TSTP Solution File: SYN784-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN784-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 23:57:17 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN784-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 07:33:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(ssPv4_type, type, (
% 0.20/0.48 ssPv4: $i > $o)).
% 0.20/0.48 tff(skf3_type, type, (
% 0.20/0.48 skf3: $i > $i)).
% 0.20/0.48 tff(elem_0_type, type, (
% 0.20/0.48 elem_0: $i)).
% 0.20/0.48 tff(ssPv2_type, type, (
% 0.20/0.48 ssPv2: $i > $o)).
% 0.20/0.48 tff(ssPv3_type, type, (
% 0.20/0.48 ssPv3: $i > $o)).
% 0.20/0.48 tff(skf2_type, type, (
% 0.20/0.48 skf2: $i > $i)).
% 0.20/0.48 tff(ssPv1_type, type, (
% 0.20/0.48 ssPv1: $i > $o)).
% 0.20/0.48 tff(ssRr_type, type, (
% 0.20/0.48 ssRr: ( $i * $i ) > $o)).
% 0.20/0.48 tff(1,assumption,(~ssPv4(skf3(elem!0))), introduced(assumption)).
% 0.20/0.48 tff(2,assumption,(~ssPv3(elem!0)), introduced(assumption)).
% 0.20/0.48 tff(3,assumption,(~ssPv3(skf3(elem!0))), introduced(assumption)).
% 0.20/0.48 tff(4,assumption,(~ssPv2(skf3(elem!0))), introduced(assumption)).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (^[U: $i] : refl(ssRr(skf3(U), U) <=> ssRr(skf3(U), U))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(8,axiom,(![U: $i] : ssRr(skf3(U), U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.48 tff(10,plain,(
% 0.20/0.48 ![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.48 inference(skolemize,[status(sab)],[9])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(elem!0), elem!0)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (ssRr(skf3(elem!0), elem!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) <=> (((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(W, V))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.48 tff(19,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(V))) | ssPv3(U)) | ssPv2(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.48 tff(22,plain,(
% 0.20/0.48 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[21])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (ssPv2(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv2(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[29, 23, 13])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (~ssPv2(elem!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[30, 4, 3, 2])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (^[V: $i, U: $i] : refl((ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) <=> (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V)) <=> ((ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv3(V)))), rewrite(((ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V)) <=> ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.48 tff(37,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.48 tff(40,plain,(
% 0.20/0.48 ![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[39])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 ((ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (ssPv2(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv4(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[47, 41, 13])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (~ssPv4(elem!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[48, 31, 2, 4])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) <=> (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(U, V)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) <=> ((ssPv4(V) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)))), rewrite(((ssPv4(V) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) <=> ((ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W))) | ssPv3(U)))), rewrite(((ssPv4(V) | (~ssRr(U, V)) | ssPv3(W) | (~ssRr(U, W))) | ssPv3(U)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) | ssPv4(U)))), rewrite(((ssPv4(V) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W))) | ssPv4(U)) <=> (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.48 tff(55,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv3(W)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.48 tff(58,plain,(
% 0.20/0.48 ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[57])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 ((ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[65, 59, 13])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (ssPv4(skf3(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[66, 49, 3, 2])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (^[U: $i] : refl(ssRr(U, skf2(U)) <=> ssRr(U, skf2(U)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(71,axiom,(![U: $i] : ssRr(U, skf2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.48 tff(73,plain,(
% 0.20/0.48 ![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.48 inference(skolemize,[status(sab)],[72])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(elem!0, skf2(elem!0))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (ssRr(elem!0, skf2(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V)) <=> ((ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv4(V)))), rewrite(((ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv4(V)) <=> (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V)) <=> (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.49 tff(82,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | ssPv2(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause19')).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.49 tff(85,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[84])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ((ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(elem!0) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 ((~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[92, 86, 13, 76])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (~ssPv3(skf2(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[93, 67, 31, 49])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[100, 59, 76])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (ssPv4(skf2(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[101, 94, 2, 49])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 ((ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 (ssPv3(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[108, 23, 76])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (~ssPv2(skf2(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[109, 94, 2, 31])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 ((ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[116, 41, 76])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[117, 110, 94, 102, 31])).
% 0.20/0.49 tff(119,plain,(ssPv2(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (ssPv2(skf3(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[119, 2, 3])).
% 0.20/0.49 tff(121,assumption,(~ssPv4(skf2(elem!0))), introduced(assumption)).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (ssPv4(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[66, 1, 3, 2])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U))) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.49 tff(128,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv1(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause16')).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.49 tff(131,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[130])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(skf3(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 ((~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv4(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[138, 132, 13])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (ssPv1(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[139, 122, 3, 120])).
% 0.20/0.49 tff(141,assumption,(ssPv4(elem!0)), introduced(assumption)).
% 0.20/0.49 tff(142,assumption,(ssPv2(skf3(elem!0))), introduced(assumption)).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssPv2(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv4(V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.50 tff(148,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.20/0.50 tff(151,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[150])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 ((ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[155, 153])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[158, 152, 13, 76])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (ssPv3(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[159, 121, 142, 141])).
% 0.20/0.50 tff(161,assumption,(ssPv1(elem!0)), introduced(assumption)).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (^[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(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U)) <=> ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.50 tff(167,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.50 tff(170,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[169])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 (((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 ((~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[177, 171, 76])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (~ssPv2(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[178, 121, 2, 161])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) <=> ((ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv2(X)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv2(X)) <=> (ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) <=> (ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V)) <=> ((ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(V)))), rewrite(((ssPv2(X) | ssPv1(U) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(V)) <=> (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V)) <=> (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.50 tff(185,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) | ssPv1(U)) | ssPv4(W)) | ssPv2(X)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.20/0.50 tff(188,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[187])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 ((ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[191])).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[192, 190])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv1(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[195, 189, 13, 76])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (ssPv1(skf3(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[196, 179, 2, 121])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) <=> (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[198])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) <=> (((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv1(V))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) | ssPv2(X)))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[201])).
