479,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssRr(W, Y))) | ssPv1(V)) | ssPv3(Y)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause21')).
% 1.94/1.51 tff(480,plain,
% 1.94/1.51 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.94/1.51 tff(481,plain,
% 1.94/1.51 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[480, 476])).
% 1.94/1.51 tff(482,plain,(
% 1.94/1.51 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(skolemize,[status(sab)],[481])).
% 1.94/1.51 tff(483,plain,
% 1.94/1.51 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[482, 475])).
% 1.94/1.51 tff(484,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(485,plain,
% 1.94/1.51 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(486,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[485])).
% 1.94/1.51 tff(487,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(transitivity,[status(thm)],[486, 484])).
% 1.94/1.51 tff(488,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(489,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.94/1.51 tff(490,plain,
% 1.94/1.51 (ssPv2(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[489, 483, 155, 252])).
% 1.94/1.51 tff(491,plain,
% 1.94/1.51 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[490, 472, 4, 473])).
% 1.94/1.51 tff(492,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(493,plain,
% 1.94/1.51 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(494,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[493])).
% 1.94/1.51 tff(495,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(transitivity,[status(thm)],[494, 492])).
% 1.94/1.51 tff(496,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(497,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[496, 495])).
% 1.94/1.51 tff(498,plain,
% 1.94/1.51 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[497, 101, 14, 155])).
% 1.94/1.51 tff(499,plain,
% 1.94/1.51 (ssPv1(skf1(elem!0))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[498, 491, 1, 472])).
% 1.94/1.51 tff(500,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(501,plain,
% 1.94/1.51 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(502,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[501])).
% 1.94/1.51 tff(503,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(transitivity,[status(thm)],[502, 500])).
% 1.94/1.51 tff(504,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(505,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.94/1.51 tff(506,plain,
% 1.94/1.51 ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[505, 62, 14, 155])).
% 1.94/1.51 tff(507,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[506, 499, 491, 472, 250])).
% 1.94/1.51 tff(508,plain,(ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(509,plain,
% 1.94/1.51 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[508, 250, 1, 4, 471])).
% 1.94/1.51 tff(510,plain,
% 1.94/1.51 (~ssPv1(skf1(elem!0))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[239, 509, 153, 2, 1])).
% 1.94/1.51 tff(511,plain,
% 1.94/1.51 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[247, 510, 1, 509])).
% 1.94/1.51 tff(512,plain,
% 1.94/1.51 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[287, 511, 4, 250])).
% 1.94/1.51 tff(513,assumption,(~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 1.94/1.51 tff(514,assumption,(~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))), introduced(assumption)).
% 1.94/1.51 tff(515,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(516,plain,
% 1.94/1.51 ((ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(517,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[516])).
% 1.94/1.51 tff(518,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(transitivity,[status(thm)],[517, 515])).
% 1.94/1.51 tff(519,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(520,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.94/1.51 tff(521,plain,
% 1.94/1.51 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[520, 122, 252, 382])).
% 1.94/1.51 tff(522,plain,
% 1.94/1.51 (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[521, 514, 250, 513])).
% 1.94/1.51 tff(523,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(524,plain,
% 1.94/1.51 ((ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(rewrite,[status(thm)],[])).
% 1.94/1.51 tff(525,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.51 inference(monotonicity,[status(thm)],[524])).
% 1.94/1.51 tff(526,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.51 inference(transitivity,[status(thm)],[525, 523])).
% 1.94/1.51 tff(527,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.51 inference(quant_inst,[status(thm)],[])).
% 1.94/1.51 tff(528,plain,
% 1.94/1.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.94/1.51 tff(529,plain,
% 1.94/1.51 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[528, 101, 252, 382])).
% 1.94/1.51 tff(530,plain,
% 1.94/1.51 ($false),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[529, 522, 514, 250, 513])).
% 1.94/1.51 tff(531,plain,(ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.51 tff(532,plain,
% 1.94/1.51 (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[531, 512, 250])).
% 1.94/1.51 tff(533,plain,
% 1.94/1.51 (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.51 inference(unit_resolution,[status(thm)],[379, 512, 2, 4])).
% 1.94/1.51 tff(534,plain,
% 1.94/1.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(535,plain,
% 1.94/1.52 ((ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(536,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[535])).
% 1.94/1.52 tff(537,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[536, 534])).
% 1.94/1.52 tff(538,plain,
% 1.94/1.52 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(539,plain,
% 1.94/1.52 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0))))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[538, 537])).
% 1.94/1.52 tff(540,plain,
% 1.94/1.52 (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[539, 26, 14, 155])).
% 1.94/1.52 tff(541,plain,
% 1.94/1.52 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[540, 510, 1, 250])).
% 1.94/1.52 tff(542,plain,
% 1.94/1.52 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X))))),
% 1.94/1.52 inference(bind,[status(th)],[])).
% 1.94/1.52 tff(543,plain,
% 1.94/1.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(quant_intro,[status(thm)],[542])).
% 1.94/1.52 tff(544,plain,
% 1.94/1.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(545,plain,
% 1.94/1.52 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(X))))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(X)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(X))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssPv2(W))) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(X))) | (~ssPv2(W))))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(X))) | (~ssPv2(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv2(X)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssPv2(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv2(X))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssPv2(W))) | (~ssPv4(W))) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv2(X))) | (~ssPv4(W))))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv2(X))) | (~ssPv4(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssPv2(W))) | (~ssPv4(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))))),
% 1.94/1.52 inference(bind,[status(th)],[])).
% 1.94/1.52 tff(546,plain,
% 1.94/1.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssPv2(W))) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(quant_intro,[status(thm)],[545])).
% 1.94/1.52 tff(547,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv2(X))) | (~ssPv2(W))) | (~ssPv4(W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause19')).
% 1.94/1.52 tff(548,plain,
% 1.94/1.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[547, 546])).
% 1.94/1.52 tff(549,plain,
% 1.94/1.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[548, 544])).
% 1.94/1.52 tff(550,plain,(
% 1.94/1.52 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(skolemize,[status(sab)],[549])).
% 1.94/1.52 tff(551,plain,
% 1.94/1.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[550, 543])).
% 1.94/1.52 tff(552,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(553,plain,
% 1.94/1.52 (((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(554,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[553])).
% 1.94/1.52 tff(555,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[554, 552])).
% 1.94/1.52 tff(556,plain,
% 1.94/1.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(557,plain,
% 1.94/1.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.94/1.52 tff(558,plain,
% 1.94/1.52 ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[557, 551, 252, 382])).
% 1.94/1.52 tff(559,plain,
% 1.94/1.52 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[558, 532, 511, 541])).
% 1.94/1.52 tff(560,assumption,(~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 1.94/1.52 tff(561,assumption,(~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), introduced(assumption)).
% 1.94/1.52 tff(562,assumption,(~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 1.94/1.52 tff(563,plain,
% 1.94/1.52 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(564,plain,
% 1.94/1.52 (ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[563, 12])).
% 1.94/1.52 tff(565,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(566,plain,
% 1.94/1.52 ((ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(567,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[566])).
% 1.94/1.52 tff(568,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[567, 565])).
% 1.94/1.52 tff(569,plain,
% 1.94/1.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(570,plain,
% 1.94/1.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.94/1.52 tff(571,plain,
% 1.94/1.52 (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[570, 262, 382, 564])).
% 1.94/1.52 tff(572,plain,
% 1.94/1.52 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[571, 560, 562, 561])).
% 1.94/1.52 tff(573,plain,
% 1.94/1.52 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[389, 560, 175, 562])).
% 1.94/1.52 tff(574,plain,
% 1.94/1.52 (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[521, 573, 250, 513])).
% 1.94/1.52 tff(575,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(576,plain,
% 1.94/1.52 ((ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(577,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[576])).
% 1.94/1.52 tff(578,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[577, 575])).
% 1.94/1.52 tff(579,plain,
% 1.94/1.52 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(580,plain,
% 1.94/1.52 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[579, 578])).
% 1.94/1.52 tff(581,plain,
% 1.94/1.52 (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[580, 280, 382, 564])).
% 1.94/1.52 tff(582,plain,
% 1.94/1.52 ($false),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[581, 574, 572, 561, 560])).
% 1.94/1.52 tff(583,plain,(ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.52 tff(584,plain,
% 1.94/1.52 (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[583, 559, 250, 512, 533, 509])).
% 1.94/1.52 tff(585,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(586,plain,
% 1.94/1.52 (((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(587,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(monotonicity,[status(thm)],[586])).
% 1.94/1.52 tff(588,plain,
% 1.94/1.52 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.52 inference(transitivity,[status(thm)],[587, 585])).
% 1.94/1.52 tff(589,plain,
% 1.94/1.52 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(quant_inst,[status(thm)],[])).
% 1.94/1.52 tff(590,plain,
% 1.94/1.52 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.94/1.52 tff(591,plain,
% 1.94/1.52 ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[590, 318, 252, 382])).
% 1.94/1.52 tff(592,plain,
% 1.94/1.52 (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.52 inference(unit_resolution,[status(thm)],[591, 584, 511, 532])).
% 1.94/1.52 tff(593,plain,
% 1.94/1.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.52 inference(rewrite,[status(thm)],[])).
% 1.94/1.52 tff(594,plain,
% 1.94/1.52 (((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(595,plain,
% 1.94/1.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(monotonicity,[status(thm)],[594])).
% 1.94/1.53 tff(596,plain,
% 1.94/1.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(transitivity,[status(thm)],[595, 593])).
% 1.94/1.53 tff(597,plain,
% 1.94/1.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.53 inference(quant_inst,[status(thm)],[])).
% 1.94/1.53 tff(598,plain,
% 1.94/1.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.94/1.53 tff(599,plain,
% 1.94/1.53 (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[598, 336, 382, 564])).
% 1.94/1.53 tff(600,plain,
% 1.94/1.53 (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[599, 592, 471, 512])).
% 1.94/1.53 tff(601,plain,
% 1.94/1.53 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[389, 559, 509, 533])).
% 1.94/1.53 tff(602,plain,
% 1.94/1.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(603,plain,
% 1.94/1.53 (((~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(604,plain,
% 1.94/1.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(monotonicity,[status(thm)],[603])).
% 1.94/1.53 tff(605,plain,
% 1.94/1.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(transitivity,[status(thm)],[604, 602])).
% 1.94/1.53 tff(606,plain,
% 1.94/1.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(quant_inst,[status(thm)],[])).
% 1.94/1.53 tff(607,plain,
% 1.94/1.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.94/1.53 tff(608,plain,
% 1.94/1.53 (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[607, 354, 382, 564])).
% 1.94/1.53 tff(609,plain,
% 1.94/1.53 (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[608, 592, 471, 512])).
% 1.94/1.53 tff(610,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(611,plain,
% 1.94/1.53 ((ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) <=> (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(612,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(monotonicity,[status(thm)],[611])).
% 1.94/1.53 tff(613,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(transitivity,[status(thm)],[612, 610])).
% 1.94/1.53 tff(614,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.53 inference(quant_inst,[status(thm)],[])).
% 1.94/1.53 tff(615,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.94/1.53 tff(616,plain,
% 1.94/1.53 (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[615, 372, 382, 564])).
% 1.94/1.53 tff(617,plain,
% 1.94/1.53 (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[616, 609, 471, 559])).
% 1.94/1.53 tff(618,plain,
% 1.94/1.53 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(quant_inst,[status(thm)],[])).
% 1.94/1.53 tff(619,plain,
% 1.94/1.53 (ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[618, 12])).
% 1.94/1.53 tff(620,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(621,plain,
% 1.94/1.53 ((ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(622,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(monotonicity,[status(thm)],[621])).
% 1.94/1.53 tff(623,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(transitivity,[status(thm)],[622, 620])).
% 1.94/1.53 tff(624,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(quant_inst,[status(thm)],[])).
% 1.94/1.53 tff(625,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.94/1.53 tff(626,plain,
% 1.94/1.53 ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[625, 165, 564, 619])).
% 1.94/1.53 tff(627,plain,
% 1.94/1.53 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[626, 617, 601, 600])).
% 1.94/1.53 tff(628,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(629,plain,
% 1.94/1.53 (((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(630,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 1.94/1.53 inference(monotonicity,[status(thm)],[629])).
% 1.94/1.53 tff(631,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(transitivity,[status(thm)],[630, 628])).
% 1.94/1.53 tff(632,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(quant_inst,[status(thm)],[])).
% 1.94/1.53 tff(633,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(modus_ponens,[status(thm)],[632, 631])).
% 1.94/1.53 tff(634,plain,
% 1.94/1.53 ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[633, 204, 564, 619])).
% 1.94/1.53 tff(635,plain,
% 1.94/1.53 (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.53 inference(unit_resolution,[status(thm)],[634, 627, 601, 584])).
% 1.94/1.53 tff(636,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(637,plain,
% 1.94/1.53 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(rewrite,[status(thm)],[])).
% 1.94/1.53 tff(638,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 1.94/1.53 inference(monotonicity,[status(thm)],[637])).
% 1.94/1.53 tff(639,plain,
% 1.94/1.53 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 1.94/1.53 inference(transitivity,[status(thm)],[638, 636])).
% 1.94/1.53 tff(640,plain,
% 1.94/1.53 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.54 inference(quant_inst,[status(thm)],[])).
% 1.94/1.54 tff(641,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.94/1.54 tff(642,plain,
% 1.94/1.54 ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[641, 80, 564, 619])).
% 1.94/1.54 tff(643,plain,
% 1.94/1.54 ($false),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[642, 635, 627, 584, 592])).
% 1.94/1.54 tff(644,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.54 tff(645,plain,
% 1.94/1.54 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[644, 1, 4, 2])).
% 1.94/1.54 tff(646,plain,
% 1.94/1.54 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X))) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X))))),
% 1.94/1.54 inference(bind,[status(th)],[])).
% 1.94/1.54 tff(647,plain,
% 1.94/1.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(quant_intro,[status(thm)],[646])).
% 1.94/1.54 tff(648,plain,
% 1.94/1.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(649,plain,
% 1.94/1.54 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X))) | (~ssPv4(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X))) | (~ssPv4(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) | ssPv3(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X))) | ssPv3(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W)) <=> ((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X))) | ssPv3(W)))), rewrite(((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv1(X))) | ssPv3(W)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))))),
% 1.94/1.54 inference(bind,[status(th)],[])).
% 1.94/1.54 tff(650,plain,
% 1.94/1.54 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(quant_intro,[status(thm)],[649])).
% 1.94/1.54 tff(651,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv4(W))) | ssPv3(V)) | ssPv3(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause15')).
% 1.94/1.54 tff(652,plain,
% 1.94/1.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.94/1.54 tff(653,plain,
% 1.94/1.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[652, 648])).
% 1.94/1.54 tff(654,plain,(
% 1.94/1.54 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(skolemize,[status(sab)],[653])).
% 1.94/1.54 tff(655,plain,
% 1.94/1.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[654, 647])).
% 1.94/1.54 tff(656,plain,
% 1.94/1.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(657,plain,
% 1.94/1.54 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(658,plain,
% 1.94/1.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(monotonicity,[status(thm)],[657])).
% 1.94/1.54 tff(659,plain,
% 1.94/1.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(transitivity,[status(thm)],[658, 656])).
% 1.94/1.54 tff(660,plain,
% 1.94/1.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(quant_inst,[status(thm)],[])).
% 1.94/1.54 tff(661,plain,
% 1.94/1.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(W)) | (~ssPv1(X)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.94/1.54 tff(662,plain,
% 1.94/1.54 ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[661, 655, 155, 252])).
% 1.94/1.54 tff(663,plain,
% 1.94/1.54 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[662, 645, 1, 408])).
% 1.94/1.54 tff(664,plain,
% 1.94/1.54 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[361, 663, 2, 1])).
% 1.94/1.54 tff(665,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(666,plain,
% 1.94/1.54 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(667,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(monotonicity,[status(thm)],[666])).
% 1.94/1.54 tff(668,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(transitivity,[status(thm)],[667, 665])).
% 1.94/1.54 tff(669,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(quant_inst,[status(thm)],[])).
% 1.94/1.54 tff(670,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[669, 668])).
% 1.94/1.54 tff(671,plain,
% 1.94/1.54 (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[670, 122, 155, 252])).
% 1.94/1.54 tff(672,plain,
% 1.94/1.54 (ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[671, 472, 2, 663])).
% 1.94/1.54 tff(673,plain,
% 1.94/1.54 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W)) <=> (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W)))),
% 1.94/1.54 inference(bind,[status(th)],[])).
% 1.94/1.54 tff(674,plain,
% 1.94/1.54 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(quant_intro,[status(thm)],[673])).
% 1.94/1.54 tff(675,plain,
% 1.94/1.54 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(676,plain,
% 1.94/1.54 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(X, Y))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) <=> (((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | ssPv4(Y)))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) | ssPv3(Z)) <=> ((ssPv4(Y) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | ssPv3(Z)))), rewrite(((ssPv4(Y) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | ssPv3(Z)) <=> (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) | ssPv3(Z)) <=> (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) | ssPv3(Z)) | ssPv3(W)) <=> ((ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | ssPv3(W)))), rewrite(((ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | ssPv3(W)) <=> (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))), ((((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) | ssPv3(Z)) | ssPv3(W)) <=> (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))))),
% 1.94/1.54 inference(bind,[status(th)],[])).
% 1.94/1.54 tff(677,plain,
% 1.94/1.54 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) | ssPv3(Z)) | ssPv3(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(quant_intro,[status(thm)],[676])).
% 1.94/1.54 tff(678,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | ssPv4(Y)) | ssPv3(Z)) | ssPv3(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.94/1.54 tff(679,plain,
% 1.94/1.54 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.94/1.54 tff(680,plain,
% 1.94/1.54 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[679, 675])).
% 1.94/1.54 tff(681,plain,(
% 1.94/1.54 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(skolemize,[status(sab)],[680])).
% 1.94/1.54 tff(682,plain,
% 1.94/1.54 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[681, 674])).
% 1.94/1.54 tff(683,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(684,plain,
% 1.94/1.54 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0)))) <=> (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(685,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.54 inference(monotonicity,[status(thm)],[684])).
% 1.94/1.54 tff(686,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(transitivity,[status(thm)],[685, 683])).
% 1.94/1.54 tff(687,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))))),
% 1.94/1.54 inference(quant_inst,[status(thm)],[])).
% 1.94/1.54 tff(688,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.94/1.54 tff(689,plain,
% 1.94/1.54 (ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[688, 682, 155, 252])).
% 1.94/1.54 tff(690,plain,
% 1.94/1.54 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[689, 672, 1, 472])).
% 1.94/1.54 tff(691,plain,
% 1.94/1.54 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))),
% 1.94/1.54 inference(bind,[status(th)],[])).
% 1.94/1.54 tff(692,plain,
% 1.94/1.54 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(quant_intro,[status(thm)],[691])).
% 1.94/1.54 tff(693,plain,
% 1.94/1.54 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(694,plain,
% 1.94/1.54 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X))) <=> ((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) <=> ((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) <=> (((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))))), rewrite((((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Y))) <=> ((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) <=> ((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) | ssPv2(Y)) <=> (((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(Y)))), rewrite((((~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) | ssPv2(Y)) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) | ssPv2(Y)) | ssPv2(W)) <=> ((ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)))), rewrite(((ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y))) | ssPv2(W)) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))), (((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) | ssPv2(Y)) | ssPv2(W)) <=> (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))))),
% 1.94/1.54 inference(bind,[status(th)],[])).
% 1.94/1.54 tff(695,plain,
% 1.94/1.54 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) | ssPv2(Y)) | ssPv2(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(quant_intro,[status(thm)],[694])).
% 1.94/1.54 tff(696,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssRr(W, Y))) | ssPv2(Y)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause28')).
% 1.94/1.54 tff(697,plain,
% 1.94/1.54 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[696, 695])).
% 1.94/1.54 tff(698,plain,
% 1.94/1.54 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[697, 693])).
% 1.94/1.54 tff(699,plain,(
% 1.94/1.54 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(skolemize,[status(sab)],[698])).