% 0.20/0.50 tff(203,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.20/0.50 tff(206,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[205])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 ((ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[209])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[210, 208])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 ((~ssPv3(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[213, 207, 13, 76])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[214, 197, 179, 161, 160])).
% 0.20/0.51 tff(216,plain,(ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)) | ssPv3(elem!0) | (~ssPv2(skf3(elem!0))) | (~ssPv4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (ssPv4(skf2(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[216, 140, 2, 120, 122])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(X))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.51 tff(223,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv2(X))) | (~ssPv1(V))) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.20/0.51 tff(226,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[225])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[229])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[230, 228])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 ((~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[233, 227, 13, 76])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (~ssPv2(skf2(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[234, 217, 1, 140])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i] : refl((ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[236])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> (((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(U))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv3(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[239])).
% 0.20/0.51 tff(241,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv3(W)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause18')).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.20/0.51 tff(244,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[243])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 ((ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[247])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[248, 246])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ((~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[251, 245, 76])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 235, 217, 2, 140])).
% 0.20/0.51 tff(254,plain,(ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (ssPv4(skf3(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[254, 2, 3])).
% 0.20/0.51 tff(256,assumption,(~ssPv4(elem!0)), introduced(assumption)).
% 0.20/0.51 tff(257,assumption,(ssPv4(skf3(elem!0))), introduced(assumption)).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 (ssPv3(skf2(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[101, 256, 2, 121])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[259])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 (^[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(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.41/0.51 inference(quant_intro,[status(thm)],[262])).
% 0.41/0.51 tff(264,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv4(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.41/0.51 tff(265,plain,
% 0.41/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.41/0.51 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.41/0.51 tff(266,plain,
% 0.41/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.41/0.51 inference(modus_ponens,[status(thm)],[265, 261])).
% 0.41/0.51 tff(267,plain,(
% 0.41/0.51 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.41/0.51 inference(skolemize,[status(sab)],[266])).
% 0.41/0.51 tff(268,plain,
% 0.41/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))),
% 0.41/0.51 inference(modus_ponens,[status(thm)],[267, 260])).
% 0.41/0.51 tff(269,plain,
% 0.41/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.41/0.51 inference(rewrite,[status(thm)],[])).
% 0.41/0.51 tff(270,plain,
% 0.41/0.51 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.41/0.51 inference(rewrite,[status(thm)],[])).
% 0.41/0.51 tff(271,plain,
% 0.41/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))))),
% 0.41/0.51 inference(monotonicity,[status(thm)],[270])).
% 0.41/0.51 tff(272,plain,
% 0.41/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.41/0.51 inference(transitivity,[status(thm)],[271, 269])).
% 0.41/0.51 tff(273,plain,
% 0.41/0.51 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv2(skf3(elem!0))))),
% 0.41/0.51 inference(quant_inst,[status(thm)],[])).
% 0.41/0.51 tff(274,plain,
% 0.41/0.51 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.41/0.51 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.41/0.51 tff(275,plain,
% 0.41/0.51 ((~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[274, 268, 13])).
% 0.41/0.51 tff(276,plain,
% 0.41/0.51 (~ssPv2(elem!0)),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[275, 256, 142, 257])).
% 0.41/0.51 tff(277,plain,
% 0.41/0.51 ($false),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[93, 276, 258, 257, 256])).
% 0.41/0.51 tff(278,plain,(ssPv4(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.51 tff(279,plain,
% 0.41/0.51 (ssPv4(elem!0)),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[278, 121, 120, 2, 255])).
% 0.41/0.51 tff(280,plain,
% 0.41/0.51 (ssPv1(elem!0)),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[139, 279, 3, 120])).
% 0.41/0.51 tff(281,plain,
% 0.41/0.51 ($false),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[216, 280, 279, 2, 120, 121])).
% 0.41/0.51 tff(282,plain,(ssPv4(skf2(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.51 tff(283,plain,
% 0.41/0.51 (ssPv4(skf2(elem!0))),
% 0.41/0.51 inference(unit_resolution,[status(thm)],[282, 2, 3])).
% 0.41/0.51 tff(284,assumption,(ssPv4(skf2(elem!0))), introduced(assumption)).
% 0.41/0.51 tff(285,plain,
% 0.41/0.51 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.41/0.51 inference(bind,[status(th)],[])).
% 0.41/0.51 tff(286,plain,
% 0.41/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.51 inference(quant_intro,[status(thm)],[285])).
% 0.41/0.51 tff(287,plain,
% 0.41/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.51 inference(rewrite,[status(thm)],[])).
% 0.41/0.51 tff(288,plain,
% 0.41/0.51 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssPv2(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V)) <=> ((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)))), rewrite(((ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V)) <=> (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(289,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[288])).
% 0.41/0.52 tff(290,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | ssPv3(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.41/0.52 tff(291,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.41/0.52 tff(292,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.41/0.52 tff(293,plain,(
% 0.41/0.52 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.52 inference(skolemize,[status(sab)],[292])).
% 0.41/0.52 tff(294,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.41/0.52 tff(295,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(296,plain,
% 0.41/0.52 ((ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(297,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)))),
% 0.41/0.52 inference(monotonicity,[status(thm)],[296])).
% 0.41/0.52 tff(298,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.41/0.52 inference(transitivity,[status(thm)],[297, 295])).
% 0.41/0.52 tff(299,plain,
% 0.41/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.41/0.52 inference(quant_inst,[status(thm)],[])).