% 1.94/1.54 tff(700,plain,
% 1.94/1.54 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[699, 692])).
% 1.94/1.54 tff(701,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(702,plain,
% 1.94/1.54 ((ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(rewrite,[status(thm)],[])).
% 1.94/1.54 tff(703,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.54 inference(monotonicity,[status(thm)],[702])).
% 1.94/1.54 tff(704,plain,
% 1.94/1.54 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.54 inference(transitivity,[status(thm)],[703, 701])).
% 1.94/1.54 tff(705,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(quant_inst,[status(thm)],[])).
% 1.94/1.54 tff(706,plain,
% 1.94/1.54 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.94/1.54 tff(707,plain,
% 1.94/1.54 (ssPv2(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[706, 700, 155, 252])).
% 1.94/1.54 tff(708,plain,
% 1.94/1.54 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 1.94/1.54 inference(unit_resolution,[status(thm)],[707, 690, 4, 645])).
% 1.94/1.55 tff(709,plain,
% 1.94/1.55 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))))),
% 1.94/1.55 inference(bind,[status(th)],[])).
% 1.94/1.55 tff(710,plain,
% 1.94/1.55 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(quant_intro,[status(thm)],[709])).
% 1.94/1.55 tff(711,plain,
% 1.94/1.55 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(712,plain,
% 1.94/1.55 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv2(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv2(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv2(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv2(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv2(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(W))))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) <=> ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv3(Y)) <=> (((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) | ssPv3(Y)))), rewrite((((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))))),
% 1.94/1.55 inference(bind,[status(th)],[])).
% 1.94/1.55 tff(713,plain,
% 1.94/1.55 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv3(Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(quant_intro,[status(thm)],[712])).
% 1.94/1.55 tff(714,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | (~ssPv3(W))) | ssPv3(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.94/1.55 tff(715,plain,
% 1.94/1.55 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.94/1.55 tff(716,plain,
% 1.94/1.55 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[715, 711])).
% 1.94/1.55 tff(717,plain,(
% 1.94/1.55 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(skolemize,[status(sab)],[716])).
% 1.94/1.55 tff(718,plain,
% 1.94/1.55 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[717, 710])).
% 1.94/1.55 tff(719,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(720,plain,
% 1.94/1.55 ((ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(721,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(monotonicity,[status(thm)],[720])).
% 1.94/1.55 tff(722,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(transitivity,[status(thm)],[721, 719])).
% 1.94/1.55 tff(723,plain,
% 1.94/1.55 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 1.94/1.55 inference(quant_inst,[status(thm)],[])).
% 1.94/1.55 tff(724,plain,
% 1.94/1.55 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[723, 722])).
% 1.94/1.55 tff(725,plain,
% 1.94/1.55 ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[724, 718, 14, 155])).
% 1.94/1.55 tff(726,plain,
% 1.94/1.55 (~ssPv1(skf1(elem!0))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[725, 708, 153, 472])).
% 1.94/1.55 tff(727,plain,
% 1.94/1.55 (~ssPv2(skf1(elem!0))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[325, 708, 645, 664])).
% 1.94/1.55 tff(728,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(729,plain,
% 1.94/1.55 ((ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(730,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.55 inference(monotonicity,[status(thm)],[729])).
% 1.94/1.55 tff(731,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(transitivity,[status(thm)],[730, 728])).
% 1.94/1.55 tff(732,plain,
% 1.94/1.55 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)))),
% 1.94/1.55 inference(quant_inst,[status(thm)],[])).
% 1.94/1.55 tff(733,plain,
% 1.94/1.55 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[732, 731])).
% 1.94/1.55 tff(734,plain,
% 1.94/1.55 (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[733, 372, 14, 155])).
% 1.94/1.55 tff(735,plain,
% 1.94/1.55 ($false),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[734, 727, 726, 472, 664])).
% 1.94/1.55 tff(736,plain,(ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.55 tff(737,plain,
% 1.94/1.55 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[736, 1, 4, 2])).
% 1.94/1.55 tff(738,plain,
% 1.94/1.55 (~ssPv1(skf1(elem!0))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[239, 737, 153, 2, 1])).
% 1.94/1.55 tff(739,plain,
% 1.94/1.55 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[247, 738, 1, 737])).
% 1.94/1.55 tff(740,plain,
% 1.94/1.55 (~ssPv2(skf1(elem!0))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[325, 739, 645, 664])).
% 1.94/1.55 tff(741,plain,
% 1.94/1.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(742,plain,
% 1.94/1.55 (((~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(743,plain,
% 1.94/1.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.55 inference(monotonicity,[status(thm)],[742])).
% 1.94/1.55 tff(744,plain,
% 1.94/1.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(transitivity,[status(thm)],[743, 741])).
% 1.94/1.55 tff(745,plain,
% 1.94/1.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))))),
% 1.94/1.55 inference(quant_inst,[status(thm)],[])).
% 1.94/1.55 tff(746,plain,
% 1.94/1.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(V)) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.94/1.55 tff(747,plain,
% 1.94/1.55 (ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[746, 463, 14, 155])).
% 1.94/1.55 tff(748,plain,
% 1.94/1.55 (~ssPv4(skf1(elem!0))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[747, 740, 2, 645])).
% 1.94/1.55 tff(749,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(750,plain,
% 1.94/1.55 ((ssPv2(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(751,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0))))),
% 1.94/1.55 inference(monotonicity,[status(thm)],[750])).
% 1.94/1.55 tff(752,plain,
% 1.94/1.55 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)))),
% 1.94/1.55 inference(transitivity,[status(thm)],[751, 749])).
% 1.94/1.55 tff(753,plain,
% 1.94/1.55 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(elem!0)))),
% 1.94/1.55 inference(quant_inst,[status(thm)],[])).
% 1.94/1.55 tff(754,plain,
% 1.94/1.55 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.94/1.55 tff(755,plain,
% 1.94/1.55 (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(elem!0))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[754, 165, 16, 14])).
% 1.94/1.55 tff(756,plain,
% 1.94/1.55 ($false),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[755, 748, 740, 1, 453])).
% 1.94/1.55 tff(757,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.55 tff(758,plain,
% 1.94/1.55 (ssPv3(skf1(skf1(elem!0)))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[757, 4, 2])).
% 1.94/1.55 tff(759,assumption,(ssPv3(skf1(skf1(elem!0)))), introduced(assumption)).
% 1.94/1.55 tff(760,plain,
% 1.94/1.55 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) <=> (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))))),
% 1.94/1.55 inference(bind,[status(th)],[])).
% 1.94/1.55 tff(761,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(quant_intro,[status(thm)],[760])).
% 1.94/1.55 tff(762,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(763,plain,
% 1.94/1.55 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(X))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))) | (~ssPv3(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv1(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv1(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv1(V)) <=> (ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv1(V)) <=> (ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(W)) <=> ((ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv2(W)))), rewrite(((ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv2(W)) <=> (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(W)) <=> (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))))),
% 1.94/1.55 inference(bind,[status(th)],[])).
% 1.94/1.55 tff(764,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(quant_intro,[status(thm)],[763])).
% 1.94/1.55 tff(765,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 1.94/1.55 tff(766,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.94/1.55 tff(767,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[766, 762])).
% 1.94/1.55 tff(768,plain,(
% 1.94/1.55 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(skolemize,[status(sab)],[767])).
% 1.94/1.55 tff(769,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[768, 761])).
% 1.94/1.55 tff(770,plain,
% 1.94/1.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(771,plain,
% 1.94/1.55 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(772,plain,
% 1.94/1.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.55 inference(monotonicity,[status(thm)],[771])).
% 1.94/1.55 tff(773,plain,
% 1.94/1.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.55 inference(transitivity,[status(thm)],[772, 770])).
% 1.94/1.55 tff(774,plain,
% 1.94/1.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(quant_inst,[status(thm)],[])).
% 1.94/1.55 tff(775,plain,
% 1.94/1.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.55 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.94/1.55 tff(776,plain,
% 1.94/1.55 (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[775, 769, 155, 252])).
% 1.94/1.55 tff(777,plain,
% 1.94/1.55 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 1.94/1.55 inference(unit_resolution,[status(thm)],[776, 473, 4, 759])).
% 1.94/1.55 tff(778,plain,
% 1.94/1.55 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))) <=> (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))))),
% 1.94/1.55 inference(bind,[status(th)],[])).
% 1.94/1.55 tff(779,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.55 inference(quant_intro,[status(thm)],[778])).
% 1.94/1.55 tff(780,plain,
% 1.94/1.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.55 inference(rewrite,[status(thm)],[])).
% 1.94/1.55 tff(781,plain,
% 1.94/1.55 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv1(V)) <=> (ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) <=> (ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(X)) <=> ((ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv2(X)))), rewrite(((ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv2(X)) <=> (ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(X)) <=> (ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(X)) | ssPv2(W)) <=> ((ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))) | ssPv2(W)))), rewrite(((ssPv1(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W))) | ssPv2(W)) <=> (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(X)) | ssPv2(W)) <=> (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))))),
% 1.94/1.56 inference(bind,[status(th)],[])).
% 1.94/1.56 tff(782,plain,
% 1.94/1.56 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(X)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.56 inference(quant_intro,[status(thm)],[781])).
% 1.94/1.56 tff(783,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv1(V)) | ssPv2(X)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 1.94/1.56 tff(784,plain,
% 1.94/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[783, 782])).
% 1.94/1.56 tff(785,plain,
% 1.94/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[784, 780])).
% 1.94/1.56 tff(786,plain,(
% 1.94/1.56 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.56 inference(skolemize,[status(sab)],[785])).
% 1.94/1.56 tff(787,plain,
% 1.94/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[786, 779])).
% 1.94/1.56 tff(788,plain,
% 1.94/1.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.56 inference(rewrite,[status(thm)],[])).
% 1.94/1.56 tff(789,plain,
% 1.94/1.56 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.56 inference(rewrite,[status(thm)],[])).
% 1.94/1.56 tff(790,plain,
% 1.94/1.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 1.94/1.56 inference(monotonicity,[status(thm)],[789])).
% 1.94/1.56 tff(791,plain,
% 1.94/1.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.56 inference(transitivity,[status(thm)],[790, 788])).
% 1.94/1.56 tff(792,plain,
% 1.94/1.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 1.94/1.56 inference(quant_inst,[status(thm)],[])).
% 1.94/1.56 tff(793,plain,
% 1.94/1.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[792, 791])).
% 1.94/1.56 tff(794,plain,
% 1.94/1.56 (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.56 inference(unit_resolution,[status(thm)],[793, 787, 155, 252])).
% 1.94/1.56 tff(795,plain,
% 1.94/1.56 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 1.94/1.56 inference(unit_resolution,[status(thm)],[794, 473, 4, 759])).
% 1.94/1.56 tff(796,plain,
% 1.94/1.56 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))) <=> (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))))),
% 1.94/1.56 inference(bind,[status(th)],[])).
% 1.94/1.56 tff(797,plain,
% 1.94/1.56 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(quant_intro,[status(thm)],[796])).
% 1.94/1.56 tff(798,plain,
% 1.94/1.56 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(rewrite,[status(thm)],[])).
% 1.94/1.56 tff(799,plain,
% 1.94/1.56 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(X, Y))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(Z))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv3(W))) <=> (((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(W))))), rewrite((((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(W))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv3(W))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))))), ((((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv3(W))) | ssPv4(Y)) <=> (((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))) | ssPv4(Y)))), rewrite((((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))), ((((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv3(W))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))))),
% 1.94/1.56 inference(bind,[status(th)],[])).
% 1.94/1.56 tff(800,plain,
% 1.94/1.56 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv3(W))) | ssPv4(Y)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(quant_intro,[status(thm)],[799])).
% 1.94/1.56 tff(801,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv3(W))) | ssPv4(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.94/1.56 tff(802,plain,
% 1.94/1.56 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[801, 800])).
% 1.94/1.56 tff(803,plain,
% 1.94/1.56 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[802, 798])).
% 1.94/1.56 tff(804,plain,(
% 1.94/1.56 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(skolemize,[status(sab)],[803])).
% 1.94/1.56 tff(805,plain,
% 1.94/1.56 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[804, 797])).
% 1.94/1.56 tff(806,plain,
% 1.94/1.56 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.56 inference(rewrite,[status(thm)],[])).
% 1.94/1.56 tff(807,plain,
% 1.94/1.56 ((ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.56 inference(rewrite,[status(thm)],[])).
% 1.94/1.56 tff(808,plain,
% 1.94/1.56 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 1.94/1.56 inference(monotonicity,[status(thm)],[807])).
% 1.94/1.56 tff(809,plain,
% 1.94/1.56 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 1.94/1.56 inference(transitivity,[status(thm)],[808, 806])).
% 1.94/1.56 tff(810,plain,
% 1.94/1.56 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))))),
% 1.94/1.56 inference(quant_inst,[status(thm)],[])).
% 1.94/1.56 tff(811,plain,
% 1.94/1.56 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.56 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.94/1.56 tff(812,plain,
% 1.94/1.56 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.56 inference(unit_resolution,[status(thm)],[811, 805, 14, 155])).
% 1.94/1.56 tff(813,plain,
% 1.94/1.56 ($false),
% 1.94/1.56 inference(unit_resolution,[status(thm)],[812, 795, 777, 194, 759])).
% 1.94/1.56 tff(814,plain,(ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.94/1.56 tff(815,plain,
% 1.94/1.56 (ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 1.94/1.56 inference(unit_resolution,[status(thm)],[814, 153, 758, 4])).
% 1.94/1.56 tff(816,plain,
% 1.94/1.56 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) <=> (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)))),
% 1.94/1.56 inference(bind,[status(th)],[])).
% 1.94/1.56 tff(817,plain,
% 1.94/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.94/1.56 inference(quant_intro,[status(thm)],[816])).
% 1.94/1.56 tff(818,plain,
% 1.94/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 1.94/1.56 inference(rewrite,[status(thm)],[])).
% 1.94/1.56 tff(819,plain,
% 1.94/1.56 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) <=> ((ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(X)))), rewrite(((ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(X)) <=> (ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) <=> (ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) | ssPv1(W)) <=> ((ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)))), rewrite(((ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(W)) <=> (ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) | ssPv1(W)) <=> (ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) | ssPv1(W)) | ssPv4(W)) <=> ((ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) | ssPv4(W)))), rewrite(((ssPv2(V) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W)) | ssPv4(W)) <=> (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) | ssPv1(W)) | ssPv4(W)) <=> (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))))),
% 2.01/1.56 inference(bind,[status(th)],[])).
% 2.01/1.56 tff(820,plain,
% 2.01/1.56 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) | ssPv1(W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 2.01/1.56 inference(quant_intro,[status(thm)],[819])).
% 2.01/1.56 tff(821,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv2(V)) | ssPv1(X)) | ssPv1(W)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 2.01/1.56 tff(822,plain,
% 2.01/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 2.01/1.56 inference(modus_ponens,[status(thm)],[821, 820])).
% 2.01/1.56 tff(823,plain,
% 2.01/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 2.01/1.56 inference(modus_ponens,[status(thm)],[822, 818])).
% 2.01/1.56 tff(824,plain,(
% 2.01/1.56 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 2.01/1.56 inference(skolemize,[status(sab)],[823])).
% 2.01/1.56 tff(825,plain,
% 2.01/1.56 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))),
% 2.01/1.56 inference(modus_ponens,[status(thm)],[824, 817])).
% 2.01/1.56 tff(826,plain,
% 2.01/1.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.56 inference(rewrite,[status(thm)],[])).
% 2.01/1.56 tff(827,plain,
% 2.01/1.56 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0)))) <=> (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.56 inference(rewrite,[status(thm)],[])).
% 2.01/1.56 tff(828,plain,
% 2.01/1.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.56 inference(monotonicity,[status(thm)],[827])).
% 2.01/1.56 tff(829,plain,
% 2.01/1.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.56 inference(transitivity,[status(thm)],[828, 826])).
% 2.01/1.56 tff(830,plain,
% 2.01/1.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))))),
% 2.01/1.56 inference(quant_inst,[status(thm)],[])).
% 2.01/1.56 tff(831,plain,
% 2.01/1.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(modus_ponens,[status(thm)],[830, 829])).
% 2.01/1.56 tff(832,plain,
% 2.01/1.56 (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[831, 825, 155, 252])).
% 2.01/1.56 tff(833,plain,
% 2.01/1.56 (ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[832, 3, 2, 250])).
% 2.01/1.56 tff(834,plain,
% 2.01/1.56 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.56 inference(rewrite,[status(thm)],[])).
% 2.01/1.56 tff(835,plain,
% 2.01/1.56 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.56 inference(rewrite,[status(thm)],[])).
% 2.01/1.56 tff(836,plain,
% 2.01/1.56 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.56 inference(monotonicity,[status(thm)],[835])).
% 2.01/1.56 tff(837,plain,
% 2.01/1.56 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.56 inference(transitivity,[status(thm)],[836, 834])).
% 2.01/1.56 tff(838,plain,
% 2.01/1.56 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(quant_inst,[status(thm)],[])).
% 2.01/1.56 tff(839,plain,
% 2.01/1.56 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.56 inference(modus_ponens,[status(thm)],[838, 837])).
% 2.01/1.56 tff(840,plain,
% 2.01/1.56 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[839, 805, 155, 252])).
% 2.01/1.56 tff(841,plain,
% 2.01/1.56 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[840, 173, 758, 833])).
% 2.01/1.56 tff(842,plain,
% 2.01/1.56 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[289, 3, 4, 250])).
% 2.01/1.56 tff(843,plain,
% 2.01/1.56 (ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[794, 842, 4, 758])).
% 2.01/1.56 tff(844,plain,
% 2.01/1.56 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.56 inference(unit_resolution,[status(thm)],[269, 3, 4, 250])).
% 2.01/1.56 tff(845,assumption,(ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))), introduced(assumption)).
% 2.01/1.56 tff(846,assumption,(ssPv2(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 2.01/1.56 tff(847,assumption,(ssPv1(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 2.01/1.56 tff(848,assumption,(ssPv3(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 2.01/1.56 tff(849,plain,
% 2.01/1.56 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.56 inference(rewrite,[status(thm)],[])).
% 2.01/1.56 tff(850,plain,
% 2.01/1.56 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.56 inference(rewrite,[status(thm)],[])).
% 2.01/1.56 tff(851,plain,
% 2.01/1.56 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.56 inference(monotonicity,[status(thm)],[850])).
% 2.01/1.56 tff(852,plain,
% 2.01/1.56 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.56 inference(transitivity,[status(thm)],[851, 849])).
% 2.01/1.56 tff(853,plain,
% 2.01/1.56 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.56 inference(quant_inst,[status(thm)],[])).
% 2.01/1.56 tff(854,plain,
% 2.01/1.56 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(modus_ponens,[status(thm)],[853, 852])).
% 2.01/1.57 tff(855,plain,
% 2.01/1.57 ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[854, 222, 382, 564])).
% 2.01/1.57 tff(856,plain,
% 2.01/1.57 (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[855, 845, 848, 847])).
% 2.01/1.57 tff(857,assumption,(ssPv4(skf1(skf1(skf1(skf1(elem!0)))))), introduced(assumption)).
% 2.01/1.57 tff(858,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(859,plain,
% 2.01/1.57 ((ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(860,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.57 inference(monotonicity,[status(thm)],[859])).
% 2.01/1.57 tff(861,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(transitivity,[status(thm)],[860, 858])).
% 2.01/1.57 tff(862,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(quant_inst,[status(thm)],[])).
% 2.01/1.57 tff(863,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(modus_ponens,[status(thm)],[862, 861])).
% 2.01/1.57 tff(864,plain,
% 2.01/1.57 ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[863, 141, 382, 564])).
% 2.01/1.57 tff(865,plain,
% 2.01/1.57 (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[864, 845, 857, 847])).
% 2.01/1.57 tff(866,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(867,plain,
% 2.01/1.57 (((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(868,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.57 inference(monotonicity,[status(thm)],[867])).
% 2.01/1.57 tff(869,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(transitivity,[status(thm)],[868, 866])).
% 2.01/1.57 tff(870,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(quant_inst,[status(thm)],[])).
% 2.01/1.57 tff(871,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(modus_ponens,[status(thm)],[870, 869])).
% 2.01/1.57 tff(872,plain,
% 2.01/1.57 ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[871, 318, 382, 564])).
% 2.01/1.57 tff(873,plain,
% 2.01/1.57 ($false),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[872, 865, 856, 846, 845])).
% 2.01/1.57 tff(874,plain,((~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.57 tff(875,plain,
% 2.01/1.57 (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[874, 833, 841, 843, 844])).
% 2.01/1.57 tff(876,plain,
% 2.01/1.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(877,plain,
% 2.01/1.57 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(878,plain,
% 2.01/1.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(monotonicity,[status(thm)],[877])).
% 2.01/1.57 tff(879,plain,
% 2.01/1.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(transitivity,[status(thm)],[878, 876])).
% 2.01/1.57 tff(880,plain,
% 2.01/1.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(quant_inst,[status(thm)],[])).
% 2.01/1.57 tff(881,plain,
% 2.01/1.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(modus_ponens,[status(thm)],[880, 879])).
% 2.01/1.57 tff(882,plain,
% 2.01/1.57 ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[881, 44, 382, 564])).
% 2.01/1.57 tff(883,plain,
% 2.01/1.57 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[882, 875, 843, 841])).
% 2.01/1.57 tff(884,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(885,plain,
% 2.01/1.57 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(886,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.57 inference(monotonicity,[status(thm)],[885])).
% 2.01/1.57 tff(887,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(transitivity,[status(thm)],[886, 884])).
% 2.01/1.57 tff(888,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(quant_inst,[status(thm)],[])).
% 2.01/1.57 tff(889,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(modus_ponens,[status(thm)],[888, 887])).
% 2.01/1.57 tff(890,plain,
% 2.01/1.57 ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[889, 805, 382, 564])).
% 2.01/1.57 tff(891,plain,
% 2.01/1.57 (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[890, 883, 844, 875])).
% 2.01/1.57 tff(892,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(893,plain,
% 2.01/1.57 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(894,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.57 inference(monotonicity,[status(thm)],[893])).
% 2.01/1.57 tff(895,plain,
% 2.01/1.57 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.57 inference(transitivity,[status(thm)],[894, 892])).
% 2.01/1.57 tff(896,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.01/1.57 inference(quant_inst,[status(thm)],[])).
% 2.01/1.57 tff(897,plain,
% 2.01/1.57 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.57 inference(modus_ponens,[status(thm)],[896, 895])).
% 2.01/1.57 tff(898,plain,
% 2.01/1.57 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[897, 300, 155, 252])).
% 2.01/1.57 tff(899,plain,
% 2.01/1.57 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.01/1.57 inference(unit_resolution,[status(thm)],[898, 843, 4, 842])).
% 2.01/1.57 tff(900,plain,
% 2.01/1.57 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl(((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) <=> ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))))),
% 2.01/1.57 inference(bind,[status(th)],[])).
% 2.01/1.57 tff(901,plain,
% 2.01/1.57 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.57 inference(quant_intro,[status(thm)],[900])).
% 2.01/1.57 tff(902,plain,
% 2.01/1.57 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.57 inference(rewrite,[status(thm)],[])).
% 2.01/1.57 tff(903,plain,
% 2.01/1.57 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(Y))))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(Y))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) <=> (((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> (((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(Z))))), rewrite((((~ssPv2(Y)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(Z))) <=> ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv4(W))) <=> (((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(W))))), rewrite((((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(W))) <=> ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))), ((((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv4(W))) <=> ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))))),
% 2.01/1.58 inference(bind,[status(th)],[])).
% 2.01/1.58 tff(904,plain,
% 2.01/1.58 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv4(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.58 inference(quant_intro,[status(thm)],[903])).
% 2.01/1.58 tff(905,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssPv2(Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv4(W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 2.01/1.58 tff(906,plain,
% 2.01/1.58 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[905, 904])).
% 2.01/1.58 tff(907,plain,
% 2.01/1.58 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[906, 902])).
% 2.01/1.58 tff(908,plain,(
% 2.01/1.58 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.58 inference(skolemize,[status(sab)],[907])).
% 2.01/1.58 tff(909,plain,
% 2.01/1.58 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[908, 901])).
% 2.01/1.58 tff(910,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(911,plain,
% 2.01/1.58 (((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(912,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(monotonicity,[status(thm)],[911])).
% 2.01/1.58 tff(913,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(transitivity,[status(thm)],[912, 910])).
% 2.01/1.58 tff(914,plain,
% 2.01/1.58 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.58 inference(quant_inst,[status(thm)],[])).
% 2.01/1.58 tff(915,plain,
% 2.01/1.58 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[914, 913])).
% 2.01/1.58 tff(916,plain,
% 2.01/1.58 ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[915, 909, 252, 382])).
% 2.01/1.58 tff(917,plain,
% 2.01/1.58 (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[916, 883, 844, 899])).
% 2.01/1.58 tff(918,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(919,plain,
% 2.01/1.58 ((ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(920,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.01/1.58 inference(monotonicity,[status(thm)],[919])).
% 2.01/1.58 tff(921,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.58 inference(transitivity,[status(thm)],[920, 918])).
% 2.01/1.58 tff(922,plain,
% 2.01/1.58 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(quant_inst,[status(thm)],[])).
% 2.01/1.58 tff(923,plain,
% 2.01/1.58 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[922, 921])).
% 2.01/1.58 tff(924,plain,
% 2.01/1.58 (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[923, 300, 564, 619])).
% 2.01/1.58 tff(925,plain,
% 2.01/1.58 (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[924, 917, 875, 891])).
% 2.01/1.58 tff(926,plain,
% 2.01/1.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(927,plain,
% 2.01/1.58 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(928,plain,
% 2.01/1.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.58 inference(monotonicity,[status(thm)],[927])).
% 2.01/1.58 tff(929,plain,
% 2.01/1.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.58 inference(transitivity,[status(thm)],[928, 926])).
% 2.01/1.58 tff(930,plain,
% 2.01/1.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(quant_inst,[status(thm)],[])).
% 2.01/1.58 tff(931,plain,
% 2.01/1.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[930, 929])).
% 2.01/1.58 tff(932,plain,
% 2.01/1.58 ((~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[931, 787, 564, 619])).
% 2.01/1.58 tff(933,plain,
% 2.01/1.58 ($false),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[932, 925, 917, 891, 883])).
% 2.01/1.58 tff(934,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.58 tff(935,plain,
% 2.01/1.58 (ssPv4(skf1(skf1(elem!0)))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[934, 250, 4, 2])).
% 2.01/1.58 tff(936,plain,
% 2.01/1.58 ($false),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[470, 935, 250, 4, 815])).
% 2.01/1.58 tff(937,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.58 tff(938,plain,
% 2.01/1.58 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[937, 4, 2])).
% 2.01/1.58 tff(939,assumption,(~ssPv2(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 2.01/1.58 tff(940,plain,
% 2.01/1.58 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[898, 939, 4, 847])).
% 2.01/1.58 tff(941,assumption,(ssPv1(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 2.01/1.58 tff(942,plain,
% 2.01/1.58 (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[707, 939, 4, 941])).
% 2.01/1.58 tff(943,plain,
% 2.01/1.58 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) <=> (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))))),
% 2.01/1.58 inference(bind,[status(th)],[])).
% 2.01/1.58 tff(944,plain,
% 2.01/1.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(quant_intro,[status(thm)],[943])).
% 2.01/1.58 tff(945,plain,
% 2.01/1.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(946,plain,
% 2.01/1.58 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) <=> (((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(W))))), rewrite((((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(W))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv4(Y)) <=> (((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv4(Y)))), rewrite((((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv4(Y)) | ssPv2(W)) <=> ((ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv2(W)))), rewrite(((ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W))) | ssPv2(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv4(Y)) | ssPv2(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))))),
% 2.01/1.58 inference(bind,[status(th)],[])).
% 2.01/1.58 tff(947,plain,
% 2.01/1.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv4(Y)) | ssPv2(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(quant_intro,[status(thm)],[946])).
% 2.01/1.58 tff(948,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv3(W))) | ssPv4(Y)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause27')).
% 2.01/1.58 tff(949,plain,
% 2.01/1.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[948, 947])).
% 2.01/1.58 tff(950,plain,
% 2.01/1.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[949, 945])).
% 2.01/1.58 tff(951,plain,(
% 2.01/1.58 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(skolemize,[status(sab)],[950])).
% 2.01/1.58 tff(952,plain,
% 2.01/1.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[951, 944])).
% 2.01/1.58 tff(953,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(954,plain,
% 2.01/1.58 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(955,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.58 inference(monotonicity,[status(thm)],[954])).
% 2.01/1.58 tff(956,plain,
% 2.01/1.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.58 inference(transitivity,[status(thm)],[955, 953])).
% 2.01/1.58 tff(957,plain,
% 2.01/1.58 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 2.01/1.58 inference(quant_inst,[status(thm)],[])).
% 2.01/1.58 tff(958,plain,
% 2.01/1.58 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[957, 956])).
% 2.01/1.58 tff(959,plain,
% 2.01/1.58 (ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[958, 952, 155, 252])).
% 2.01/1.58 tff(960,plain,
% 2.01/1.58 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.58 inference(unit_resolution,[status(thm)],[959, 942, 4, 759])).
% 2.01/1.58 tff(961,plain,
% 2.01/1.58 (^[W: $i, V: $i, U: $i] : refl(((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) <=> ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))))),
% 2.01/1.58 inference(bind,[status(th)],[])).
% 2.01/1.58 tff(962,plain,
% 2.01/1.58 (![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(quant_intro,[status(thm)],[961])).
% 2.01/1.58 tff(963,plain,
% 2.01/1.58 (![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(rewrite,[status(thm)],[])).
% 2.01/1.58 tff(964,plain,
% 2.01/1.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv1(W))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv1(W))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) | (~ssPv4(W))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) | (~ssPv4(W))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) | (~ssPv4(W))) <=> ((~ssPv4(W)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) | (~ssPv4(W))) <=> ((~ssPv4(W)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(W)) <=> (((~ssPv4(W)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) | ssPv2(W)))), rewrite((((~ssPv4(W)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V))) | ssPv2(W)) <=> ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(W)) <=> ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))))),
% 2.01/1.58 inference(bind,[status(th)],[])).
% 2.01/1.58 tff(965,plain,
% 2.01/1.58 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(quant_intro,[status(thm)],[964])).
% 2.01/1.58 tff(966,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssPv1(W))) | (~ssPv4(W))) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 2.01/1.58 tff(967,plain,
% 2.01/1.58 (![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[966, 965])).
% 2.01/1.58 tff(968,plain,
% 2.01/1.58 (![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[967, 963])).
% 2.01/1.58 tff(969,plain,(
% 2.01/1.58 ![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(skolemize,[status(sab)],[968])).
% 2.01/1.58 tff(970,plain,
% 2.01/1.58 (![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))),
% 2.01/1.58 inference(modus_ponens,[status(thm)],[969, 962])).
% 2.01/1.58 tff(971,plain,
% 2.01/1.58 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(972,plain,
% 2.01/1.59 (((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(973,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.59 inference(monotonicity,[status(thm)],[972])).
% 2.01/1.59 tff(974,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(transitivity,[status(thm)],[973, 971])).
% 2.01/1.59 tff(975,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(quant_inst,[status(thm)],[])).
% 2.01/1.59 tff(976,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[975, 974])).
% 2.01/1.59 tff(977,plain,
% 2.01/1.59 (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[976, 970, 252, 382])).
% 2.01/1.59 tff(978,plain,
% 2.01/1.59 (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[977, 939, 941, 940])).
% 2.01/1.59 tff(979,plain,
% 2.01/1.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(980,plain,
% 2.01/1.59 ((ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(981,plain,
% 2.01/1.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(monotonicity,[status(thm)],[980])).
% 2.01/1.59 tff(982,plain,
% 2.01/1.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(transitivity,[status(thm)],[981, 979])).
% 2.01/1.59 tff(983,plain,
% 2.01/1.59 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(quant_inst,[status(thm)],[])).
% 2.01/1.59 tff(984,plain,
% 2.01/1.59 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[983, 982])).
% 2.01/1.59 tff(985,plain,
% 2.01/1.59 ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[984, 141, 252, 382])).
% 2.01/1.59 tff(986,plain,
% 2.01/1.59 (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[985, 978, 941, 940])).
% 2.01/1.59 tff(987,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(988,plain,
% 2.01/1.59 ((ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(989,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(monotonicity,[status(thm)],[988])).
% 2.01/1.59 tff(990,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(transitivity,[status(thm)],[989, 987])).
% 2.01/1.59 tff(991,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(quant_inst,[status(thm)],[])).
% 2.01/1.59 tff(992,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[991, 990])).
% 2.01/1.59 tff(993,plain,
% 2.01/1.59 ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[992, 44, 252, 382])).
% 2.01/1.59 tff(994,plain,
% 2.01/1.59 ($false),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[993, 986, 960, 941, 940])).
% 2.01/1.59 tff(995,plain,(ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.59 tff(996,plain,
% 2.01/1.59 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[995, 938, 4, 758, 815])).
% 2.01/1.59 tff(997,assumption,(ssPv2(skf1(elem!0))), introduced(assumption)).
% 2.01/1.59 tff(998,plain,
% 2.01/1.59 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[325, 249, 941, 997])).
% 2.01/1.59 tff(999,plain,
% 2.01/1.59 ($false),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[812, 998, 249, 194, 759])).
% 2.01/1.59 tff(1000,plain,((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.59 tff(1001,plain,
% 2.01/1.59 (~ssPv2(skf1(elem!0))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1000, 996, 758, 938, 153])).
% 2.01/1.59 tff(1002,plain,
% 2.01/1.59 (~ssPv4(skf1(elem!0))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[747, 1001, 2, 938])).
% 2.01/1.59 tff(1003,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1004,plain,
% 2.01/1.59 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1005,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(monotonicity,[status(thm)],[1004])).
% 2.01/1.59 tff(1006,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(transitivity,[status(thm)],[1005, 1003])).
% 2.01/1.59 tff(1007,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(quant_inst,[status(thm)],[])).
% 2.01/1.59 tff(1008,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 2.01/1.59 tff(1009,plain,
% 2.01/1.59 (ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1008, 262, 14, 155])).
% 2.01/1.59 tff(1010,plain,
% 2.01/1.59 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1009, 1002, 2, 1001])).
% 2.01/1.59 tff(1011,plain,
% 2.01/1.59 (ssPv2(skf1(elem!0))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[307, 3, 4, 938])).
% 2.01/1.59 tff(1012,plain,
% 2.01/1.59 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1000, 1011, 758, 938, 153])).
% 2.01/1.59 tff(1013,plain,
% 2.01/1.59 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)) <=> (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)))),
% 2.01/1.59 inference(bind,[status(th)],[])).
% 2.01/1.59 tff(1014,plain,
% 2.01/1.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(quant_intro,[status(thm)],[1013])).
% 2.01/1.59 tff(1015,plain,
% 2.01/1.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1016,plain,
% 2.01/1.59 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) <=> ((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(X)))), rewrite(((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(X)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) | ssPv1(W)) <=> ((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X)) | ssPv1(W)))), rewrite(((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X)) | ssPv1(W)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) | ssPv1(W)) <=> (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) | ssPv1(W)) | ssPv4(W)) <=> ((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)) | ssPv4(W)))), rewrite(((ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X)) | ssPv4(W)) <=> (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) | ssPv1(W)) | ssPv4(W)) <=> (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))))),
% 2.01/1.59 inference(bind,[status(th)],[])).
% 2.01/1.59 tff(1017,plain,
% 2.01/1.59 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) | ssPv1(W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(quant_intro,[status(thm)],[1016])).
% 2.01/1.59 tff(1018,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | ssPv4(V)) | ssPv2(X)) | ssPv1(W)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 2.01/1.59 tff(1019,plain,
% 2.01/1.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 2.01/1.59 tff(1020,plain,
% 2.01/1.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[1019, 1015])).
% 2.01/1.59 tff(1021,plain,(
% 2.01/1.59 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(skolemize,[status(sab)],[1020])).
% 2.01/1.59 tff(1022,plain,
% 2.01/1.59 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[1021, 1014])).
% 2.01/1.59 tff(1023,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1024,plain,
% 2.01/1.59 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1025,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(monotonicity,[status(thm)],[1024])).
% 2.01/1.59 tff(1026,plain,
% 2.01/1.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(transitivity,[status(thm)],[1025, 1023])).
% 2.01/1.59 tff(1027,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(quant_inst,[status(thm)],[])).
% 2.01/1.59 tff(1028,plain,
% 2.01/1.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 2.01/1.59 tff(1029,plain,
% 2.01/1.59 (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1028, 1022, 155, 252])).
% 2.01/1.59 tff(1030,plain,
% 2.01/1.59 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1029, 1012, 2, 3])).
% 2.01/1.59 tff(1031,plain,
% 2.01/1.59 ($false),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[707, 1030, 1012, 4, 938])).
% 2.01/1.59 tff(1032,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.59 tff(1033,plain,
% 2.01/1.59 (ssPv4(skf1(skf1(elem!0)))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1032, 4, 2])).
% 2.01/1.59 tff(1034,plain,
% 2.01/1.59 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[812, 996, 153, 758])).
% 2.01/1.59 tff(1035,assumption,(ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))), introduced(assumption)).
% 2.01/1.59 tff(1036,assumption,(ssPv4(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 2.01/1.59 tff(1037,plain,
% 2.01/1.59 (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[985, 1035, 941, 1036])).
% 2.01/1.59 tff(1038,plain,
% 2.01/1.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1039,plain,
% 2.01/1.59 ((ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(rewrite,[status(thm)],[])).
% 2.01/1.59 tff(1040,plain,
% 2.01/1.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.59 inference(monotonicity,[status(thm)],[1039])).
% 2.01/1.59 tff(1041,plain,
% 2.01/1.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.59 inference(transitivity,[status(thm)],[1040, 1038])).
% 2.01/1.59 tff(1042,plain,
% 2.01/1.59 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(quant_inst,[status(thm)],[])).
% 2.01/1.59 tff(1043,plain,
% 2.01/1.59 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 2.01/1.59 tff(1044,plain,
% 2.01/1.59 ((~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1043, 222, 252, 382])).
% 2.01/1.59 tff(1045,plain,
% 2.01/1.59 (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1044, 1035, 941, 175])).
% 2.01/1.59 tff(1046,plain,
% 2.01/1.59 ($false),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[591, 1045, 1037, 249, 1035])).
% 2.01/1.59 tff(1047,plain,((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.59 tff(1048,plain,
% 2.01/1.59 (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[1047, 996, 938, 1010, 1034])).
% 2.01/1.59 tff(1049,plain,
% 2.01/1.59 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.59 inference(unit_resolution,[status(thm)],[993, 1048, 938, 1034])).
% 2.01/1.60 tff(1050,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1051,plain,
% 2.01/1.60 (((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1052,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.60 inference(monotonicity,[status(thm)],[1051])).
% 2.01/1.60 tff(1053,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(transitivity,[status(thm)],[1052, 1050])).
% 2.01/1.60 tff(1054,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 2.01/1.60 inference(quant_inst,[status(thm)],[])).
% 2.01/1.60 tff(1055,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.60 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 2.01/1.60 tff(1056,plain,
% 2.01/1.60 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1055, 909, 155, 252])).
% 2.01/1.60 tff(1057,plain,
% 2.01/1.60 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1056, 1049, 1033, 1010])).
% 2.01/1.60 tff(1058,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1059,plain,
% 2.01/1.60 ((ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1060,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.60 inference(monotonicity,[status(thm)],[1059])).
% 2.01/1.60 tff(1061,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(transitivity,[status(thm)],[1060, 1058])).
% 2.01/1.60 tff(1062,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.60 inference(quant_inst,[status(thm)],[])).
% 2.01/1.60 tff(1063,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.60 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 2.01/1.60 tff(1064,plain,
% 2.01/1.60 ((~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1063, 805, 252, 382])).