% 0.41/0.52 tff(300,plain,
% 0.41/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.41/0.52 tff(301,plain,
% 0.41/0.52 (ssPv3(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[300, 294, 13, 76])).
% 0.41/0.52 tff(302,plain,
% 0.41/0.52 (ssPv3(skf2(elem!0))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[301, 276, 142, 284])).
% 0.41/0.52 tff(303,plain,
% 0.41/0.52 ($false),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[93, 302, 276, 257, 256])).
% 0.41/0.52 tff(304,plain,(ssPv4(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv4(skf2(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.52 tff(305,plain,
% 0.41/0.52 (ssPv4(elem!0)),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[304, 255, 120, 283])).
% 0.41/0.52 tff(306,plain,
% 0.41/0.52 (ssPv1(elem!0)),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[139, 305, 3, 120])).
% 0.41/0.52 tff(307,plain,
% 0.41/0.52 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(308,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[307])).
% 0.41/0.52 tff(309,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(310,plain,
% 0.41/0.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(311,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[310])).
% 0.41/0.52 tff(312,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause23')).
% 0.41/0.52 tff(313,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.41/0.52 tff(314,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.41/0.52 tff(315,plain,(
% 0.41/0.52 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(skolemize,[status(sab)],[314])).
% 0.41/0.52 tff(316,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[315, 308])).
% 0.41/0.52 tff(317,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(318,plain,
% 0.41/0.52 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(319,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.41/0.52 inference(monotonicity,[status(thm)],[318])).
% 0.41/0.52 tff(320,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.41/0.52 inference(transitivity,[status(thm)],[319, 317])).
% 0.41/0.52 tff(321,plain,
% 0.41/0.52 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)))),
% 0.41/0.52 inference(quant_inst,[status(thm)],[])).
% 0.41/0.52 tff(322,plain,
% 0.41/0.52 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.41/0.52 tff(323,plain,
% 0.41/0.52 ((~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[322, 316, 13, 76])).
% 0.41/0.52 tff(324,plain,
% 0.41/0.52 (ssPv1(skf2(elem!0))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[323, 306, 255, 305])).
% 0.41/0.52 tff(325,plain,
% 0.41/0.52 (ssPv2(skf2(elem!0))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[252, 306, 2, 283])).
% 0.41/0.52 tff(326,plain,
% 0.41/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(327,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[326])).
% 0.41/0.52 tff(328,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(329,plain,
% 0.41/0.52 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssPv2(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(330,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[329])).
% 0.41/0.52 tff(331,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.41/0.52 tff(332,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.41/0.52 tff(333,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.41/0.52 tff(334,plain,(
% 0.41/0.52 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(skolemize,[status(sab)],[333])).
% 0.41/0.52 tff(335,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[334, 327])).
% 0.41/0.52 tff(336,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(337,plain,
% 0.41/0.52 (((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(338,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))))),
% 0.41/0.52 inference(monotonicity,[status(thm)],[337])).
% 0.41/0.52 tff(339,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.41/0.52 inference(transitivity,[status(thm)],[338, 336])).
% 0.41/0.52 tff(340,plain,
% 0.41/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.41/0.52 inference(quant_inst,[status(thm)],[])).
% 0.41/0.52 tff(341,plain,
% 0.41/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.41/0.52 tff(342,plain,
% 0.41/0.52 ((~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[341, 335, 13, 76])).
% 0.41/0.52 tff(343,plain,
% 0.41/0.52 ($false),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[342, 325, 324, 120, 306])).
% 0.41/0.52 tff(344,plain,(ssPv3(elem!0) | ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.52 tff(345,plain,
% 0.41/0.52 (ssPv3(skf3(elem!0))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[344, 2])).
% 0.41/0.52 tff(346,assumption,(~ssPv3(skf2(elem!0))), introduced(assumption)).
% 0.41/0.52 tff(347,plain,
% 0.41/0.52 (^[V: $i, U: $i] : refl((ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) <=> (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(348,plain,
% 0.41/0.52 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[347])).
% 0.41/0.52 tff(349,plain,
% 0.41/0.52 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(350,plain,
% 0.41/0.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) <=> ((ssPv4(U) | (~ssRr(U, V))) | ssPv2(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V))) | ssPv2(V)) <=> (ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) <=> (ssPv2(V) | ssPv4(U) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) <=> ((ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv3(V)))), rewrite(((ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) <=> (ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V)) <=> ((ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv4(V)))), rewrite(((ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V))) | ssPv4(V)) <=> (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V)) <=> (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(351,plain,
% 0.41/0.52 (![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V)) <=> ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[350])).
% 0.41/0.52 tff(352,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv4(U)) | ssPv2(V)) | ssPv3(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.41/0.52 tff(353,plain,
% 0.41/0.52 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.41/0.52 tff(354,plain,
% 0.41/0.52 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.41/0.52 tff(355,plain,(
% 0.41/0.52 ![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(skolemize,[status(sab)],[354])).
% 0.41/0.52 tff(356,plain,
% 0.41/0.52 (![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[355, 348])).
% 0.41/0.52 tff(357,plain,
% 0.41/0.52 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(358,plain,
% 0.41/0.52 ((ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(359,plain,
% 0.41/0.52 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)))),
% 0.41/0.52 inference(monotonicity,[status(thm)],[358])).
% 0.41/0.52 tff(360,plain,
% 0.41/0.52 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.52 inference(transitivity,[status(thm)],[359, 357])).
% 0.41/0.52 tff(361,plain,
% 0.41/0.52 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.41/0.52 inference(quant_inst,[status(thm)],[])).
% 0.41/0.52 tff(362,plain,
% 0.41/0.52 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.41/0.52 tff(363,plain,
% 0.41/0.52 (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[362, 356, 76])).