% 2.01/1.60 tff(1065,plain,
% 2.01/1.60 (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1064, 1049, 1048, 1010])).
% 2.01/1.60 tff(1066,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1067,plain,
% 2.01/1.60 ((ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1068,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.60 inference(monotonicity,[status(thm)],[1067])).
% 2.01/1.60 tff(1069,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.60 inference(transitivity,[status(thm)],[1068, 1066])).
% 2.01/1.60 tff(1070,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.60 inference(quant_inst,[status(thm)],[])).
% 2.01/1.60 tff(1071,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.60 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 2.01/1.60 tff(1072,plain,
% 2.01/1.60 (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1071, 300, 382, 564])).
% 2.01/1.60 tff(1073,plain,
% 2.01/1.60 (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1072, 1065, 1048, 1057])).
% 2.01/1.60 tff(1074,plain,
% 2.01/1.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1075,plain,
% 2.01/1.60 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1076,plain,
% 2.01/1.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.60 inference(monotonicity,[status(thm)],[1075])).
% 2.01/1.60 tff(1077,plain,
% 2.01/1.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.60 inference(transitivity,[status(thm)],[1076, 1074])).
% 2.01/1.60 tff(1078,plain,
% 2.01/1.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(quant_inst,[status(thm)],[])).
% 2.01/1.60 tff(1079,plain,
% 2.01/1.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.60 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 2.01/1.60 tff(1080,plain,
% 2.01/1.60 ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1079, 787, 382, 564])).
% 2.01/1.60 tff(1081,plain,
% 2.01/1.60 ($false),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1080, 1073, 1065, 1049, 1057])).
% 2.01/1.60 tff(1082,plain,(ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.60 tff(1083,plain,
% 2.01/1.60 (ssPv2(skf1(skf1(elem!0)))),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1082, 2])).
% 2.01/1.60 tff(1084,plain,
% 2.01/1.60 (ssPv1(elem!0)),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[33, 5, 3, 2])).
% 2.01/1.60 tff(1085,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1086,plain,
% 2.01/1.60 ((ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(elem!0)) <=> (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1087,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0)))),
% 2.01/1.60 inference(monotonicity,[status(thm)],[1086])).
% 2.01/1.60 tff(1088,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0))),
% 2.01/1.60 inference(transitivity,[status(thm)],[1087, 1085])).
% 2.01/1.60 tff(1089,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(elem!0))),
% 2.01/1.60 inference(quant_inst,[status(thm)],[])).
% 2.01/1.60 tff(1090,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0)),
% 2.01/1.60 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 2.01/1.60 tff(1091,plain,
% 2.01/1.60 (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(elem!0)),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1090, 682, 16, 14])).
% 2.01/1.60 tff(1092,plain,
% 2.01/1.60 (ssPv3(elem!0)),
% 2.01/1.60 inference(unit_resolution,[status(thm)],[1091, 5, 1083, 3])).
% 2.01/1.60 tff(1093,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1094,plain,
% 2.01/1.60 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(elem!0)) | (~ssPv1(elem!0))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)))),
% 2.01/1.60 inference(rewrite,[status(thm)],[])).
% 2.01/1.60 tff(1095,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0))))),
% 2.01/1.60 inference(monotonicity,[status(thm)],[1094])).
% 2.01/1.60 tff(1096,plain,
% 2.01/1.60 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)))),
% 2.01/1.60 inference(transitivity,[status(thm)],[1095, 1093])).
% 2.01/1.60 tff(1097,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(elem!0)) | (~ssPv1(elem!0)))),
% 2.01/1.60 inference(quant_inst,[status(thm)],[])).
% 2.01/1.60 tff(1098,plain,
% 2.01/1.60 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0))),
% 2.01/1.60 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 2.01/1.61 tff(1099,plain,
% 2.01/1.61 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1098, 718, 16, 14])).
% 2.01/1.61 tff(1100,plain,
% 2.01/1.61 ($false),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1099, 1092, 1084, 1083, 1])).
% 2.01/1.61 tff(1101,plain,(ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.61 tff(1102,plain,
% 2.01/1.61 (ssPv3(skf1(elem!0))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1101, 1, 3, 2])).
% 2.01/1.61 tff(1103,plain,
% 2.01/1.61 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))) <=> (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))))),
% 2.01/1.61 inference(bind,[status(th)],[])).
% 2.01/1.61 tff(1104,plain,
% 2.01/1.61 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(quant_intro,[status(thm)],[1103])).
% 2.01/1.61 tff(1105,plain,
% 2.01/1.61 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1106,plain,
% 2.01/1.61 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) <=> ((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(X, Y))))), rewrite((((~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> (((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(Z))))), rewrite((((~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(Z))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) <=> (((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv1(W))))), rewrite((((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv1(W))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))))), ((((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv3(Y)) <=> (((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))) | ssPv3(Y)))), rewrite((((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))), ((((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))))),
% 2.01/1.61 inference(bind,[status(th)],[])).
% 2.01/1.61 tff(1107,plain,
% 2.01/1.61 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv3(Y)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(quant_intro,[status(thm)],[1106])).
% 2.01/1.61 tff(1108,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv3(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 2.01/1.61 tff(1109,plain,
% 2.01/1.61 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 2.01/1.61 tff(1110,plain,
% 2.01/1.61 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1109, 1105])).
% 2.01/1.61 tff(1111,plain,(
% 2.01/1.61 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(skolemize,[status(sab)],[1110])).
% 2.01/1.61 tff(1112,plain,
% 2.01/1.61 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1111, 1104])).
% 2.01/1.61 tff(1113,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1114,plain,
% 2.01/1.61 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(elem!0))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1115,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0))))),
% 2.01/1.61 inference(monotonicity,[status(thm)],[1114])).
% 2.01/1.61 tff(1116,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)))),
% 2.01/1.61 inference(transitivity,[status(thm)],[1115, 1113])).
% 2.01/1.61 tff(1117,plain,
% 2.01/1.61 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))),
% 2.01/1.61 inference(quant_inst,[status(thm)],[])).
% 2.01/1.61 tff(1118,plain,
% 2.01/1.61 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 2.01/1.61 tff(1119,plain,
% 2.01/1.61 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1118, 1112, 16, 14])).
% 2.01/1.61 tff(1120,plain,
% 2.01/1.61 (~ssPv1(elem!0)),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1119, 1102, 1083, 1])).
% 2.01/1.61 tff(1121,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1122,plain,
% 2.01/1.61 ((ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(elem!0))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1123,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0))))),
% 2.01/1.61 inference(monotonicity,[status(thm)],[1122])).
% 2.01/1.61 tff(1124,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)))),
% 2.01/1.61 inference(transitivity,[status(thm)],[1123, 1121])).
% 2.01/1.61 tff(1125,plain,
% 2.01/1.61 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(elem!0)))),
% 2.01/1.61 inference(quant_inst,[status(thm)],[])).
% 2.01/1.61 tff(1126,plain,
% 2.01/1.61 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv3(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 2.01/1.61 tff(1127,plain,
% 2.01/1.61 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1126, 805, 16, 14])).
% 2.01/1.61 tff(1128,plain,
% 2.01/1.61 (~ssPv3(elem!0)),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1127, 1102, 1083, 3])).
% 2.01/1.61 tff(1129,plain,
% 2.01/1.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1130,plain,
% 2.01/1.61 (((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv4(skf1(elem!0))) <=> (ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1131,plain,
% 2.01/1.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0)))),
% 2.01/1.61 inference(monotonicity,[status(thm)],[1130])).
% 2.01/1.61 tff(1132,plain,
% 2.01/1.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0))),
% 2.01/1.61 inference(transitivity,[status(thm)],[1131, 1129])).
% 2.01/1.61 tff(1133,plain,
% 2.01/1.61 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv4(skf1(elem!0)))),
% 2.01/1.61 inference(quant_inst,[status(thm)],[])).
% 2.01/1.61 tff(1134,plain,
% 2.01/1.61 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0)),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 2.01/1.61 tff(1135,plain,
% 2.01/1.61 (ssPv1(elem!0) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv3(elem!0)),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1134, 336, 16, 14])).
% 2.01/1.61 tff(1136,plain,
% 2.01/1.61 (ssPv4(skf1(elem!0))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1135, 1128, 1083, 1120])).
% 2.01/1.61 tff(1137,assumption,(~ssPv4(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 2.01/1.61 tff(1138,plain,
% 2.01/1.61 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[361, 1137, 2, 1])).
% 2.01/1.61 tff(1139,plain,
% 2.01/1.61 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[343, 1137, 2, 1])).
% 2.01/1.61 tff(1140,plain,
% 2.01/1.61 (ssPv4(skf1(skf1(elem!0)))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[832, 1139, 2, 250])).
% 2.01/1.61 tff(1141,plain,
% 2.01/1.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1142,plain,
% 2.01/1.61 ((ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1143,plain,
% 2.01/1.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.61 inference(monotonicity,[status(thm)],[1142])).
% 2.01/1.61 tff(1144,plain,
% 2.01/1.61 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.61 inference(transitivity,[status(thm)],[1143, 1141])).
% 2.01/1.61 tff(1145,plain,
% 2.01/1.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.61 inference(quant_inst,[status(thm)],[])).
% 2.01/1.61 tff(1146,plain,
% 2.01/1.61 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 2.01/1.61 tff(1147,plain,
% 2.01/1.61 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1146, 445, 155, 252])).
% 2.01/1.61 tff(1148,plain,
% 2.01/1.61 ($false),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1147, 1140, 1138, 1083, 1])).
% 2.01/1.61 tff(1149,plain,(ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.61 tff(1150,plain,
% 2.01/1.61 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1149, 1, 2, 250])).
% 2.01/1.61 tff(1151,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1152,plain,
% 2.01/1.61 ((ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1153,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.61 inference(monotonicity,[status(thm)],[1152])).
% 2.01/1.61 tff(1154,plain,
% 2.01/1.61 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(transitivity,[status(thm)],[1153, 1151])).
% 2.01/1.61 tff(1155,plain,
% 2.01/1.61 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 2.01/1.61 inference(quant_inst,[status(thm)],[])).
% 2.01/1.61 tff(1156,plain,
% 2.01/1.61 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | ssPv1(V) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.01/1.61 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 2.01/1.61 tff(1157,plain,
% 2.01/1.61 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1156, 483, 14, 155])).
% 2.01/1.61 tff(1158,plain,
% 2.01/1.61 (ssPv2(skf1(elem!0))),
% 2.01/1.61 inference(unit_resolution,[status(thm)],[1157, 1, 1083, 250])).
% 2.01/1.61 tff(1159,plain,
% 2.01/1.61 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W))))),
% 2.01/1.61 inference(bind,[status(th)],[])).
% 2.01/1.61 tff(1160,plain,
% 2.01/1.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.61 inference(quant_intro,[status(thm)],[1159])).
% 2.01/1.61 tff(1161,plain,
% 2.01/1.61 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.61 inference(rewrite,[status(thm)],[])).
% 2.01/1.61 tff(1162,plain,
% 2.01/1.61 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssPv4(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> (((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv4(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) <=> ((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> (((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv4(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(X))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv2(W))) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))) | (~ssPv2(W))))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))) | (~ssPv2(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv2(W))) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv2(W))) | ssPv3(W)) <=> (((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)) | (~ssPv2(W))) | ssPv3(W)))), rewrite((((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)) | (~ssPv2(W))) | ssPv3(W)) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv2(W))) | ssPv3(W)) <=> ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))))),
% 2.01/1.62 inference(bind,[status(th)],[])).
% 2.01/1.62 tff(1163,plain,
% 2.01/1.62 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv2(W))) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.62 inference(quant_intro,[status(thm)],[1162])).
% 2.01/1.62 tff(1164,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv2(W))) | ssPv3(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause18')).
% 2.01/1.62 tff(1165,plain,
% 2.01/1.62 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 2.01/1.62 tff(1166,plain,
% 2.01/1.62 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1165, 1161])).
% 2.01/1.62 tff(1167,plain,(
% 2.01/1.62 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.62 inference(skolemize,[status(sab)],[1166])).
% 2.01/1.62 tff(1168,plain,
% 2.01/1.62 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1167, 1160])).
% 2.01/1.62 tff(1169,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1170,plain,
% 2.01/1.62 (((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0)))) <=> (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1171,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(monotonicity,[status(thm)],[1170])).
% 2.01/1.62 tff(1172,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(transitivity,[status(thm)],[1171, 1169])).
% 2.01/1.62 tff(1173,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))))),
% 2.01/1.62 inference(quant_inst,[status(thm)],[])).
% 2.01/1.62 tff(1174,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 2.01/1.62 tff(1175,plain,
% 2.01/1.62 (ssPv3(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1174, 1168, 14, 155])).
% 2.01/1.62 tff(1176,plain,
% 2.01/1.62 (~ssPv4(skf1(skf1(elem!0)))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1175, 5, 997, 1036])).
% 2.01/1.62 tff(1177,plain,
% 2.01/1.62 (ssPv3(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1091, 1176, 1083, 5])).
% 2.01/1.62 tff(1178,plain,
% 2.01/1.62 (ssPv1(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[33, 1176, 5, 2])).
% 2.01/1.62 tff(1179,plain,
% 2.01/1.62 ($false),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1099, 1178, 1177, 1083, 1])).
% 2.01/1.62 tff(1180,plain,(ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.62 tff(1181,plain,
% 2.01/1.62 (ssPv3(skf1(elem!0))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1180, 1, 2, 1158, 1150])).
% 2.01/1.62 tff(1182,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1183,plain,
% 2.01/1.62 (((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1184,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.62 inference(monotonicity,[status(thm)],[1183])).
% 2.01/1.62 tff(1185,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(transitivity,[status(thm)],[1184, 1182])).
% 2.01/1.62 tff(1186,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(quant_inst,[status(thm)],[])).
% 2.01/1.62 tff(1187,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 2.01/1.62 tff(1188,plain,
% 2.01/1.62 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1187, 1168, 155, 252])).
% 2.01/1.62 tff(1189,plain,
% 2.01/1.62 (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1188, 1150, 1083, 1])).
% 2.01/1.62 tff(1190,plain,
% 2.01/1.62 (~ssPv1(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1119, 1181, 1083, 1])).
% 2.01/1.62 tff(1191,plain,
% 2.01/1.62 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1029, 3, 2, 562])).
% 2.01/1.62 tff(1192,assumption,(~ssPv1(elem!0)), introduced(assumption)).
% 2.01/1.62 tff(1193,plain,
% 2.01/1.62 (~ssPv3(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1127, 3, 1083, 194])).
% 2.01/1.62 tff(1194,plain,
% 2.01/1.62 (ssPv4(skf1(elem!0))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1135, 1193, 1083, 1192])).
% 2.01/1.62 tff(1195,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1196,plain,
% 2.01/1.62 (((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1197,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(monotonicity,[status(thm)],[1196])).
% 2.01/1.62 tff(1198,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(transitivity,[status(thm)],[1197, 1195])).
% 2.01/1.62 tff(1199,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(quant_inst,[status(thm)],[])).
% 2.01/1.62 tff(1200,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 2.01/1.62 tff(1201,plain,
% 2.01/1.62 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1200, 551, 14, 155])).
% 2.01/1.62 tff(1202,plain,
% 2.01/1.62 ($false),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1201, 1194, 1191, 1083, 997])).
% 2.01/1.62 tff(1203,plain,(ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | ssPv1(elem!0) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.62 tff(1204,plain,
% 2.01/1.62 (ssPv4(skf1(skf1(elem!0)))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1203, 1158, 1190, 2, 1189, 1181])).
% 2.01/1.62 tff(1205,plain,
% 2.01/1.62 (ssPv2(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[416, 1204, 1190, 1])).
% 2.01/1.62 tff(1206,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1207,plain,
% 2.01/1.62 (((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1208,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0)))))),
% 2.01/1.62 inference(monotonicity,[status(thm)],[1207])).
% 2.01/1.62 tff(1209,plain,
% 2.01/1.62 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 2.01/1.62 inference(transitivity,[status(thm)],[1208, 1206])).
% 2.01/1.62 tff(1210,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 2.01/1.62 inference(quant_inst,[status(thm)],[])).
% 2.01/1.62 tff(1211,plain,
% 2.01/1.62 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0)))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 2.01/1.62 tff(1212,plain,
% 2.01/1.62 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv2(skf1(elem!0)))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1211, 551, 16, 14])).
% 2.01/1.62 tff(1213,plain,
% 2.01/1.62 (~ssPv4(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1212, 1205, 1083, 1158])).
% 2.01/1.62 tff(1214,plain,
% 2.01/1.62 ($false),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[434, 1213, 1205, 1181, 1204])).
% 2.01/1.62 tff(1215,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.62 tff(1216,plain,
% 2.01/1.62 (ssPv3(skf1(skf1(elem!0)))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1215, 250, 2])).
% 2.01/1.62 tff(1217,plain,
% 2.01/1.62 (ssPv1(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[33, 3, 5, 2])).
% 2.01/1.62 tff(1218,plain,
% 2.01/1.62 (~ssPv4(elem!0)),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[51, 3, 5, 1217])).
% 2.01/1.62 tff(1219,plain,
% 2.01/1.62 ($false),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[87, 1218, 1217, 2, 759])).
% 2.01/1.62 tff(1220,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.62 tff(1221,plain,
% 2.01/1.62 (ssPv4(skf1(skf1(elem!0)))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1220, 5, 1216, 2])).
% 2.01/1.62 tff(1222,plain,
% 2.01/1.62 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1223,plain,
% 2.01/1.62 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1224,plain,
% 2.01/1.62 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(monotonicity,[status(thm)],[1223])).
% 2.01/1.62 tff(1225,plain,
% 2.01/1.62 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(transitivity,[status(thm)],[1224, 1222])).
% 2.01/1.62 tff(1226,plain,
% 2.01/1.62 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(quant_inst,[status(thm)],[])).
% 2.01/1.62 tff(1227,plain,
% 2.01/1.62 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 2.01/1.62 tff(1228,plain,
% 2.01/1.62 ((~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1227, 165, 155, 252])).
% 2.01/1.62 tff(1229,plain,
% 2.01/1.62 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1228, 1137, 1216, 939])).
% 2.01/1.62 tff(1230,plain,
% 2.01/1.62 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1228, 939, 1216, 1137])).
% 2.01/1.62 tff(1231,plain,
% 2.01/1.62 (ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[671, 472, 2, 1230])).
% 2.01/1.62 tff(1232,plain,
% 2.01/1.62 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1233,plain,
% 2.01/1.62 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(rewrite,[status(thm)],[])).
% 2.01/1.62 tff(1234,plain,
% 2.01/1.62 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(monotonicity,[status(thm)],[1233])).
% 2.01/1.62 tff(1235,plain,
% 2.01/1.62 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.62 inference(transitivity,[status(thm)],[1234, 1232])).
% 2.01/1.62 tff(1236,plain,
% 2.01/1.62 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.62 inference(quant_inst,[status(thm)],[])).
% 2.01/1.62 tff(1237,plain,
% 2.01/1.62 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | ssPv3(Z) | ssPv4(V) | (~ssRr(X, Y)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 2.01/1.62 tff(1238,plain,
% 2.01/1.62 (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.62 inference(unit_resolution,[status(thm)],[1237, 26, 155, 252])).
% 2.01/1.62 tff(1239,plain,
% 2.01/1.62 (ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1238, 562, 2, 472])).
% 2.01/1.63 tff(1240,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1241,plain,
% 2.01/1.63 (((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1242,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[1241])).
% 2.01/1.63 tff(1243,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(transitivity,[status(thm)],[1242, 1240])).
% 2.01/1.63 tff(1244,plain,
% 2.01/1.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.63 inference(quant_inst,[status(thm)],[])).
% 2.01/1.63 tff(1245,plain,
% 2.01/1.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 2.01/1.63 tff(1246,plain,
% 2.01/1.63 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1245, 336, 252, 382])).
% 2.01/1.63 tff(1247,plain,
% 2.01/1.63 (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1246, 562, 250, 472])).
% 2.01/1.63 tff(1248,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1249,plain,
% 2.01/1.63 (((~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1250,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[1249])).
% 2.01/1.63 tff(1251,plain,
% 2.01/1.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(transitivity,[status(thm)],[1250, 1248])).
% 2.01/1.63 tff(1252,plain,
% 2.01/1.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ((~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(quant_inst,[status(thm)],[])).
% 2.01/1.63 tff(1253,plain,
% 2.01/1.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv3(W) | ssPv4(X) | (~ssPv3(V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 2.01/1.63 tff(1254,plain,
% 2.01/1.63 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1253, 354, 252, 382])).
% 2.01/1.63 tff(1255,plain,
% 2.01/1.63 (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1254, 562, 250, 472])).
% 2.01/1.63 tff(1256,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1257,plain,
% 2.01/1.63 ((ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1258,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[1257])).
% 2.01/1.63 tff(1259,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(transitivity,[status(thm)],[1258, 1256])).
% 2.01/1.63 tff(1260,plain,
% 2.01/1.63 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.63 inference(quant_inst,[status(thm)],[])).
% 2.01/1.63 tff(1261,plain,
% 2.01/1.63 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.63 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 2.01/1.63 tff(1262,plain,
% 2.01/1.63 (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1261, 372, 252, 382])).
% 2.01/1.63 tff(1263,plain,
% 2.01/1.63 (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1262, 1255, 250, 939])).
% 2.01/1.63 tff(1264,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1265,plain,
% 2.01/1.63 ((ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1266,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[1265])).
% 2.01/1.63 tff(1267,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(transitivity,[status(thm)],[1266, 1264])).
% 2.01/1.63 tff(1268,plain,
% 2.01/1.63 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(quant_inst,[status(thm)],[])).
% 2.01/1.63 tff(1269,plain,
% 2.01/1.63 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(V) | ssPv4(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 2.01/1.63 tff(1270,plain,
% 2.01/1.63 ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1269, 165, 382, 564])).
% 2.01/1.63 tff(1271,plain,
% 2.01/1.63 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1270, 1263, 848, 1247])).
% 2.01/1.63 tff(1272,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1273,plain,
% 2.01/1.63 (((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1274,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[1273])).
% 2.01/1.63 tff(1275,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(transitivity,[status(thm)],[1274, 1272])).
% 2.01/1.63 tff(1276,plain,
% 2.01/1.63 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(quant_inst,[status(thm)],[])).
% 2.01/1.63 tff(1277,plain,
% 2.01/1.63 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 2.01/1.63 tff(1278,plain,
% 2.01/1.63 ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1277, 204, 382, 564])).
% 2.01/1.63 tff(1279,plain,
% 2.01/1.63 (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.63 inference(unit_resolution,[status(thm)],[1278, 1271, 848, 1239])).
% 2.01/1.63 tff(1280,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1281,plain,
% 2.01/1.63 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.63 inference(rewrite,[status(thm)],[])).
% 2.01/1.63 tff(1282,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.63 inference(monotonicity,[status(thm)],[1281])).
% 2.01/1.63 tff(1283,plain,
% 2.01/1.63 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.64 inference(transitivity,[status(thm)],[1282, 1280])).
% 2.01/1.64 tff(1284,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(1285,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 2.01/1.64 tff(1286,plain,
% 2.01/1.64 ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1285, 80, 382, 564])).
% 2.01/1.64 tff(1287,plain,
% 2.01/1.64 ($false),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1286, 1279, 1271, 1239, 562])).
% 2.01/1.64 tff(1288,plain,(ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.64 tff(1289,plain,
% 2.01/1.64 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1288, 472, 250, 939, 2, 1230])).
% 2.01/1.64 tff(1290,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1291,plain,
% 2.01/1.64 (((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1292,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[1291])).
% 2.01/1.64 tff(1293,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(transitivity,[status(thm)],[1292, 1290])).
% 2.01/1.64 tff(1294,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(1295,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 2.01/1.64 tff(1296,plain,
% 2.01/1.64 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1295, 318, 155, 252])).
% 2.01/1.64 tff(1297,plain,
% 2.01/1.64 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1296, 1289, 1083, 1231])).
% 2.01/1.64 tff(1298,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1299,plain,
% 2.01/1.64 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1300,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[1299])).
% 2.01/1.64 tff(1301,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(transitivity,[status(thm)],[1300, 1298])).
% 2.01/1.64 tff(1302,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(1303,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 2.01/1.64 tff(1304,plain,
% 2.01/1.64 (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1303, 280, 252, 382])).
% 2.01/1.64 tff(1305,plain,
% 2.01/1.64 (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1304, 1297, 939, 1231])).
% 2.01/1.64 tff(1306,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1307,plain,
% 2.01/1.64 ((ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1308,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[1307])).
% 2.01/1.64 tff(1309,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(transitivity,[status(thm)],[1308, 1306])).
% 2.01/1.64 tff(1310,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(1311,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | ssPv2(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 2.01/1.64 tff(1312,plain,
% 2.01/1.64 (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1311, 262, 252, 382])).
% 2.01/1.64 tff(1313,plain,
% 2.01/1.64 ($false),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1312, 1305, 1297, 939, 1137])).
% 2.01/1.64 tff(1314,plain,(ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.64 tff(1315,plain,
% 2.01/1.64 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1314, 1137, 939, 250, 2])).
% 2.01/1.64 tff(1316,plain,
% 2.01/1.64 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1056, 1315, 91, 1229])).
% 2.01/1.64 tff(1317,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1318,plain,
% 2.01/1.64 ((ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1319,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[1318])).
% 2.01/1.64 tff(1320,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(transitivity,[status(thm)],[1319, 1317])).
% 2.01/1.64 tff(1321,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(1322,plain,
% 2.01/1.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W) | ssPv2(X))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 2.01/1.64 tff(1323,plain,
% 2.01/1.64 (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1322, 1022, 252, 382])).
% 2.01/1.64 tff(1324,plain,
% 2.01/1.64 (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1323, 1316, 250, 1137])).
% 2.01/1.64 tff(1325,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1326,plain,
% 2.01/1.64 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(rewrite,[status(thm)],[])).
% 2.01/1.64 tff(1327,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.64 inference(monotonicity,[status(thm)],[1326])).
% 2.01/1.64 tff(1328,plain,
% 2.01/1.64 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.64 inference(transitivity,[status(thm)],[1327, 1325])).
% 2.01/1.64 tff(1329,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(quant_inst,[status(thm)],[])).
% 2.01/1.64 tff(1330,plain,
% 2.01/1.64 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssPv1(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 2.01/1.64 tff(1331,plain,
% 2.01/1.64 (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1330, 700, 252, 382])).
% 2.01/1.64 tff(1332,plain,
% 2.01/1.64 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.64 inference(unit_resolution,[status(thm)],[1331, 1316, 939, 1324])).
% 2.01/1.64 tff(1333,plain,
% 2.01/1.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1334,plain,
% 2.01/1.65 ((ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1335,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[1334])).
% 2.01/1.65 tff(1336,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(transitivity,[status(thm)],[1335, 1333])).
% 2.01/1.65 tff(1337,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(1338,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(X) | (~ssPv3(W)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 2.01/1.65 tff(1339,plain,
% 2.01/1.65 (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1338, 787, 252, 382])).
% 2.01/1.65 tff(1340,plain,
% 2.01/1.65 (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1339, 1316, 939, 1315])).
% 2.01/1.65 tff(1341,plain,
% 2.01/1.65 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1262, 1324, 250, 939])).
% 2.01/1.65 tff(1342,assumption,(ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), introduced(assumption)).
% 2.01/1.65 tff(1343,assumption,(ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))), introduced(assumption)).
% 2.01/1.65 tff(1344,assumption,(~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))), introduced(assumption)).
% 2.01/1.65 tff(1345,plain,
% 2.01/1.65 (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[616, 1344, 473, 560])).
% 2.01/1.65 tff(1346,plain,
% 2.01/1.65 (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[890, 1345, 848, 1343])).
% 2.01/1.65 tff(1347,plain,
% 2.01/1.65 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[626, 1345, 1343, 1346])).
% 2.01/1.65 tff(1348,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1349,plain,
% 2.01/1.65 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1350,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[1349])).
% 2.01/1.65 tff(1351,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(transitivity,[status(thm)],[1350, 1348])).
% 2.01/1.65 tff(1352,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(1353,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 2.01/1.65 tff(1354,plain,
% 2.01/1.65 ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1353, 44, 564, 619])).
% 2.01/1.65 tff(1355,plain,
% 2.01/1.65 (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1354, 1344, 1342, 1035])).
% 2.01/1.65 tff(1356,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1357,plain,
% 2.01/1.65 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1358,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[1357])).
% 2.01/1.65 tff(1359,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(transitivity,[status(thm)],[1358, 1356])).
% 2.01/1.65 tff(1360,plain,
% 2.01/1.65 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(1361,plain,
% 2.01/1.65 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 2.01/1.65 tff(1362,plain,
% 2.01/1.65 ((~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1361, 222, 564, 619])).
% 2.01/1.65 tff(1363,plain,
% 2.01/1.65 (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1362, 1355, 1343, 1342])).
% 2.01/1.65 tff(1364,plain,
% 2.01/1.65 ($false),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[634, 1363, 1347, 1343, 1342])).
% 2.01/1.65 tff(1365,plain,(ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.01/1.65 tff(1366,plain,
% 2.01/1.65 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1365, 1341, 1340, 1229, 1324, 1332, 1316])).
% 2.01/1.65 tff(1367,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1368,plain,
% 2.01/1.65 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1369,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[1368])).
% 2.01/1.65 tff(1370,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(transitivity,[status(thm)],[1369, 1367])).
% 2.01/1.65 tff(1371,plain,
% 2.01/1.65 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(1372,plain,
% 2.01/1.65 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 2.01/1.65 tff(1373,plain,
% 2.01/1.65 ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1372, 952, 382, 564])).
% 2.01/1.65 tff(1374,plain,
% 2.01/1.65 (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1373, 1366, 1316, 1229])).
% 2.01/1.65 tff(1375,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1376,plain,
% 2.01/1.65 ((ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1377,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[1376])).
% 2.01/1.65 tff(1378,plain,
% 2.01/1.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(transitivity,[status(thm)],[1377, 1375])).
% 2.01/1.65 tff(1379,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(1380,plain,
% 2.01/1.65 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 2.01/1.65 tff(1381,plain,
% 2.01/1.65 ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1380, 769, 382, 564])).
% 2.01/1.65 tff(1382,plain,
% 2.01/1.65 (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(unit_resolution,[status(thm)],[1381, 1324, 1229, 1316])).
% 2.01/1.65 tff(1383,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1384,plain,
% 2.01/1.65 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(rewrite,[status(thm)],[])).
% 2.01/1.65 tff(1385,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.65 inference(monotonicity,[status(thm)],[1384])).
% 2.01/1.65 tff(1386,plain,
% 2.01/1.65 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.65 inference(transitivity,[status(thm)],[1385, 1383])).
% 2.01/1.65 tff(1387,plain,
% 2.01/1.65 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.65 inference(quant_inst,[status(thm)],[])).
% 2.01/1.65 tff(1388,plain,
% 2.01/1.65 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 2.01/1.66 tff(1389,plain,
% 2.01/1.66 (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1388, 300, 252, 382])).
% 2.01/1.66 tff(1390,plain,
% 2.01/1.66 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1389, 1340, 939, 1316])).
% 2.01/1.66 tff(1391,plain,
% 2.01/1.66 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(1392,plain,
% 2.01/1.66 (((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(1393,plain,
% 2.01/1.66 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.66 inference(monotonicity,[status(thm)],[1392])).
% 2.01/1.66 tff(1394,plain,
% 2.01/1.66 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.66 inference(transitivity,[status(thm)],[1393, 1391])).
% 2.01/1.66 tff(1395,plain,
% 2.01/1.66 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.66 inference(quant_inst,[status(thm)],[])).
% 2.01/1.66 tff(1396,plain,
% 2.01/1.66 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.66 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 2.01/1.66 tff(1397,plain,
% 2.01/1.66 ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1396, 909, 382, 564])).
% 2.01/1.66 tff(1398,plain,
% 2.01/1.66 (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1397, 1366, 1390, 1341])).
% 2.01/1.66 tff(1399,plain,
% 2.01/1.66 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.66 inference(quant_inst,[status(thm)],[])).
% 2.01/1.66 tff(1400,plain,
% 2.01/1.66 (ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.01/1.66 inference(unit_resolution,[status(thm)],[1399, 12])).
% 2.01/1.66 tff(1401,plain,
% 2.01/1.66 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(1402,plain,
% 2.01/1.66 (((~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.01/1.66 inference(rewrite,[status(thm)],[])).
% 2.01/1.66 tff(1403,plain,
% 2.01/1.66 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.01/1.66 inference(monotonicity,[status(thm)],[1402])).
% 2.01/1.66 tff(1404,plain,
% 2.01/1.66 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(transitivity,[status(thm)],[1403, 1401])).
% 2.10/1.66 tff(1405,plain,
% 2.10/1.66 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.66 inference(quant_inst,[status(thm)],[])).
% 2.10/1.66 tff(1406,plain,
% 2.10/1.66 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 2.10/1.66 tff(1407,plain,
% 2.10/1.66 ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1406, 970, 619, 1400])).
% 2.10/1.66 tff(1408,plain,
% 2.10/1.66 (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1407, 1398, 1382, 1374])).
% 2.10/1.66 tff(1409,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(rewrite,[status(thm)],[])).
% 2.10/1.66 tff(1410,plain,
% 2.10/1.66 ((ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(rewrite,[status(thm)],[])).
% 2.10/1.66 tff(1411,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.66 inference(monotonicity,[status(thm)],[1410])).
% 2.10/1.66 tff(1412,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(transitivity,[status(thm)],[1411, 1409])).
% 2.10/1.66 tff(1413,plain,
% 2.10/1.66 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(quant_inst,[status(thm)],[])).
% 2.10/1.66 tff(1414,plain,
% 2.10/1.66 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 2.10/1.66 tff(1415,plain,
% 2.10/1.66 ((~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1414, 141, 619, 1400])).
% 2.10/1.66 tff(1416,plain,
% 2.10/1.66 (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1415, 1408, 1382, 1374])).
% 2.10/1.66 tff(1417,plain,
% 2.10/1.66 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(rewrite,[status(thm)],[])).
% 2.10/1.66 tff(1418,plain,
% 2.10/1.66 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(rewrite,[status(thm)],[])).
% 2.10/1.66 tff(1419,plain,
% 2.10/1.66 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(monotonicity,[status(thm)],[1418])).
% 2.10/1.66 tff(1420,plain,
% 2.10/1.66 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(transitivity,[status(thm)],[1419, 1417])).
% 2.10/1.66 tff(1421,plain,
% 2.10/1.66 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(quant_inst,[status(thm)],[])).
% 2.10/1.66 tff(1422,plain,
% 2.10/1.66 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.66 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 2.10/1.66 tff(1423,plain,
% 2.10/1.66 (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1422, 44, 619, 1400])).
% 2.10/1.66 tff(1424,plain,
% 2.10/1.66 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1423, 1416, 1382, 1374])).
% 2.10/1.66 tff(1425,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.66 inference(rewrite,[status(thm)],[])).
% 2.10/1.66 tff(1426,plain,
% 2.10/1.66 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.66 inference(rewrite,[status(thm)],[])).
% 2.10/1.66 tff(1427,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))))),
% 2.10/1.66 inference(monotonicity,[status(thm)],[1426])).
% 2.10/1.66 tff(1428,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.66 inference(transitivity,[status(thm)],[1427, 1425])).
% 2.10/1.66 tff(1429,plain,
% 2.10/1.66 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(quant_inst,[status(thm)],[])).
% 2.10/1.66 tff(1430,plain,
% 2.10/1.66 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 2.10/1.66 tff(1431,plain,
% 2.10/1.66 (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1430, 952, 619, 1400])).
% 2.10/1.66 tff(1432,plain,
% 2.10/1.66 (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.66 inference(unit_resolution,[status(thm)],[1431, 1416, 1366, 1398])).
% 2.10/1.66 tff(1433,plain,
% 2.10/1.66 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1434,plain,
% 2.10/1.67 ((ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))) <=> (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1435,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.67 inference(monotonicity,[status(thm)],[1434])).
% 2.10/1.67 tff(1436,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.67 inference(transitivity,[status(thm)],[1435, 1433])).
% 2.10/1.67 tff(1437,plain,
% 2.10/1.67 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.67 inference(quant_inst,[status(thm)],[])).
% 2.10/1.67 tff(1438,plain,
% 2.10/1.67 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 2.10/1.67 tff(1439,plain,
% 2.10/1.67 (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1438, 62, 619, 1400])).
% 2.10/1.67 tff(1440,plain,
% 2.10/1.67 (ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1439, 1432, 1382, 1408])).
% 2.10/1.67 tff(1441,plain,
% 2.10/1.67 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))),
% 2.10/1.67 inference(bind,[status(th)],[])).
% 2.10/1.67 tff(1442,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(quant_intro,[status(thm)],[1441])).
% 2.10/1.67 tff(1443,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1444,plain,
% 2.10/1.67 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> (((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(Z))))), rewrite((((~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv3(Z))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) <=> (((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) <=> ((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv4(Y)) <=> (((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(Y)))), rewrite((((~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))))),
% 2.10/1.67 inference(bind,[status(th)],[])).
% 2.10/1.67 tff(1445,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv4(Y)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(quant_intro,[status(thm)],[1444])).
% 2.10/1.67 tff(1446,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv3(Z))) | (~ssPv1(W))) | ssPv4(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 2.10/1.67 tff(1447,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 2.10/1.67 tff(1448,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1447, 1443])).
% 2.10/1.67 tff(1449,plain,(
% 2.10/1.67 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(skolemize,[status(sab)],[1448])).
% 2.10/1.67 tff(1450,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1449, 1442])).
% 2.10/1.67 tff(1451,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1452,plain,
% 2.10/1.67 ((ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1453,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))))),
% 2.10/1.67 inference(monotonicity,[status(thm)],[1452])).
% 2.10/1.67 tff(1454,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))))),
% 2.10/1.67 inference(transitivity,[status(thm)],[1453, 1451])).
% 2.10/1.67 tff(1455,plain,
% 2.10/1.67 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.67 inference(quant_inst,[status(thm)],[])).
% 2.10/1.67 tff(1456,plain,
% 2.10/1.67 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))), skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 2.10/1.67 tff(1457,plain,
% 2.10/1.67 (ssPv4(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1456, 1450, 619, 1400])).
% 2.10/1.67 tff(1458,plain,
% 2.10/1.67 ($false),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1457, 1440, 1424, 1382, 1416])).
% 2.10/1.67 tff(1459,plain,(ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.67 tff(1460,plain,
% 2.10/1.67 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1459, 939, 250, 1221, 2])).
% 2.10/1.67 tff(1461,plain,
% 2.10/1.67 (~ssPv2(skf1(elem!0))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1175, 1460, 5, 1221])).
% 2.10/1.67 tff(1462,plain,
% 2.10/1.67 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W)) <=> (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W)))),
% 2.10/1.67 inference(bind,[status(th)],[])).
% 2.10/1.67 tff(1463,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(quant_intro,[status(thm)],[1462])).
% 2.10/1.67 tff(1464,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1465,plain,
% 2.10/1.67 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) <=> ((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) <=> (((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(Z))))), rewrite((((~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv2(Z))) <=> ((~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) <=> ((~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) | ssPv1(Y)) <=> (((~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(Y)))), rewrite((((~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) | ssPv1(Y)) <=> (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) | ssPv1(Y)) | ssPv2(W)) <=> ((ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(W)))), rewrite(((ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv2(W)) <=> (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))), ((((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) | ssPv1(Y)) | ssPv2(W)) <=> (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))))),
% 2.10/1.67 inference(bind,[status(th)],[])).
% 2.10/1.67 tff(1466,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) | ssPv1(Y)) | ssPv2(W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(quant_intro,[status(thm)],[1465])).