% 0.41/0.52 tff(364,plain,
% 0.41/0.52 (ssPv2(skf2(elem!0))),
% 0.41/0.52 inference(unit_resolution,[status(thm)],[363, 346, 256, 121])).
% 0.41/0.52 tff(365,plain,
% 0.41/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) <=> (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(366,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[365])).
% 0.41/0.52 tff(367,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(rewrite,[status(thm)],[])).
% 0.41/0.52 tff(368,plain,
% 0.41/0.52 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> (((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(V, W))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(V, W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(X)))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V)) <=> ((ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(V)))), rewrite(((ssPv4(X) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W))) | ssPv4(V)) <=> (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V)) <=> (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))))),
% 0.41/0.52 inference(bind,[status(th)],[])).
% 0.41/0.52 tff(369,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(quant_intro,[status(thm)],[368])).
% 0.41/0.52 tff(370,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssRr(V, X))) | ssPv4(X)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.41/0.52 tff(371,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.41/0.52 tff(372,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.41/0.52 tff(373,plain,(
% 0.41/0.52 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(skolemize,[status(sab)],[372])).
% 0.41/0.52 tff(374,plain,
% 0.41/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))),
% 0.41/0.52 inference(modus_ponens,[status(thm)],[373, 366])).
% 0.41/0.52 tff(375,plain,
% 0.41/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(376,plain,
% 0.41/0.53 ((ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(377,plain,
% 0.41/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)))),
% 0.41/0.53 inference(monotonicity,[status(thm)],[376])).
% 0.41/0.53 tff(378,plain,
% 0.41/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.53 inference(transitivity,[status(thm)],[377, 375])).
% 0.41/0.53 tff(379,plain,
% 0.41/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.41/0.53 inference(quant_inst,[status(thm)],[])).
% 0.41/0.53 tff(380,plain,
% 0.41/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.41/0.53 tff(381,plain,
% 0.41/0.53 ((~ssPv2(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[380, 374, 13, 76])).
% 0.41/0.53 tff(382,plain,
% 0.41/0.53 (~ssPv3(skf3(elem!0))),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[381, 364, 121, 256])).
% 0.41/0.53 tff(383,plain,
% 0.41/0.53 (^[W: $i, V: $i, U: $i] : refl((ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))))),
% 0.41/0.53 inference(bind,[status(th)],[])).
% 0.41/0.53 tff(384,plain,
% 0.41/0.53 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(quant_intro,[status(thm)],[383])).
% 0.41/0.53 tff(385,plain,
% 0.41/0.53 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(386,plain,
% 0.41/0.53 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | (~ssRr(V, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W))) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V)) <=> (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))))),
% 0.41/0.53 inference(bind,[status(th)],[])).
% 0.41/0.53 tff(387,plain,
% 0.41/0.53 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(quant_intro,[status(thm)],[386])).
% 0.41/0.53 tff(388,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv4(W)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause9')).
% 0.41/0.53 tff(389,plain,
% 0.41/0.53 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.41/0.53 tff(390,plain,
% 0.41/0.53 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[389, 385])).
% 0.41/0.53 tff(391,plain,(
% 0.41/0.53 ![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(skolemize,[status(sab)],[390])).
% 0.41/0.53 tff(392,plain,
% 0.41/0.53 (![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[391, 384])).
% 0.41/0.53 tff(393,plain,
% 0.41/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(394,plain,
% 0.41/0.53 ((ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(395,plain,
% 0.41/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[394])).
% 0.43/0.53 tff(396,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.43/0.53 inference(transitivity,[status(thm)],[395, 393])).
% 0.43/0.53 tff(397,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(398,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.43/0.53 tff(399,plain,
% 0.43/0.53 (ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[398, 392, 13, 76])).
% 0.43/0.53 tff(400,plain,
% 0.43/0.53 (~ssPv3(elem!0)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[399, 121, 256, 4])).
% 0.43/0.53 tff(401,plain,
% 0.43/0.53 (ssPv3(skf3(elem!0))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[119, 400, 4])).
% 0.43/0.53 tff(402,plain,
% 0.43/0.53 (ssPv3(skf2(elem!0))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[101, 400, 121, 256])).
% 0.43/0.53 tff(403,plain,
% 0.43/0.53 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(404,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[403])).
% 0.43/0.53 tff(405,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(406,plain,
% 0.43/0.53 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> (((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv3(X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) <=> (((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V)) <=> (((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(V)))), rewrite((((~ssPv3(X)) | (~ssPv3(U)) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(V)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V)) <=> ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(407,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[406])).
% 0.43/0.53 tff(408,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.43/0.53 tff(409,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.43/0.53 tff(410,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.43/0.53 tff(411,plain,(
% 0.43/0.53 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(skolemize,[status(sab)],[410])).
% 0.43/0.53 tff(412,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[411, 404])).
% 0.43/0.53 tff(413,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(414,plain,
% 0.43/0.53 (((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(415,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0)))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[414])).
% 0.43/0.53 tff(416,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0))),
% 0.43/0.53 inference(transitivity,[status(thm)],[415, 413])).
% 0.43/0.53 tff(417,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(418,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.43/0.53 tff(419,plain,
% 0.43/0.53 ((~ssPv3(skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[418, 412, 13, 76])).
% 0.43/0.53 tff(420,plain,
% 0.43/0.53 (ssPv4(skf3(elem!0))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[419, 402, 401, 400])).
% 0.43/0.53 tff(421,plain,
% 0.43/0.53 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(422,plain,
% 0.43/0.53 (ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[421, 11])).
% 0.43/0.53 tff(423,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(424,plain,
% 0.43/0.53 ((ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(425,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[424])).
% 0.43/0.53 tff(426,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.53 inference(transitivity,[status(thm)],[425, 423])).