% 2.10/1.67 tff(1467,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssRr(W, Z))) | (~ssPv2(Z))) | ssPv1(Y)) | ssPv2(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 2.10/1.67 tff(1468,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 2.10/1.67 tff(1469,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1468, 1464])).
% 2.10/1.67 tff(1470,plain,(
% 2.10/1.67 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(skolemize,[status(sab)],[1469])).
% 2.10/1.67 tff(1471,plain,
% 2.10/1.67 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1470, 1463])).
% 2.10/1.67 tff(1472,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1473,plain,
% 2.10/1.67 ((ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1474,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.67 inference(monotonicity,[status(thm)],[1473])).
% 2.10/1.67 tff(1475,plain,
% 2.10/1.67 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.67 inference(transitivity,[status(thm)],[1474, 1472])).
% 2.10/1.67 tff(1476,plain,
% 2.10/1.67 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(elem!0)))),
% 2.10/1.67 inference(quant_inst,[status(thm)],[])).
% 2.10/1.67 tff(1477,plain,
% 2.10/1.67 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.67 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 2.10/1.67 tff(1478,plain,
% 2.10/1.67 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1477, 1471, 14, 155])).
% 2.10/1.67 tff(1479,plain,
% 2.10/1.67 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1478, 1461, 1083, 250])).
% 2.10/1.67 tff(1480,plain,
% 2.10/1.67 (~ssPv1(skf1(elem!0))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[506, 1479, 939, 250])).
% 2.10/1.67 tff(1481,plain,
% 2.10/1.67 ($false),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[734, 1480, 1479, 1461, 1460])).
% 2.10/1.67 tff(1482,plain,(ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.67 tff(1483,plain,
% 2.10/1.67 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.10/1.67 inference(unit_resolution,[status(thm)],[1482, 5, 250, 2])).
% 2.10/1.67 tff(1484,plain,
% 2.10/1.67 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1485,plain,
% 2.10/1.67 (((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.67 inference(rewrite,[status(thm)],[])).
% 2.10/1.67 tff(1486,plain,
% 2.10/1.67 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.67 inference(monotonicity,[status(thm)],[1485])).
% 2.10/1.67 tff(1487,plain,
% 2.10/1.67 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(transitivity,[status(thm)],[1486, 1484])).
% 2.10/1.68 tff(1488,plain,
% 2.10/1.68 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(quant_inst,[status(thm)],[])).
% 2.10/1.68 tff(1489,plain,
% 2.10/1.68 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 2.10/1.68 tff(1490,plain,
% 2.10/1.68 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1489, 551, 155, 252])).
% 2.10/1.68 tff(1491,plain,
% 2.10/1.68 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1490, 1483, 1083, 1221])).
% 2.10/1.68 tff(1492,plain,
% 2.10/1.68 (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1323, 1137, 250, 1491])).
% 2.10/1.68 tff(1493,plain,
% 2.10/1.68 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1494,plain,
% 2.10/1.68 (((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1495,plain,
% 2.10/1.68 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.10/1.68 inference(monotonicity,[status(thm)],[1494])).
% 2.10/1.68 tff(1496,plain,
% 2.10/1.68 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.68 inference(transitivity,[status(thm)],[1495, 1493])).
% 2.10/1.68 tff(1497,plain,
% 2.10/1.68 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(quant_inst,[status(thm)],[])).
% 2.10/1.68 tff(1498,plain,
% 2.10/1.68 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 2.10/1.68 tff(1499,plain,
% 2.10/1.68 (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1498, 427, 252, 382])).
% 2.10/1.68 tff(1500,plain,
% 2.10/1.68 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1499, 1492, 1483, 1137])).
% 2.10/1.68 tff(1501,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1502,plain,
% 2.10/1.68 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1503,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(monotonicity,[status(thm)],[1502])).
% 2.10/1.68 tff(1504,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(transitivity,[status(thm)],[1503, 1501])).
% 2.10/1.68 tff(1505,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(quant_inst,[status(thm)],[])).
% 2.10/1.68 tff(1506,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | ssPv3(V) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 2.10/1.68 tff(1507,plain,
% 2.10/1.68 (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1506, 101, 155, 252])).
% 2.10/1.68 tff(1508,plain,
% 2.10/1.68 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1507, 1500, 2, 1491])).
% 2.10/1.68 tff(1509,plain,
% 2.10/1.68 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)))),
% 2.10/1.68 inference(bind,[status(th)],[])).
% 2.10/1.68 tff(1510,plain,
% 2.10/1.68 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(quant_intro,[status(thm)],[1509])).
% 2.10/1.68 tff(1511,plain,
% 2.10/1.68 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1512,plain,
% 2.10/1.68 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) <=> ((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv3(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv3(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) <=> (((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(Y)))), rewrite((((~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) <=> (ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) | ssPv3(W)) <=> ((ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(W)))), rewrite(((ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | ssPv3(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) | ssPv3(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) | ssPv3(W)) | ssPv4(W)) <=> ((ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)) | ssPv4(W)))), rewrite(((ssPv4(Y) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W)) | ssPv4(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))), (((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) | ssPv3(W)) | ssPv4(W)) <=> (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))))),
% 2.10/1.68 inference(bind,[status(th)],[])).
% 2.10/1.68 tff(1513,plain,
% 2.10/1.68 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) | ssPv3(W)) | ssPv4(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(quant_intro,[status(thm)],[1512])).
% 2.10/1.68 tff(1514,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | ssPv4(Y)) | ssPv3(W)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause24')).
% 2.10/1.68 tff(1515,plain,
% 2.10/1.68 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 2.10/1.68 tff(1516,plain,
% 2.10/1.68 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1515, 1511])).
% 2.10/1.68 tff(1517,plain,(
% 2.10/1.68 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(skolemize,[status(sab)],[1516])).
% 2.10/1.68 tff(1518,plain,
% 2.10/1.68 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1517, 1510])).
% 2.10/1.68 tff(1519,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1520,plain,
% 2.10/1.68 ((ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0))) <=> (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1521,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(monotonicity,[status(thm)],[1520])).
% 2.10/1.68 tff(1522,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(transitivity,[status(thm)],[1521, 1519])).
% 2.10/1.68 tff(1523,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(elem!0)))),
% 2.10/1.68 inference(quant_inst,[status(thm)],[])).
% 2.10/1.68 tff(1524,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 2.10/1.68 tff(1525,plain,
% 2.10/1.68 (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1524, 1518, 14, 155])).
% 2.10/1.68 tff(1526,plain,
% 2.10/1.68 (ssPv4(skf1(elem!0))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1525, 1508, 5, 1137])).
% 2.10/1.68 tff(1527,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1528,plain,
% 2.10/1.68 (((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1529,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.68 inference(monotonicity,[status(thm)],[1528])).
% 2.10/1.68 tff(1530,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(transitivity,[status(thm)],[1529, 1527])).
% 2.10/1.68 tff(1531,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(elem!0))))),
% 2.10/1.68 inference(quant_inst,[status(thm)],[])).
% 2.10/1.68 tff(1532,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 2.10/1.68 tff(1533,plain,
% 2.10/1.68 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1532, 909, 14, 155])).
% 2.10/1.68 tff(1534,plain,
% 2.10/1.68 ($false),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1533, 1526, 1508, 1216, 1483])).
% 2.10/1.68 tff(1535,plain,(ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.68 tff(1536,plain,
% 2.10/1.68 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1535, 5, 2, 250])).
% 2.10/1.68 tff(1537,plain,
% 2.10/1.68 (~ssPv2(skf1(elem!0))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1175, 1536, 5, 1221])).
% 2.10/1.68 tff(1538,plain,
% 2.10/1.68 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1478, 1537, 1083, 250])).
% 2.10/1.68 tff(1539,plain,
% 2.10/1.68 (ssPv1(skf1(elem!0))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[734, 1538, 1537, 1536])).
% 2.10/1.68 tff(1540,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1541,plain,
% 2.10/1.68 ((ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1542,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.68 inference(monotonicity,[status(thm)],[1541])).
% 2.10/1.68 tff(1543,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.68 inference(transitivity,[status(thm)],[1542, 1540])).
% 2.10/1.68 tff(1544,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))),
% 2.10/1.68 inference(quant_inst,[status(thm)],[])).
% 2.10/1.68 tff(1545,plain,
% 2.10/1.68 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.10/1.68 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 2.10/1.68 tff(1546,plain,
% 2.10/1.68 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1545, 1112, 14, 155])).
% 2.10/1.68 tff(1547,plain,
% 2.10/1.68 ($false),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1546, 1539, 1538, 1216, 1483])).
% 2.10/1.68 tff(1548,plain,(ssPv3(skf1(elem!0)) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.68 tff(1549,plain,
% 2.10/1.68 (ssPv3(skf1(elem!0))),
% 2.10/1.68 inference(unit_resolution,[status(thm)],[1548, 250, 2])).
% 2.10/1.68 tff(1550,assumption,(ssPv2(skf1(skf1(elem!0)))), introduced(assumption)).
% 2.10/1.68 tff(1551,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1552,plain,
% 2.10/1.68 (((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0))))),
% 2.10/1.68 inference(rewrite,[status(thm)],[])).
% 2.10/1.68 tff(1553,plain,
% 2.10/1.68 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0)))))),
% 2.10/1.69 inference(monotonicity,[status(thm)],[1552])).
% 2.10/1.69 tff(1554,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0))))),
% 2.10/1.69 inference(transitivity,[status(thm)],[1553, 1551])).
% 2.10/1.69 tff(1555,plain,
% 2.10/1.69 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(elem!0)))),
% 2.10/1.69 inference(quant_inst,[status(thm)],[])).
% 2.10/1.69 tff(1556,plain,
% 2.10/1.69 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((~ssPv2(Y)) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0)))),
% 2.10/1.69 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 2.10/1.69 tff(1557,plain,
% 2.10/1.69 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | (~ssPv3(skf1(elem!0)))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1556, 909, 16, 14])).
% 2.10/1.69 tff(1558,plain,
% 2.10/1.69 (~ssPv4(elem!0)),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1557, 194, 1550, 759])).
% 2.10/1.69 tff(1559,plain,
% 2.10/1.69 (~ssPv3(elem!0)),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1127, 3, 1550, 194])).
% 2.10/1.69 tff(1560,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1561,plain,
% 2.10/1.69 ((ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(elem!0)) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1562,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0)))),
% 2.10/1.69 inference(monotonicity,[status(thm)],[1561])).
% 2.10/1.69 tff(1563,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0))),
% 2.10/1.69 inference(transitivity,[status(thm)],[1562, 1560])).
% 2.10/1.69 tff(1564,plain,
% 2.10/1.69 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(elem!0))),
% 2.10/1.69 inference(quant_inst,[status(thm)],[])).
% 2.10/1.69 tff(1565,plain,
% 2.10/1.69 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0)),
% 2.10/1.69 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 2.10/1.69 tff(1566,plain,
% 2.10/1.69 ((~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0)),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1565, 1518, 16, 14])).
% 2.10/1.69 tff(1567,plain,
% 2.10/1.69 ($false),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1566, 1559, 3, 759, 1558])).
% 2.10/1.69 tff(1568,plain,(ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.69 tff(1569,plain,
% 2.10/1.69 (ssPv4(skf1(skf1(elem!0)))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1568, 1216, 1083, 1549])).
% 2.10/1.69 tff(1570,plain,
% 2.10/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1571,plain,
% 2.10/1.69 ((ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1572,plain,
% 2.10/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.69 inference(monotonicity,[status(thm)],[1571])).
% 2.10/1.69 tff(1573,plain,
% 2.10/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.69 inference(transitivity,[status(thm)],[1572, 1570])).
% 2.10/1.69 tff(1574,plain,
% 2.10/1.69 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 2.10/1.69 inference(quant_inst,[status(thm)],[])).
% 2.10/1.69 tff(1575,plain,
% 2.10/1.69 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(V) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.10/1.69 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 2.10/1.69 tff(1576,plain,
% 2.10/1.69 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1575, 769, 14, 155])).
% 2.10/1.69 tff(1577,plain,
% 2.10/1.69 (ssPv2(skf1(elem!0))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1576, 1569, 250, 1549])).
% 2.10/1.69 tff(1578,plain,
% 2.10/1.69 (~ssPv4(elem!0)),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1557, 1549, 1083, 1216])).
% 2.10/1.69 tff(1579,plain,
% 2.10/1.69 (~ssPv2(elem!0)),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[434, 1569, 1549, 1578])).
% 2.10/1.69 tff(1580,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1581,plain,
% 2.10/1.69 ((ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(elem!0)) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1582,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0)))))),
% 2.10/1.69 inference(monotonicity,[status(thm)],[1581])).
% 2.10/1.69 tff(1583,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))))),
% 2.10/1.69 inference(transitivity,[status(thm)],[1582, 1580])).
% 2.10/1.69 tff(1584,plain,
% 2.10/1.69 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(elem!0))),
% 2.10/1.69 inference(quant_inst,[status(thm)],[])).
% 2.10/1.69 tff(1585,plain,
% 2.10/1.69 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0)))),
% 2.10/1.69 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 2.10/1.69 tff(1586,plain,
% 2.10/1.69 ((~ssPv3(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0)))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1585, 1471, 16, 14])).
% 2.10/1.69 tff(1587,plain,
% 2.10/1.69 ($false),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1586, 1579, 1577, 2, 1216])).
% 2.10/1.69 tff(1588,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.69 tff(1589,plain,
% 2.10/1.69 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1588, 2])).
% 2.10/1.69 tff(1590,plain,
% 2.10/1.69 (ssPv2(skf1(elem!0))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[747, 1136, 2, 1589])).
% 2.10/1.69 tff(1591,plain,
% 2.10/1.69 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1201, 1590, 1083, 1136])).
% 2.10/1.69 tff(1592,plain,
% 2.10/1.69 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1203, 1590, 1120, 2, 3, 1102])).
% 2.10/1.69 tff(1593,plain,
% 2.10/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1594,plain,
% 2.10/1.69 (((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1595,plain,
% 2.10/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.10/1.69 inference(monotonicity,[status(thm)],[1594])).
% 2.10/1.69 tff(1596,plain,
% 2.10/1.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.10/1.69 inference(transitivity,[status(thm)],[1595, 1593])).
% 2.10/1.69 tff(1597,plain,
% 2.10/1.69 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.69 inference(quant_inst,[status(thm)],[])).
% 2.10/1.69 tff(1598,plain,
% 2.10/1.69 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.69 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 2.10/1.69 tff(1599,plain,
% 2.10/1.69 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1598, 427, 155, 252])).
% 2.10/1.69 tff(1600,plain,
% 2.10/1.69 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1599, 1592, 1083, 3])).
% 2.10/1.69 tff(1601,plain,
% 2.10/1.69 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1188, 1592, 1083, 1])).
% 2.10/1.69 tff(1602,plain,
% 2.10/1.69 (~ssPv1(skf1(elem!0))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[237, 1601, 1, 1136])).
% 2.10/1.69 tff(1603,plain,
% 2.10/1.69 ($false),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[498, 1602, 1600, 1, 1591])).
% 2.10/1.69 tff(1604,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.69 tff(1605,plain,
% 2.10/1.69 (ssPv3(skf1(skf1(elem!0)))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1604, 3, 2])).
% 2.10/1.69 tff(1606,plain,
% 2.10/1.69 (~ssPv3(skf1(elem!0))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1568, 1605, 1083, 3])).
% 2.10/1.69 tff(1607,plain,
% 2.10/1.69 ($false),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1220, 1606, 1605, 3, 2])).
% 2.10/1.69 tff(1608,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.69 tff(1609,plain,
% 2.10/1.69 (ssPv4(skf1(skf1(elem!0)))),
% 2.10/1.69 inference(unit_resolution,[status(thm)],[1608, 2])).
% 2.10/1.69 tff(1610,assumption,(~ssPv2(skf1(elem!0))), introduced(assumption)).
% 2.10/1.69 tff(1611,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1612,plain,
% 2.10/1.69 ((ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.10/1.69 inference(rewrite,[status(thm)],[])).
% 2.10/1.69 tff(1613,plain,
% 2.10/1.69 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.69 inference(monotonicity,[status(thm)],[1612])).
% 2.14/1.69 tff(1614,plain,
% 2.14/1.69 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.69 inference(transitivity,[status(thm)],[1613, 1611])).
% 2.14/1.69 tff(1615,plain,
% 2.14/1.69 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 2.14/1.69 inference(quant_inst,[status(thm)],[])).
% 2.14/1.69 tff(1616,plain,
% 2.14/1.69 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.69 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 2.14/1.69 tff(1617,plain,
% 2.14/1.69 ((~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[1616, 280, 14, 155])).
% 2.14/1.69 tff(1618,plain,
% 2.14/1.69 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[1617, 1610, 2, 1083])).
% 2.14/1.69 tff(1619,plain,
% 2.14/1.69 (~ssPv4(skf1(elem!0))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[747, 1610, 2, 1589])).
% 2.14/1.69 tff(1620,plain,
% 2.14/1.69 ($false),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[1009, 1619, 1618, 2, 1610])).
% 2.14/1.69 tff(1621,plain,(ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.69 tff(1622,plain,
% 2.14/1.69 (ssPv2(skf1(elem!0))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[1621, 2])).
% 2.14/1.69 tff(1623,plain,
% 2.14/1.69 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[1147, 1, 1083, 1609])).
% 2.14/1.69 tff(1624,plain,
% 2.14/1.69 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[361, 1623, 2, 1])).
% 2.14/1.69 tff(1625,plain,
% 2.14/1.69 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[325, 1624, 1589, 1622])).
% 2.14/1.69 tff(1626,plain,
% 2.14/1.69 (ssPv3(skf1(elem!0))),
% 2.14/1.69 inference(unit_resolution,[status(thm)],[1175, 1624, 1622, 1609])).
% 2.14/1.69 tff(1627,plain,
% 2.14/1.69 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) <=> (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))))),
% 2.14/1.69 inference(bind,[status(th)],[])).
% 2.14/1.69 tff(1628,plain,
% 2.14/1.69 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.69 inference(quant_intro,[status(thm)],[1627])).
% 2.14/1.69 tff(1629,plain,
% 2.14/1.69 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1630,plain,
% 2.14/1.70 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(X))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv4(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))) | (~ssPv3(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(X))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv2(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv2(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(W)) <=> ((ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv4(W)))), rewrite(((ssPv2(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X))) | ssPv4(W)) <=> (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(W)) <=> (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))))),
% 2.14/1.70 inference(bind,[status(th)],[])).
% 2.14/1.70 tff(1631,plain,
% 2.14/1.70 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.70 inference(quant_intro,[status(thm)],[1630])).
% 2.14/1.70 tff(1632,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv4(X))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause12')).
% 2.14/1.70 tff(1633,plain,
% 2.14/1.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1632, 1631])).
% 2.14/1.70 tff(1634,plain,
% 2.14/1.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1633, 1629])).
% 2.14/1.70 tff(1635,plain,(
% 2.14/1.70 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.70 inference(skolemize,[status(sab)],[1634])).
% 2.14/1.70 tff(1636,plain,
% 2.14/1.70 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1635, 1628])).
% 2.14/1.70 tff(1637,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1638,plain,
% 2.14/1.70 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1639,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.70 inference(monotonicity,[status(thm)],[1638])).
% 2.14/1.70 tff(1640,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(transitivity,[status(thm)],[1639, 1637])).
% 2.14/1.70 tff(1641,plain,
% 2.14/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(quant_inst,[status(thm)],[])).
% 2.14/1.70 tff(1642,plain,
% 2.14/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 2.14/1.70 tff(1643,plain,
% 2.14/1.70 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1642, 1636, 14, 155])).
% 2.14/1.70 tff(1644,plain,
% 2.14/1.70 (ssPv4(skf1(elem!0))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1643, 1625, 1626, 1609])).
% 2.14/1.70 tff(1645,plain,
% 2.14/1.70 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1646,plain,
% 2.14/1.70 ((ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1647,plain,
% 2.14/1.70 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.70 inference(monotonicity,[status(thm)],[1646])).