% 0.43/0.53 tff(427,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(428,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.43/0.53 tff(429,plain,
% 0.43/0.53 ((~ssPv4(skf3(elem!0))) | ssPv3(elem!0) | ssPv4(elem!0) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[428, 152, 13, 422])).
% 0.43/0.53 tff(430,plain,
% 0.43/0.53 (~ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[429, 420, 256, 400])).
% 0.43/0.53 tff(431,plain,
% 0.43/0.53 (~ssPv2(skf2(elem!0))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[381, 401, 121, 256])).
% 0.43/0.53 tff(432,plain,
% 0.43/0.53 (ssPv1(skf3(elem!0))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[196, 431, 400, 121])).
% 0.43/0.53 tff(433,plain,
% 0.43/0.53 (^[V: $i, U: $i] : refl((ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(434,plain,
% 0.43/0.53 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) <=> ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[433])).
% 0.43/0.53 tff(435,plain,
% 0.43/0.53 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) <=> ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(436,plain,
% 0.43/0.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V))) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(437,plain,
% 0.43/0.54 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.54 inference(quant_intro,[status(thm)],[436])).
% 0.43/0.54 tff(438,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.43/0.54 tff(439,plain,
% 0.43/0.54 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.43/0.54 tff(440,plain,
% 0.43/0.54 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[439, 435])).
% 0.43/0.54 tff(441,plain,(
% 0.43/0.54 ![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.54 inference(skolemize,[status(sab)],[440])).
% 0.43/0.54 tff(442,plain,
% 0.43/0.54 (![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[441, 434])).
% 0.43/0.54 tff(443,plain,
% 0.43/0.54 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(444,plain,
% 0.43/0.54 ((ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0)))) <=> (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(445,plain,
% 0.43/0.54 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[444])).
% 0.43/0.54 tff(446,plain,
% 0.43/0.54 (((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(transitivity,[status(thm)],[445, 443])).
% 0.43/0.54 tff(447,plain,
% 0.43/0.54 ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(448,plain,
% 0.43/0.54 ((~![V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssPv1(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.43/0.54 tff(449,plain,
% 0.43/0.54 (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[448, 442, 422])).
% 0.43/0.54 tff(450,plain,
% 0.43/0.54 ($false),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[449, 432, 420, 4, 430])).
% 0.43/0.54 tff(451,plain,(ssPv4(skf2(elem!0)) | ssPv2(skf3(elem!0)) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.54 tff(452,plain,
% 0.43/0.54 (ssPv2(skf3(elem!0))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[451, 121, 256])).
% 0.43/0.54 tff(453,plain,
% 0.43/0.54 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(454,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(quant_intro,[status(thm)],[453])).
% 0.43/0.54 tff(455,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(456,plain,
% 0.43/0.54 (^[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(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(457,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(quant_intro,[status(thm)],[456])).
% 0.43/0.54 tff(458,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.43/0.54 tff(459,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.43/0.54 tff(460,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[459, 455])).
% 0.43/0.54 tff(461,plain,(
% 0.43/0.54 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(skolemize,[status(sab)],[460])).
% 0.43/0.54 tff(462,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[461, 454])).
% 0.43/0.54 tff(463,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(464,plain,
% 0.43/0.54 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(465,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[464])).
% 0.43/0.54 tff(466,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0))),
% 0.43/0.54 inference(transitivity,[status(thm)],[465, 463])).
% 0.43/0.54 tff(467,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv1(elem!0)))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(468,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.43/0.54 tff(469,plain,
% 0.43/0.54 ((~ssPv1(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv4(elem!0)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[468, 462, 76])).
% 0.43/0.54 tff(470,plain,
% 0.43/0.54 (~ssPv1(elem!0)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[469, 364, 121, 256])).
% 0.43/0.54 tff(471,plain,
% 0.43/0.54 (ssPv3(elem!0)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[101, 346, 121, 256])).
% 0.43/0.54 tff(472,assumption,(~ssPv1(elem!0)), introduced(assumption)).
% 0.43/0.54 tff(473,assumption,(ssPv3(elem!0)), introduced(assumption)).
% 0.43/0.54 tff(474,assumption,(~ssPv2(elem!0)), introduced(assumption)).
% 0.43/0.54 tff(475,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(476,plain,
% 0.43/0.54 ((ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(477,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[476])).
% 0.43/0.54 tff(478,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.54 inference(transitivity,[status(thm)],[477, 475])).
% 0.43/0.54 tff(479,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(elem!0) | ssPv1(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(480,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.43/0.54 tff(481,plain,
% 0.43/0.54 (ssPv3(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(elem!0) | ssPv1(skf3(skf3(elem!0)))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[480, 189, 13, 422])).
% 0.43/0.54 tff(482,plain,
% 0.43/0.54 (ssPv1(skf3(skf3(elem!0)))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[481, 474, 256, 3])).
% 0.43/0.54 tff(483,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(484,plain,
% 0.43/0.54 ((ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0))))) <=> ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(485,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[484])).
% 0.43/0.54 tff(486,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(transitivity,[status(thm)],[485, 483])).
% 0.43/0.54 tff(487,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(488,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.43/0.54 tff(489,plain,
% 0.43/0.54 ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[488, 462, 422])).
% 0.43/0.54 tff(490,plain,
% 0.43/0.54 (ssPv4(skf3(skf3(elem!0)))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[489, 482, 142, 1])).
% 0.43/0.54 tff(491,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(492,plain,
% 0.43/0.54 ((ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(493,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[492])).
% 0.43/0.54 tff(494,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(transitivity,[status(thm)],[493, 491])).
% 0.43/0.54 tff(495,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(496,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.43/0.54 tff(497,plain,
% 0.43/0.54 ((~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssPv1(skf3(skf3(elem!0))))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[496, 207, 13, 422])).
% 0.43/0.54 tff(498,plain,
% 0.43/0.54 (~ssPv1(skf3(elem!0))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[497, 474, 473, 482])).
% 0.43/0.54 tff(499,plain,
% 0.43/0.54 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(500,plain,
% 0.43/0.54 (ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[499, 11])).
% 0.43/0.54 tff(501,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(502,plain,
% 0.43/0.54 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0))) <=> (ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(503,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[502])).
% 0.43/0.54 tff(504,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(transitivity,[status(thm)],[503, 501])).
% 0.43/0.55 tff(505,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(506,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.43/0.55 tff(507,plain,
% 0.43/0.55 (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[506, 316, 422, 500])).
% 0.43/0.55 tff(508,plain,
% 0.43/0.55 (~ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[507, 490, 482, 498])).
% 0.43/0.55 tff(509,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(510,plain,
% 0.43/0.55 ((ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(511,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0)))))))),
% 0.43/0.55 inference(monotonicity,[status(thm)],[510])).
% 0.43/0.55 tff(512,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.55 inference(transitivity,[status(thm)],[511, 509])).
% 0.43/0.55 tff(513,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf3(elem!0)) | (~ssPv2(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(514,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.43/0.55 tff(515,plain,
% 0.43/0.55 (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[514, 152, 422, 500])).
% 0.43/0.55 tff(516,plain,
% 0.43/0.55 (~ssPv2(skf3(skf3(skf3(elem!0))))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[515, 490, 3, 1])).
% 0.43/0.55 tff(517,plain,
% 0.43/0.55 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))))),
% 0.43/0.55 inference(bind,[status(th)],[])).
% 0.43/0.55 tff(518,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(quant_intro,[status(thm)],[517])).
% 0.43/0.55 tff(519,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(520,plain,
% 0.43/0.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(W, V))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssRr(W, V))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))))),
% 0.43/0.55 inference(bind,[status(th)],[])).
% 0.43/0.55 tff(521,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(quant_intro,[status(thm)],[520])).
% 0.43/0.55 tff(522,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv4(U)) | ssPv2(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 0.43/0.55 tff(523,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.43/0.55 tff(524,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[523, 519])).
% 0.43/0.55 tff(525,plain,(
% 0.43/0.55 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(skolemize,[status(sab)],[524])).
% 0.43/0.55 tff(526,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[525, 518])).
% 0.43/0.55 tff(527,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(528,plain,
% 0.43/0.55 ((ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))) <=> ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(529,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.55 inference(monotonicity,[status(thm)],[528])).
% 0.43/0.55 tff(530,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(transitivity,[status(thm)],[529, 527])).
% 0.43/0.55 tff(531,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(532,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0))))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.43/0.55 tff(533,plain,
% 0.43/0.55 ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv4(skf3(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(skf3(elem!0))))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[532, 526, 500])).
% 0.43/0.55 tff(534,plain,
% 0.43/0.55 ($false),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[533, 516, 508, 482, 490])).
% 0.43/0.55 tff(535,plain,(ssPv2(elem!0) | ssPv3(skf3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.55 tff(536,plain,
% 0.43/0.55 (ssPv2(elem!0)),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[535, 1, 3, 142, 473, 256])).
% 0.43/0.55 tff(537,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(538,plain,
% 0.43/0.55 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(539,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))))),
% 0.43/0.55 inference(monotonicity,[status(thm)],[538])).
% 0.43/0.55 tff(540,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(transitivity,[status(thm)],[539, 537])).
% 0.43/0.55 tff(541,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0) | (~ssPv1(skf3(elem!0))))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(542,plain,
% 0.43/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.43/0.55 tff(543,plain,
% 0.43/0.55 (ssPv4(skf3(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[542, 462, 13])).
% 0.43/0.55 tff(544,plain,
% 0.43/0.55 (~ssPv1(skf3(elem!0))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[543, 536, 1, 256])).
% 0.43/0.55 tff(545,plain,
% 0.43/0.55 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))))),
% 0.43/0.55 inference(bind,[status(th)],[])).
% 0.43/0.55 tff(546,plain,
% 0.43/0.55 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(quant_intro,[status(thm)],[545])).
% 0.43/0.55 tff(547,plain,
% 0.43/0.55 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(548,plain,
% 0.43/0.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))))),
% 0.43/0.55 inference(bind,[status(th)],[])).
% 0.43/0.55 tff(549,plain,
% 0.43/0.55 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(quant_intro,[status(thm)],[548])).
% 0.43/0.55 tff(550,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv1(U)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.43/0.55 tff(551,plain,
% 0.43/0.55 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.43/0.55 tff(552,plain,
% 0.43/0.55 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[551, 547])).
% 0.43/0.55 tff(553,plain,(
% 0.43/0.55 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(skolemize,[status(sab)],[552])).
% 0.43/0.55 tff(554,plain,
% 0.43/0.55 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[553, 546])).
% 0.43/0.55 tff(555,plain,
% 0.43/0.55 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(556,plain,
% 0.43/0.55 (((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(557,plain,
% 0.43/0.55 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0))))),
% 0.43/0.55 inference(monotonicity,[status(thm)],[556])).
% 0.43/0.55 tff(558,plain,
% 0.43/0.55 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(transitivity,[status(thm)],[557, 555])).
% 0.43/0.55 tff(559,plain,
% 0.43/0.55 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(560,plain,
% 0.43/0.55 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.43/0.55 tff(561,plain,
% 0.43/0.55 (ssPv1(elem!0) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[560, 554, 13])).
% 0.43/0.55 tff(562,plain,
% 0.43/0.55 ($false),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[561, 544, 536, 473, 472])).