% 2.14/1.70 tff(1648,plain,
% 2.14/1.70 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(transitivity,[status(thm)],[1647, 1645])).
% 2.14/1.70 tff(1649,plain,
% 2.14/1.70 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))))),
% 2.14/1.70 inference(quant_inst,[status(thm)],[])).
% 2.14/1.70 tff(1650,plain,
% 2.14/1.70 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 2.14/1.70 tff(1651,plain,
% 2.14/1.70 ((~ssPv4(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1650, 141, 14, 155])).
% 2.14/1.70 tff(1652,plain,
% 2.14/1.70 (~ssPv1(skf1(elem!0))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1651, 1644, 1624, 1625])).
% 2.14/1.70 tff(1653,plain,
% 2.14/1.70 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[247, 1652, 1, 1625])).
% 2.14/1.70 tff(1654,plain,
% 2.14/1.70 ($false),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[498, 1653, 1652, 1, 1625])).
% 2.14/1.70 tff(1655,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.70 tff(1656,plain,
% 2.14/1.70 (ssPv3(skf1(skf1(elem!0)))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1655, 2])).
% 2.14/1.70 tff(1657,plain,
% 2.14/1.70 (ssPv2(elem!0)),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1586, 1656, 2, 1622])).
% 2.14/1.70 tff(1658,plain,
% 2.14/1.70 (~ssPv4(elem!0)),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1212, 1657, 1083, 1622])).
% 2.14/1.70 tff(1659,plain,
% 2.14/1.70 (~ssPv3(skf1(elem!0))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[434, 1658, 1609, 1657])).
% 2.14/1.70 tff(1660,plain,
% 2.14/1.70 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1175, 1659, 1622, 1609])).
% 2.14/1.70 tff(1661,plain,
% 2.14/1.70 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1662,plain,
% 2.14/1.70 ((ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1663,plain,
% 2.14/1.70 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.70 inference(monotonicity,[status(thm)],[1662])).
% 2.14/1.70 tff(1664,plain,
% 2.14/1.70 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(transitivity,[status(thm)],[1663, 1661])).
% 2.14/1.70 tff(1665,plain,
% 2.14/1.70 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))),
% 2.14/1.70 inference(quant_inst,[status(thm)],[])).
% 2.14/1.70 tff(1666,plain,
% 2.14/1.70 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 2.14/1.70 tff(1667,plain,
% 2.14/1.70 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1666, 1450, 14, 155])).
% 2.14/1.70 tff(1668,plain,
% 2.14/1.70 (~ssPv1(skf1(elem!0))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1667, 1660, 1589, 1656])).
% 2.14/1.70 tff(1669,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1670,plain,
% 2.14/1.70 ((ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1671,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.70 inference(monotonicity,[status(thm)],[1670])).
% 2.14/1.70 tff(1672,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(transitivity,[status(thm)],[1671, 1669])).
% 2.14/1.70 tff(1673,plain,
% 2.14/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(elem!0)))),
% 2.14/1.70 inference(quant_inst,[status(thm)],[])).
% 2.14/1.70 tff(1674,plain,
% 2.14/1.70 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv1(W))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 2.14/1.70 tff(1675,plain,
% 2.14/1.70 (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1674, 825, 14, 155])).
% 2.14/1.70 tff(1676,plain,
% 2.14/1.70 (ssPv4(skf1(elem!0))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1675, 939, 2, 1668])).
% 2.14/1.70 tff(1677,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1678,plain,
% 2.14/1.70 ((ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1679,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(monotonicity,[status(thm)],[1678])).
% 2.14/1.70 tff(1680,plain,
% 2.14/1.70 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(transitivity,[status(thm)],[1679, 1677])).
% 2.14/1.70 tff(1681,plain,
% 2.14/1.70 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(quant_inst,[status(thm)],[])).
% 2.14/1.70 tff(1682,plain,
% 2.14/1.70 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 2.14/1.70 tff(1683,plain,
% 2.14/1.70 (ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1682, 445, 14, 155])).
% 2.14/1.70 tff(1684,plain,
% 2.14/1.70 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1683, 1676, 1622, 1659])).
% 2.14/1.70 tff(1685,plain,
% 2.14/1.70 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1228, 939, 1656, 1660])).
% 2.14/1.70 tff(1686,plain,
% 2.14/1.70 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1056, 1684, 1609, 1685])).
% 2.14/1.70 tff(1687,plain,
% 2.14/1.70 (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.70 inference(unit_resolution,[status(thm)],[1339, 1686, 939, 1684])).
% 2.14/1.70 tff(1688,plain,
% 2.14/1.70 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl((ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))),
% 2.14/1.70 inference(bind,[status(th)],[])).
% 2.14/1.70 tff(1689,plain,
% 2.14/1.70 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.70 inference(quant_intro,[status(thm)],[1688])).
% 2.14/1.70 tff(1690,plain,
% 2.14/1.70 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.70 inference(rewrite,[status(thm)],[])).
% 2.14/1.70 tff(1691,plain,
% 2.14/1.70 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) <=> ((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> (((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))))), rewrite((((~ssPv1(V)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(X, Y))) <=> ((~ssPv1(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) <=> ((~ssPv1(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> (((~ssPv1(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))))), rewrite((((~ssPv1(V)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssRr(W, X))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> (((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) <=> ((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv3(Y)) <=> (((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv3(Y)))), rewrite((((~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv3(Y)) <=> (ssPv3(Y) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))))), (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv3(Y)) | ssPv4(W)) <=> ((ssPv3(Y) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(W)))), rewrite(((ssPv3(Y) | (~ssPv1(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(W)) <=> (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv3(Y)) | ssPv4(W)) <=> (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))))),
% 2.14/1.70 inference(bind,[status(th)],[])).
% 2.14/1.70 tff(1692,plain,
% 2.14/1.70 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv3(Y)) | ssPv4(W)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.70 inference(quant_intro,[status(thm)],[1691])).
% 2.14/1.70 tff(1693,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(W, U))) | (~ssRr(X, Y))) | (~ssRr(W, X))) | (~ssPv1(W))) | ssPv3(Y)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 2.14/1.70 tff(1694,plain,
% 2.14/1.70 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 2.14/1.70 tff(1695,plain,
% 2.14/1.70 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.70 inference(modus_ponens,[status(thm)],[1694, 1690])).
% 2.14/1.70 tff(1696,plain,(
% 2.14/1.70 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.71 inference(skolemize,[status(sab)],[1695])).
% 2.14/1.71 tff(1697,plain,
% 2.14/1.71 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1696, 1689])).
% 2.14/1.71 tff(1698,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1699,plain,
% 2.14/1.71 ((ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1700,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.71 inference(monotonicity,[status(thm)],[1699])).
% 2.14/1.71 tff(1701,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(transitivity,[status(thm)],[1700, 1698])).
% 2.14/1.71 tff(1702,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(quant_inst,[status(thm)],[])).
% 2.14/1.71 tff(1703,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 2.14/1.71 tff(1704,plain,
% 2.14/1.71 (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1703, 1697, 252, 382])).
% 2.14/1.71 tff(1705,plain,
% 2.14/1.71 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1704, 1687, 1589, 1660])).
% 2.14/1.71 tff(1706,plain,
% 2.14/1.71 ($false),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[397, 1705, 1687, 1589, 1684])).
% 2.14/1.71 tff(1707,plain,(ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.71 tff(1708,plain,
% 2.14/1.71 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1707, 2])).
% 2.14/1.71 tff(1709,plain,
% 2.14/1.71 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1490, 1708, 1083, 1609])).
% 2.14/1.71 tff(1710,plain,
% 2.14/1.71 (~ssPv4(skf1(elem!0))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1201, 1708, 1083, 1622])).
% 2.14/1.71 tff(1711,plain,
% 2.14/1.71 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1525, 1710, 1659, 1660])).
% 2.14/1.71 tff(1712,plain,
% 2.14/1.71 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1507, 1711, 2, 1709])).
% 2.14/1.71 tff(1713,plain,
% 2.14/1.71 ($false),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[671, 1712, 1711, 2, 1709])).
% 2.14/1.71 tff(1714,plain,(ssPv1(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.71 tff(1715,plain,
% 2.14/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1716,plain,
% 2.14/1.71 ((ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1717,plain,
% 2.14/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.71 inference(monotonicity,[status(thm)],[1716])).
% 2.14/1.71 tff(1718,plain,
% 2.14/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(transitivity,[status(thm)],[1717, 1715])).
% 2.14/1.71 tff(1719,plain,
% 2.14/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(quant_inst,[status(thm)],[])).
% 2.14/1.71 tff(1720,plain,
% 2.14/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(W) | ssPv1(X) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 2.14/1.71 tff(1721,plain,
% 2.14/1.71 (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1720, 185, 155, 252])).
% 2.14/1.71 tff(1722,plain,
% 2.14/1.71 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1721, 250, 1714, 3])).
% 2.14/1.71 tff(1723,plain,
% 2.14/1.71 ($false),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[269, 1722, 250, 4, 3])).
% 2.14/1.71 tff(1724,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.71 tff(1725,plain,
% 2.14/1.71 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1724, 3, 4])).
% 2.14/1.71 tff(1726,plain,
% 2.14/1.71 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) <=> (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))))),
% 2.14/1.71 inference(bind,[status(th)],[])).
% 2.14/1.71 tff(1727,plain,
% 2.14/1.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(quant_intro,[status(thm)],[1726])).
% 2.14/1.71 tff(1728,plain,
% 2.14/1.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1729,plain,
% 2.14/1.71 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V))) | (~ssPv1(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X)))), (((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X))))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X))) | (~ssPv1(W))))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(X))) | (~ssPv1(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))), ((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) <=> ((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) | ssPv3(V)) <=> (((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) | ssPv3(V)))), rewrite((((~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))), (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) | ssPv3(V)) | ssPv4(W)) <=> ((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) | ssPv4(W)))), rewrite(((ssPv3(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X))) | ssPv4(W)) <=> (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))), ((((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) | ssPv3(V)) | ssPv4(W)) <=> (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))))),
% 2.14/1.71 inference(bind,[status(th)],[])).
% 2.14/1.71 tff(1730,plain,
% 2.14/1.71 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) | ssPv3(V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(quant_intro,[status(thm)],[1729])).
% 2.14/1.71 tff(1731,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, U))) | (~ssRr(W, X))) | (~ssPv1(X))) | (~ssPv1(W))) | ssPv3(V)) | ssPv4(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause13')).
% 2.14/1.71 tff(1732,plain,
% 2.14/1.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 2.14/1.71 tff(1733,plain,
% 2.14/1.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1732, 1728])).
% 2.14/1.71 tff(1734,plain,(
% 2.14/1.71 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(skolemize,[status(sab)],[1733])).
% 2.14/1.71 tff(1735,plain,
% 2.14/1.71 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1734, 1727])).
% 2.14/1.71 tff(1736,plain,
% 2.14/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1737,plain,
% 2.14/1.71 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))) <=> (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1738,plain,
% 2.14/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(monotonicity,[status(thm)],[1737])).
% 2.14/1.71 tff(1739,plain,
% 2.14/1.71 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(transitivity,[status(thm)],[1738, 1736])).
% 2.14/1.71 tff(1740,plain,
% 2.14/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(quant_inst,[status(thm)],[])).
% 2.14/1.71 tff(1741,plain,
% 2.14/1.71 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1740, 1739])).
% 2.14/1.71 tff(1742,plain,
% 2.14/1.71 (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1741, 1735, 155, 252])).
% 2.14/1.71 tff(1743,plain,
% 2.14/1.71 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1742, 1725, 1714, 3])).
% 2.14/1.71 tff(1744,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1745,plain,
% 2.14/1.71 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1746,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.71 inference(monotonicity,[status(thm)],[1745])).
% 2.14/1.71 tff(1747,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(transitivity,[status(thm)],[1746, 1744])).
% 2.14/1.71 tff(1748,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(quant_inst,[status(thm)],[])).
% 2.14/1.71 tff(1749,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 2.14/1.71 tff(1750,plain,
% 2.14/1.71 (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1749, 80, 155, 252])).
% 2.14/1.71 tff(1751,plain,
% 2.14/1.71 (ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1750, 1743, 1714, 3])).
% 2.14/1.71 tff(1752,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1753,plain,
% 2.14/1.71 (((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1754,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.71 inference(monotonicity,[status(thm)],[1753])).
% 2.14/1.71 tff(1755,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.71 inference(transitivity,[status(thm)],[1754, 1752])).
% 2.14/1.71 tff(1756,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.14/1.71 inference(quant_inst,[status(thm)],[])).
% 2.14/1.71 tff(1757,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~ssPv1(Y)) | (~ssPv3(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 2.14/1.71 tff(1758,plain,
% 2.14/1.71 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1757, 204, 155, 252])).
% 2.14/1.71 tff(1759,plain,
% 2.14/1.71 (~ssPv3(skf1(skf1(elem!0)))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1758, 1751, 1714, 1743])).
% 2.14/1.71 tff(1760,plain,
% 2.14/1.71 (ssPv1(skf1(skf1(elem!0)))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[152, 5, 4])).
% 2.14/1.71 tff(1761,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0)))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1762,plain,
% 2.14/1.71 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0)))),
% 2.14/1.71 inference(rewrite,[status(thm)],[])).
% 2.14/1.71 tff(1763,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0))))),
% 2.14/1.71 inference(monotonicity,[status(thm)],[1762])).
% 2.14/1.71 tff(1764,plain,
% 2.14/1.71 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0)))),
% 2.14/1.71 inference(transitivity,[status(thm)],[1763, 1761])).
% 2.14/1.71 tff(1765,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)))),
% 2.14/1.71 inference(quant_inst,[status(thm)],[])).
% 2.14/1.71 tff(1766,plain,
% 2.14/1.71 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0))),
% 2.14/1.71 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 2.14/1.71 tff(1767,plain,
% 2.14/1.71 (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv4(elem!0) | (~ssPv1(elem!0))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1766, 1697, 16, 14])).
% 2.14/1.71 tff(1768,plain,
% 2.14/1.71 (ssPv4(elem!0)),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[1767, 1, 1760, 109])).
% 2.14/1.71 tff(1769,plain,
% 2.14/1.71 (ssPv4(skf1(skf1(elem!0)))),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[51, 1768, 5, 109])).
% 2.14/1.71 tff(1770,plain,
% 2.14/1.71 ($false),
% 2.14/1.71 inference(unit_resolution,[status(thm)],[148, 1769, 1768, 4, 109])).
% 2.14/1.71 tff(1771,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.72 tff(1772,plain,
% 2.14/1.72 (ssPv3(skf1(elem!0))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1771, 1759, 4])).
% 2.14/1.72 tff(1773,plain,
% 2.14/1.72 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[172, 1772, 4, 3])).
% 2.14/1.72 tff(1774,plain,
% 2.14/1.72 (ssPv2(skf1(elem!0))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[307, 1725, 4, 3])).
% 2.14/1.72 tff(1775,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1776,plain,
% 2.14/1.72 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0)))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1777,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.72 inference(monotonicity,[status(thm)],[1776])).
% 2.14/1.72 tff(1778,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(transitivity,[status(thm)],[1777, 1775])).
% 2.14/1.72 tff(1779,plain,
% 2.14/1.72 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(elem!0))))),
% 2.14/1.72 inference(quant_inst,[status(thm)],[])).
% 2.14/1.72 tff(1780,plain,
% 2.14/1.72 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 2.14/1.72 tff(1781,plain,
% 2.14/1.72 (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1780, 1518, 155, 252])).
% 2.14/1.72 tff(1782,plain,
% 2.14/1.72 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1781, 1759, 3, 1743])).
% 2.14/1.72 tff(1783,plain,
% 2.14/1.72 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[707, 1782, 4, 1725])).
% 2.14/1.72 tff(1784,plain,
% 2.14/1.72 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[325, 1783, 1725, 1774])).
% 2.14/1.72 tff(1785,plain,
% 2.14/1.72 (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1499, 1783, 1743, 1784])).
% 2.14/1.72 tff(1786,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1787,plain,
% 2.14/1.72 ((ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1788,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.72 inference(monotonicity,[status(thm)],[1787])).
% 2.14/1.72 tff(1789,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(transitivity,[status(thm)],[1788, 1786])).
% 2.14/1.72 tff(1790,plain,
% 2.14/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(quant_inst,[status(thm)],[])).
% 2.14/1.72 tff(1791,plain,
% 2.14/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv4(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 2.14/1.72 tff(1792,plain,
% 2.14/1.72 (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1791, 1636, 252, 382])).
% 2.14/1.72 tff(1793,plain,
% 2.14/1.72 (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1792, 1784, 1782, 1773])).
% 2.14/1.72 tff(1794,plain,
% 2.14/1.72 ($false),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1064, 1793, 1785, 1743, 1773])).
% 2.14/1.72 tff(1795,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.72 tff(1796,plain,
% 2.14/1.72 (ssPv4(skf1(skf1(elem!0)))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1795, 4])).
% 2.14/1.72 tff(1797,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1798,plain,
% 2.14/1.72 (((~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1799,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.72 inference(monotonicity,[status(thm)],[1798])).
% 2.14/1.72 tff(1800,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(transitivity,[status(thm)],[1799, 1797])).
% 2.14/1.72 tff(1801,plain,
% 2.14/1.72 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(quant_inst,[status(thm)],[])).
% 2.14/1.72 tff(1802,plain,
% 2.14/1.72 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 2.14/1.72 tff(1803,plain,
% 2.14/1.72 (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1802, 970, 155, 252])).
% 2.14/1.72 tff(1804,plain,
% 2.14/1.72 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1803, 1796, 1714, 4])).
% 2.14/1.72 tff(1805,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1806,plain,
% 2.14/1.72 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1807,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(monotonicity,[status(thm)],[1806])).
% 2.14/1.72 tff(1808,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(transitivity,[status(thm)],[1807, 1805])).
% 2.14/1.72 tff(1809,plain,
% 2.14/1.72 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(quant_inst,[status(thm)],[])).
% 2.14/1.72 tff(1810,plain,
% 2.14/1.72 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv4(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 2.14/1.72 tff(1811,plain,
% 2.14/1.72 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1810, 141, 155, 252])).
% 2.14/1.72 tff(1812,plain,
% 2.14/1.72 (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1811, 1804, 1714, 1796])).
% 2.14/1.72 tff(1813,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1814,plain,
% 2.14/1.72 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1815,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(monotonicity,[status(thm)],[1814])).
% 2.14/1.72 tff(1816,plain,
% 2.14/1.72 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(transitivity,[status(thm)],[1815, 1813])).
% 2.14/1.72 tff(1817,plain,
% 2.14/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(quant_inst,[status(thm)],[])).
% 2.14/1.72 tff(1818,plain,
% 2.14/1.72 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(V) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(X) | (~ssPv4(W)) | (~ssPv1(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 2.14/1.72 tff(1819,plain,
% 2.14/1.72 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1818, 44, 155, 252])).
% 2.14/1.72 tff(1820,plain,
% 2.14/1.72 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.14/1.72 inference(unit_resolution,[status(thm)],[1819, 1812, 1714, 1796])).
% 2.14/1.72 tff(1821,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1822,plain,
% 2.14/1.72 ((ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.72 inference(rewrite,[status(thm)],[])).
% 2.14/1.72 tff(1823,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.72 inference(monotonicity,[status(thm)],[1822])).
% 2.14/1.72 tff(1824,plain,
% 2.14/1.72 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(transitivity,[status(thm)],[1823, 1821])).
% 2.14/1.73 tff(1825,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(quant_inst,[status(thm)],[])).
% 2.14/1.73 tff(1826,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssPv1(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 2.14/1.73 tff(1827,plain,
% 2.14/1.73 ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1826, 1450, 155, 252])).
% 2.14/1.73 tff(1828,plain,
% 2.14/1.73 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1827, 1820, 1714, 1812])).
% 2.14/1.73 tff(1829,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(rewrite,[status(thm)],[])).
% 2.14/1.73 tff(1830,plain,
% 2.14/1.73 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(rewrite,[status(thm)],[])).
% 2.14/1.73 tff(1831,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.73 inference(monotonicity,[status(thm)],[1830])).