% 0.43/0.55 tff(563,plain,(ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv3(skf3(elem!0)) | (~ssPv2(skf3(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.55 tff(564,plain,
% 0.43/0.55 (ssPv4(skf3(elem!0))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[563, 471, 470, 256, 382, 452])).
% 0.43/0.55 tff(565,plain,
% 0.43/0.55 (~ssPv2(elem!0)),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[275, 564, 256, 452])).
% 0.43/0.55 tff(566,plain,
% 0.43/0.55 (ssPv1(skf3(skf3(elem!0)))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[481, 565, 256, 382])).
% 0.43/0.55 tff(567,plain,
% 0.43/0.55 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))))),
% 0.43/0.55 inference(bind,[status(th)],[])).
% 0.43/0.55 tff(568,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(quant_intro,[status(thm)],[567])).
% 0.43/0.55 tff(569,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(570,plain,
% 0.43/0.55 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(X, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) <=> (((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv1(X)))), rewrite((((~ssPv4(U)) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv1(X)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V)) <=> (((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv2(V)))), rewrite((((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv2(V)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V)) <=> ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))))),
% 0.43/0.55 inference(bind,[status(th)],[])).
% 0.43/0.55 tff(571,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(quant_intro,[status(thm)],[570])).
% 0.43/0.55 tff(572,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(X, V))) | ssPv1(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.43/0.55 tff(573,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.43/0.55 tff(574,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[573, 569])).
% 0.43/0.55 tff(575,plain,(
% 0.43/0.55 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(skolemize,[status(sab)],[574])).
% 0.43/0.55 tff(576,plain,
% 0.43/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[575, 568])).
% 0.43/0.55 tff(577,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(578,plain,
% 0.43/0.55 (((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(579,plain,
% 0.43/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0)))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[578])).
% 0.43/0.56 tff(580,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0))),
% 0.43/0.56 inference(transitivity,[status(thm)],[579, 577])).
% 0.43/0.56 tff(581,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(582,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0)),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.43/0.56 tff(583,plain,
% 0.43/0.56 ((~ssPv2(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[582, 576, 13])).
% 0.43/0.56 tff(584,plain,
% 0.43/0.56 (ssPv1(skf3(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[583, 564, 452, 565])).
% 0.43/0.56 tff(585,plain,
% 0.43/0.56 ($false),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[497, 584, 565, 471, 566])).
% 0.43/0.56 tff(586,plain,(ssPv3(skf2(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.56 tff(587,plain,
% 0.43/0.56 (ssPv3(skf2(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[586, 121, 256])).
% 0.43/0.56 tff(588,plain,
% 0.43/0.56 (ssPv3(skf3(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[282, 2, 121])).
% 0.43/0.56 tff(589,plain,
% 0.43/0.56 (~ssPv4(skf3(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[278, 2, 256, 121, 452])).
% 0.43/0.56 tff(590,plain,
% 0.43/0.56 ($false),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[419, 589, 588, 587, 2])).
% 0.43/0.56 tff(591,plain,(ssPv3(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.56 tff(592,plain,
% 0.43/0.56 (ssPv3(elem!0)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[591, 121, 256])).
% 0.43/0.56 tff(593,plain,
% 0.43/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(594,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[593])).
% 0.43/0.56 tff(595,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(596,plain,
% 0.43/0.56 (^[W: $i, V: $i, U: $i] : 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(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(597,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[596])).
% 0.43/0.56 tff(598,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssPv3(U))) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause24')).
% 0.43/0.56 tff(599,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.43/0.56 tff(600,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[599, 595])).
% 0.43/0.56 tff(601,plain,(
% 0.43/0.56 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(skolemize,[status(sab)],[600])).
% 0.43/0.56 tff(602,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[601, 594])).
% 0.43/0.56 tff(603,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(604,plain,
% 0.43/0.56 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(605,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0)))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[604])).
% 0.43/0.56 tff(606,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0))),
% 0.43/0.56 inference(transitivity,[status(thm)],[605, 603])).
% 0.43/0.56 tff(607,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(608,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0)),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.43/0.56 tff(609,plain,
% 0.43/0.56 ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[608, 602, 76])).
% 0.43/0.56 tff(610,plain,
% 0.43/0.56 (~ssPv2(skf2(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[609, 592, 256, 587])).
% 0.43/0.56 tff(611,plain,
% 0.43/0.56 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(612,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[611])).
% 0.43/0.56 tff(613,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(614,plain,
% 0.43/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(615,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[614])).
% 0.43/0.56 tff(616,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 0.43/0.56 tff(617,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.43/0.56 tff(618,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[617, 613])).
% 0.43/0.56 tff(619,plain,(
% 0.43/0.56 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(skolemize,[status(sab)],[618])).
% 0.43/0.56 tff(620,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[619, 612])).
% 0.43/0.56 tff(621,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(622,plain,
% 0.43/0.56 (((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(623,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[622])).
% 0.43/0.56 tff(624,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)))),
% 0.43/0.56 inference(transitivity,[status(thm)],[623, 621])).
% 0.43/0.56 tff(625,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(626,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.43/0.56 tff(627,plain,
% 0.43/0.56 ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[626, 620, 13, 76])).
% 0.43/0.56 tff(628,plain,
% 0.43/0.56 (ssPv1(elem!0)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[627, 592, 452, 587])).
% 0.43/0.56 tff(629,plain,
% 0.43/0.56 (~ssPv1(skf3(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[214, 628, 610, 587])).
% 0.43/0.56 tff(630,plain,
% 0.43/0.56 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(631,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[630])).
% 0.43/0.56 tff(632,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(633,plain,
% 0.43/0.56 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(V, X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv3(X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V))) <=> (((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv1(V))))), rewrite((((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V))) <=> ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(634,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[633])).