% 2.14/1.73 tff(1832,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(transitivity,[status(thm)],[1831, 1829])).
% 2.14/1.73 tff(1833,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.73 inference(quant_inst,[status(thm)],[])).
% 2.14/1.73 tff(1834,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : (ssPv2(Y) | ssPv1(X1) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | ssPv3(V) | (~ssPv1(W)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 2.14/1.73 tff(1835,plain,
% 2.14/1.73 ((~ssPv1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1834, 62, 155, 252])).
% 2.14/1.73 tff(1836,plain,
% 2.14/1.73 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1835, 1828, 1714, 1804])).
% 2.14/1.73 tff(1837,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.73 inference(rewrite,[status(thm)],[])).
% 2.14/1.73 tff(1838,plain,
% 2.14/1.73 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0)))) <=> (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.73 inference(rewrite,[status(thm)],[])).
% 2.14/1.73 tff(1839,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.14/1.73 inference(monotonicity,[status(thm)],[1838])).
% 2.14/1.73 tff(1840,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.73 inference(transitivity,[status(thm)],[1839, 1837])).
% 2.14/1.73 tff(1841,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(elem!0))))),
% 2.14/1.73 inference(quant_inst,[status(thm)],[])).
% 2.14/1.73 tff(1842,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv2(Z)) | (~ssRr(X, Y)) | (~ssPv3(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv2(W))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 2.14/1.73 tff(1843,plain,
% 2.14/1.73 (ssPv2(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1842, 1471, 155, 252])).
% 2.14/1.73 tff(1844,plain,
% 2.14/1.73 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1843, 1828, 4, 1836])).
% 2.14/1.73 tff(1845,plain,
% 2.14/1.73 (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1339, 1844, 1804, 1820])).
% 2.14/1.73 tff(1846,plain,
% 2.14/1.73 ($false),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1389, 1845, 1844, 1804, 1812])).
% 2.14/1.73 tff(1847,plain,(ssPv2(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.14/1.73 tff(1848,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(rewrite,[status(thm)],[])).
% 2.14/1.73 tff(1849,plain,
% 2.14/1.73 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(rewrite,[status(thm)],[])).
% 2.14/1.73 tff(1850,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.14/1.73 inference(monotonicity,[status(thm)],[1849])).
% 2.14/1.73 tff(1851,plain,
% 2.14/1.73 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.14/1.73 inference(transitivity,[status(thm)],[1850, 1848])).
% 2.14/1.73 tff(1852,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(quant_inst,[status(thm)],[])).
% 2.14/1.73 tff(1853,plain,
% 2.14/1.73 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv1(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 2.14/1.73 tff(1854,plain,
% 2.14/1.73 (ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1853, 1697, 155, 252])).
% 2.14/1.73 tff(1855,plain,
% 2.14/1.73 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.14/1.73 inference(unit_resolution,[status(thm)],[1854, 1722, 1714, 3])).
% 2.14/1.73 tff(1856,plain,
% 2.14/1.73 (ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.73 inference(unit_resolution,[status(thm)],[1835, 1855, 1714, 1722])).
% 2.18/1.73 tff(1857,plain,
% 2.18/1.73 (ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.73 inference(unit_resolution,[status(thm)],[531, 1722, 250])).
% 2.18/1.73 tff(1858,plain,
% 2.18/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.73 inference(rewrite,[status(thm)],[])).
% 2.18/1.73 tff(1859,plain,
% 2.18/1.73 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.73 inference(rewrite,[status(thm)],[])).
% 2.18/1.73 tff(1860,plain,
% 2.18/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.73 inference(monotonicity,[status(thm)],[1859])).
% 2.18/1.73 tff(1861,plain,
% 2.18/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.73 inference(transitivity,[status(thm)],[1860, 1858])).
% 2.18/1.73 tff(1862,plain,
% 2.18/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.18/1.73 inference(quant_inst,[status(thm)],[])).
% 2.18/1.73 tff(1863,plain,
% 2.18/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv3(Y) | (~ssPv3(Z)) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.73 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 2.18/1.73 tff(1864,plain,
% 2.18/1.73 ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.73 inference(unit_resolution,[status(thm)],[1863, 1112, 155, 252])).
% 2.18/1.73 tff(1865,plain,
% 2.18/1.73 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.18/1.73 inference(unit_resolution,[status(thm)],[1864, 1856, 1714, 1722])).
% 2.18/1.73 tff(1866,plain,
% 2.18/1.73 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.73 inference(unit_resolution,[status(thm)],[1246, 1865, 250, 1857])).
% 2.18/1.73 tff(1867,plain,
% 2.18/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.73 inference(rewrite,[status(thm)],[])).
% 2.18/1.73 tff(1868,plain,
% 2.18/1.73 ((ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0))))) <=> (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.73 inference(rewrite,[status(thm)],[])).
% 2.18/1.73 tff(1869,plain,
% 2.18/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.73 inference(monotonicity,[status(thm)],[1868])).
% 2.18/1.73 tff(1870,plain,
% 2.18/1.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.73 inference(transitivity,[status(thm)],[1869, 1867])).
% 2.18/1.73 tff(1871,plain,
% 2.18/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.73 inference(quant_inst,[status(thm)],[])).
% 2.18/1.73 tff(1872,plain,
% 2.18/1.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(V)) | ssPv3(W))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.73 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 2.18/1.73 tff(1873,plain,
% 2.18/1.73 (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.73 inference(unit_resolution,[status(thm)],[1872, 682, 252, 382])).
% 2.18/1.73 tff(1874,plain,
% 2.18/1.74 (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1873, 1865, 1722, 1857])).
% 2.18/1.74 tff(1875,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1876,plain,
% 2.18/1.74 (((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1877,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(monotonicity,[status(thm)],[1876])).
% 2.18/1.74 tff(1878,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(transitivity,[status(thm)],[1877, 1875])).
% 2.18/1.74 tff(1879,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | ((~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(quant_inst,[status(thm)],[])).
% 2.18/1.74 tff(1880,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W) | (~ssPv4(X)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 2.18/1.74 tff(1881,plain,
% 2.18/1.74 ((~ssPv2(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1880, 1168, 252, 382])).
% 2.18/1.74 tff(1882,plain,
% 2.18/1.74 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1881, 1874, 1865, 1866])).
% 2.18/1.74 tff(1883,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1884,plain,
% 2.18/1.74 ((ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1885,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.18/1.74 inference(monotonicity,[status(thm)],[1884])).
% 2.18/1.74 tff(1886,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(transitivity,[status(thm)],[1885, 1883])).
% 2.18/1.74 tff(1887,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(quant_inst,[status(thm)],[])).
% 2.18/1.74 tff(1888,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i] : (ssPv3(W) | ssPv3(V) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 2.18/1.74 tff(1889,plain,
% 2.18/1.74 ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1888, 445, 382, 564])).
% 2.18/1.74 tff(1890,plain,
% 2.18/1.74 (ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1889, 1866, 1722, 1856])).
% 2.18/1.74 tff(1891,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1892,plain,
% 2.18/1.74 (((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1893,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.18/1.74 inference(monotonicity,[status(thm)],[1892])).
% 2.18/1.74 tff(1894,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(transitivity,[status(thm)],[1893, 1891])).
% 2.18/1.74 tff(1895,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | ((~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(quant_inst,[status(thm)],[])).
% 2.18/1.74 tff(1896,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(V)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv4(W)) | (~ssPv2(W)) | (~ssPv2(X)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 2.18/1.74 tff(1897,plain,
% 2.18/1.74 ((~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1896, 551, 382, 564])).
% 2.18/1.74 tff(1898,plain,
% 2.18/1.74 (~ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1897, 1866, 1857, 1856])).
% 2.18/1.74 tff(1899,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1900,plain,
% 2.18/1.74 ((ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1901,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))))),
% 2.18/1.74 inference(monotonicity,[status(thm)],[1900])).
% 2.18/1.74 tff(1902,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(transitivity,[status(thm)],[1901, 1899])).
% 2.18/1.74 tff(1903,plain,
% 2.18/1.74 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | (ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(quant_inst,[status(thm)],[])).
% 2.18/1.74 tff(1904,plain,
% 2.18/1.74 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv3(Z) | (~ssRr(X, Y)) | (~ssPv3(V)) | ssPv1(W) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) | (~ssRr(skf1(skf1(skf1(skf1(skf1(elem!0))))), skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 2.18/1.74 tff(1905,plain,
% 2.18/1.74 (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1904, 122, 382, 564])).
% 2.18/1.74 tff(1906,plain,
% 2.18/1.74 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1905, 1898, 1855, 1890])).
% 2.18/1.74 tff(1907,plain,
% 2.18/1.74 ($false),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1304, 1906, 1882, 1856, 1855])).
% 2.18/1.74 tff(1908,plain,(ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.18/1.74 tff(1909,plain,
% 2.18/1.74 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1908, 3])).
% 2.18/1.74 tff(1910,plain,
% 2.18/1.74 (ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1742, 1909, 1714, 3])).
% 2.18/1.74 tff(1911,plain,
% 2.18/1.74 (ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1750, 1910, 1714, 3])).
% 2.18/1.74 tff(1912,plain,
% 2.18/1.74 (~ssPv3(skf1(skf1(elem!0)))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1758, 1911, 1714, 1910])).
% 2.18/1.74 tff(1913,plain,
% 2.18/1.74 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1781, 1912, 3, 1910])).
% 2.18/1.74 tff(1914,plain,
% 2.18/1.74 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1599, 1913, 1847, 3])).
% 2.18/1.74 tff(1915,plain,
% 2.18/1.74 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1188, 1913, 1847, 1912])).
% 2.18/1.74 tff(1916,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1917,plain,
% 2.18/1.74 ((ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1918,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(monotonicity,[status(thm)],[1917])).
% 2.18/1.74 tff(1919,plain,
% 2.18/1.74 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(transitivity,[status(thm)],[1918, 1916])).
% 2.18/1.74 tff(1920,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(quant_inst,[status(thm)],[])).
% 2.18/1.74 tff(1921,plain,
% 2.18/1.74 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(V) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv1(X)))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 2.18/1.74 tff(1922,plain,
% 2.18/1.74 (ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1921, 1735, 252, 382])).
% 2.18/1.74 tff(1923,plain,
% 2.18/1.74 (ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1922, 1915, 1909, 1911])).
% 2.18/1.74 tff(1924,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1925,plain,
% 2.18/1.74 ((ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0))))) <=> (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(rewrite,[status(thm)],[])).
% 2.18/1.74 tff(1926,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))))),
% 2.18/1.74 inference(monotonicity,[status(thm)],[1925])).
% 2.18/1.74 tff(1927,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.74 inference(transitivity,[status(thm)],[1926, 1924])).
% 2.18/1.74 tff(1928,plain,
% 2.18/1.74 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.74 inference(quant_inst,[status(thm)],[])).
% 2.18/1.74 tff(1929,plain,
% 2.18/1.74 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv4(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | ssPv3(W))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(skf1(elem!0)))), skf1(skf1(skf1(skf1(skf1(elem!0))))))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 2.18/1.74 tff(1930,plain,
% 2.18/1.74 (ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1929, 1518, 252, 382])).
% 2.18/1.74 tff(1931,plain,
% 2.18/1.74 (ssPv4(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1930, 1923, 1914, 1915])).
% 2.18/1.74 tff(1932,plain,
% 2.18/1.74 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1296, 1913, 1847, 1911])).
% 2.18/1.74 tff(1933,plain,
% 2.18/1.74 (ssPv2(skf1(skf1(skf1(elem!0))))),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1331, 1931, 1911, 1932])).
% 2.18/1.74 tff(1934,plain,
% 2.18/1.74 ($false),
% 2.18/1.74 inference(unit_resolution,[status(thm)],[1881, 1933, 1931, 1914, 1913])).
% 2.18/1.74 tff(1935,plain,(ssPv4(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.18/1.74 tff(1936,plain,
% 2.18/1.74 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1937,plain,
% 2.18/1.75 (((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1938,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1937])).
% 2.18/1.75 tff(1939,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))),
% 2.18/1.75 inference(transitivity,[status(thm)],[1938, 1936])).
% 2.18/1.75 tff(1940,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(elem!0)))),
% 2.18/1.75 inference(quant_inst,[status(thm)],[])).
% 2.18/1.75 tff(1941,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i, X1: $i] : ((~ssPv1(X1)) | (~ssPv2(Y)) | (~ssRr(Z, X1)) | (~ssRr(X, Y)) | (~ssPv4(V)) | (~ssRr(W, Z)) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0))),
% 2.18/1.75 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 2.18/1.75 tff(1942,plain,
% 2.18/1.75 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1941, 318, 16, 14])).
% 2.18/1.75 tff(1943,plain,
% 2.18/1.75 (~ssPv2(elem!0)),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1942, 1935, 1714, 1847])).
% 2.18/1.75 tff(1944,plain,
% 2.18/1.75 (ssPv1(elem!0)),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[416, 1, 1935, 1943])).
% 2.18/1.75 tff(1945,plain,
% 2.18/1.75 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1946,plain,
% 2.18/1.75 (((~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1947,plain,
% 2.18/1.75 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1946])).
% 2.18/1.75 tff(1948,plain,
% 2.18/1.75 (((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)))),
% 2.18/1.75 inference(transitivity,[status(thm)],[1947, 1945])).
% 2.18/1.75 tff(1949,plain,
% 2.18/1.75 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | ((~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(quant_inst,[status(thm)],[])).
% 2.18/1.75 tff(1950,plain,
% 2.18/1.75 ((~![W: $i, V: $i, U: $i] : ((~ssPv4(W)) | ssPv2(W) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)) | (~ssPv2(V)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0))),
% 2.18/1.75 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 2.18/1.75 tff(1951,plain,
% 2.18/1.75 ((~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1950, 970, 16, 14])).
% 2.18/1.75 tff(1952,plain,
% 2.18/1.75 (~ssPv4(elem!0)),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1951, 1944, 1847, 1943])).
% 2.18/1.75 tff(1953,plain,
% 2.18/1.75 ($false),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1767, 1952, 1944, 1714, 1])).
% 2.18/1.75 tff(1954,plain,(ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 2.18/1.75 tff(1955,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1956,plain,
% 2.18/1.75 ((ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1957,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1956])).
% 2.18/1.75 tff(1958,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.75 inference(transitivity,[status(thm)],[1957, 1955])).
% 2.18/1.75 tff(1959,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(quant_inst,[status(thm)],[])).
% 2.18/1.75 tff(1960,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv4(V)) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv3(W)) | (~ssPv1(W)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 2.18/1.75 tff(1961,plain,
% 2.18/1.75 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1960, 222, 155, 252])).
% 2.18/1.75 tff(1962,plain,
% 2.18/1.75 (ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1961, 857, 1714, 1954])).
% 2.18/1.75 tff(1963,plain,
% 2.18/1.75 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1296, 857, 1847, 1962])).
% 2.18/1.75 tff(1964,plain,
% 2.18/1.75 ($false),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1811, 1963, 857, 1714, 1935])).
% 2.18/1.75 tff(1965,plain,(~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.18/1.75 tff(1966,plain,
% 2.18/1.75 (ssPv3(skf1(skf1(skf1(elem!0))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1819, 1965, 1714, 1935])).
% 2.18/1.75 tff(1967,plain,
% 2.18/1.75 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[840, 1966, 1954, 1965])).
% 2.18/1.75 tff(1968,plain,
% 2.18/1.75 (ssPv1(skf1(skf1(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1339, 939, 1967, 1966])).
% 2.18/1.75 tff(1969,plain,
% 2.18/1.75 ($false),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1389, 1968, 939, 1967, 1965])).
% 2.18/1.75 tff(1970,plain,(ssPv2(skf1(skf1(skf1(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 2.18/1.75 tff(1971,plain,
% 2.18/1.75 (~ssPv4(skf1(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1533, 1970, 1954, 1966])).
% 2.18/1.75 tff(1972,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1973,plain,
% 2.18/1.75 ((ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1974,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1973])).
% 2.18/1.75 tff(1975,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)))),
% 2.18/1.75 inference(transitivity,[status(thm)],[1974, 1972])).
% 2.18/1.75 tff(1976,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))))),
% 2.18/1.75 inference(quant_inst,[status(thm)],[])).
% 2.18/1.75 tff(1977,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv2(Y) | ssPv4(X) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))),
% 2.18/1.75 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 2.18/1.75 tff(1978,plain,
% 2.18/1.75 ((~ssPv1(skf1(skf1(elem!0)))) | ssPv2(elem!0) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1977, 300, 16, 14])).
% 2.18/1.75 tff(1979,plain,
% 2.18/1.75 (ssPv2(skf1(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1978, 1971, 1714, 1943])).
% 2.18/1.75 tff(1980,plain,
% 2.18/1.75 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1981,plain,
% 2.18/1.75 (((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1982,plain,
% 2.18/1.75 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1981])).
% 2.18/1.75 tff(1983,plain,
% 2.18/1.75 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(transitivity,[status(thm)],[1982, 1980])).
% 2.18/1.75 tff(1984,plain,
% 2.18/1.75 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(quant_inst,[status(thm)],[])).
% 2.18/1.75 tff(1985,plain,
% 2.18/1.75 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv2(W)) | (~ssPv3(X)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 2.18/1.75 tff(1986,plain,
% 2.18/1.75 ((~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1985, 427, 14, 155])).
% 2.18/1.75 tff(1987,plain,
% 2.18/1.75 (~ssPv4(skf1(skf1(skf1(elem!0))))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1986, 1979, 1971, 1954])).
% 2.18/1.75 tff(1988,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1989,plain,
% 2.18/1.75 ((ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1990,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1989])).
% 2.18/1.75 tff(1991,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)))),
% 2.18/1.75 inference(transitivity,[status(thm)],[1990, 1988])).
% 2.18/1.75 tff(1992,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))))),
% 2.18/1.75 inference(quant_inst,[status(thm)],[])).
% 2.18/1.75 tff(1993,plain,
% 2.18/1.75 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | (~ssPv2(X)) | ssPv2(W) | (~ssRr(W, X)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssRr(W, Y)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0))),
% 2.18/1.75 inference(modus_ponens,[status(thm)],[1992, 1991])).
% 2.18/1.75 tff(1994,plain,
% 2.18/1.75 ((~ssPv3(skf1(skf1(elem!0)))) | ssPv2(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1993, 280, 16, 14])).
% 2.18/1.75 tff(1995,plain,
% 2.18/1.75 (ssPv1(skf1(elem!0))),
% 2.18/1.75 inference(unit_resolution,[status(thm)],[1994, 1979, 1943, 1954])).
% 2.18/1.75 tff(1996,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1997,plain,
% 2.18/1.75 ((ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.75 inference(rewrite,[status(thm)],[])).
% 2.18/1.75 tff(1998,plain,
% 2.18/1.75 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 2.18/1.75 inference(monotonicity,[status(thm)],[1997])).
% 2.18/1.76 tff(1999,plain,
% 2.18/1.76 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 2.18/1.76 inference(transitivity,[status(thm)],[1998, 1996])).
% 2.18/1.76 tff(2000,plain,
% 2.18/1.76 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(elem!0))))),
% 2.18/1.76 inference(quant_inst,[status(thm)],[])).
% 2.18/1.76 tff(2001,plain,
% 2.18/1.76 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : (ssPv1(Y) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(W, X)) | (~ssRr(X, Y)) | (~ssRr(W, U)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.76 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 2.18/1.76 tff(2002,plain,
% 2.18/1.76 (ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 2.18/1.76 inference(unit_resolution,[status(thm)],[2001, 80, 14, 155])).
% 2.18/1.76 tff(2003,plain,
% 2.18/1.76 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 2.18/1.76 inference(unit_resolution,[status(thm)],[2002, 1995, 1971, 1966])).
% 2.18/1.76 tff(2004,plain,
% 2.18/1.76 ($false),
% 2.18/1.76 inference(unit_resolution,[status(thm)],[1667, 2003, 1995, 1954, 1987])).
% 2.18/1.76 % SZS output end Proof
%------------------------------------------------------------------------------