% 0.43/0.56 tff(635,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | (~ssPv1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.43/0.56 tff(636,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.43/0.56 tff(637,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[636, 632])).
% 0.43/0.56 tff(638,plain,(
% 0.43/0.56 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(skolemize,[status(sab)],[637])).
% 0.43/0.56 tff(639,plain,
% 0.43/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[638, 631])).
% 0.43/0.56 tff(640,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(641,plain,
% 0.43/0.56 (((~ssPv4(skf3(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(642,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0)))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[641])).
% 0.43/0.56 tff(643,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))))),
% 0.43/0.56 inference(transitivity,[status(thm)],[642, 640])).
% 0.43/0.56 tff(644,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(645,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0)))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.43/0.56 tff(646,plain,
% 0.43/0.56 ((~ssPv3(skf2(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0)))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[645, 639, 13, 76])).
% 0.43/0.56 tff(647,plain,
% 0.43/0.56 (~ssPv4(skf3(elem!0))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[646, 628, 452, 587])).
% 0.43/0.56 tff(648,plain,
% 0.43/0.56 (ssPv2(elem!0)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[535, 3, 1, 142, 473, 256])).
% 0.43/0.56 tff(649,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(650,plain,
% 0.43/0.56 ((ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(651,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[650])).
% 0.43/0.56 tff(652,plain,
% 0.43/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.56 inference(transitivity,[status(thm)],[651, 649])).
% 0.43/0.56 tff(653,plain,
% 0.43/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(elem!0) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(654,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.43/0.57 tff(655,plain,
% 0.43/0.57 (ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[654, 374, 13, 422])).
% 0.43/0.57 tff(656,plain,
% 0.43/0.57 (~ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[655, 648, 256, 1])).
% 0.43/0.57 tff(657,assumption,(~ssPv1(skf3(elem!0))), introduced(assumption)).
% 0.43/0.57 tff(658,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(659,plain,
% 0.43/0.57 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(660,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[659])).
% 0.43/0.57 tff(661,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[660, 658])).
% 0.43/0.57 tff(662,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(663,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | ssPv2(W) | (~ssRr(W, V)))) | (~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.43/0.57 tff(664,plain,
% 0.43/0.57 ((~ssPv2(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[663, 23, 422])).
% 0.43/0.57 tff(665,plain,
% 0.43/0.57 (ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[664, 656, 142, 3])).
% 0.43/0.57 tff(666,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(667,plain,
% 0.43/0.57 ((ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(668,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[667])).
% 0.43/0.57 tff(669,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[668, 666])).
% 0.43/0.57 tff(670,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(671,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv4(U) | (~ssRr(U, V)) | ssPv3(U) | ssPv3(W) | (~ssRr(U, W)))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.43/0.57 tff(672,plain,
% 0.43/0.57 (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[671, 59, 422])).
% 0.43/0.57 tff(673,plain,
% 0.43/0.57 (ssPv4(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[672, 656, 3, 1])).
% 0.43/0.57 tff(674,plain,
% 0.43/0.57 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(675,plain,
% 0.43/0.57 (ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[674, 74])).
% 0.43/0.57 tff(676,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(677,plain,
% 0.43/0.57 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(678,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0))))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[677])).
% 0.43/0.57 tff(679,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[678, 676])).
% 0.43/0.57 tff(680,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(681,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | ssPv4(skf2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.43/0.57 tff(682,plain,
% 0.43/0.57 ((~ssPv2(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv4(skf2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[681, 268, 422, 675])).
% 0.43/0.57 tff(683,plain,
% 0.43/0.57 (ssPv4(skf2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[682, 665, 142, 673])).
% 0.43/0.57 tff(684,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(685,plain,
% 0.43/0.57 (((~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))) <=> (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(686,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0)))))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[685])).
% 0.43/0.57 tff(687,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[686, 684])).
% 0.43/0.57 tff(688,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0))))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(689,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf2(skf3(skf3(elem!0))))) | (~ssPv4(skf2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.43/0.57 tff(690,plain,
% 0.43/0.57 (ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv4(skf2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[689, 132, 422, 675])).
% 0.43/0.57 tff(691,plain,
% 0.43/0.57 ($false),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[690, 683, 665, 657, 656])).
% 0.43/0.57 tff(692,plain,(ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv4(elem!0) | (~ssPv3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.57 tff(693,plain,
% 0.43/0.57 (ssPv3(skf3(elem!0))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[692, 629, 452, 647, 256, 592])).
% 0.43/0.57 tff(694,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(695,plain,
% 0.43/0.57 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(696,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[695])).
% 0.43/0.57 tff(697,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[696, 694])).
% 0.43/0.57 tff(698,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(699,plain,
% 0.43/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.43/0.57 tff(700,plain,
% 0.43/0.57 (ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0) | ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[699, 392, 13, 422])).
% 0.43/0.57 tff(701,plain,
% 0.43/0.57 (ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[700, 693, 256, 647])).
% 0.43/0.57 tff(702,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(703,plain,
% 0.43/0.57 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(704,plain,
% 0.43/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[703])).
% 0.43/0.58 tff(705,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[704, 702])).
% 0.43/0.58 tff(706,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(707,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.43/0.58 tff(708,plain,
% 0.43/0.58 ((~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[707, 620, 13, 422])).
% 0.43/0.58 tff(709,plain,
% 0.43/0.58 ($false),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[708, 701, 693, 592, 629])).
% 0.43/0.58 tff(710,plain,(ssPv4(skf2(elem!0)) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.58 tff(711,plain,
% 0.43/0.58 (ssPv4(skf2(elem!0))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[710, 256])).
% 0.43/0.58 tff(712,plain,
% 0.43/0.58 (ssPv4(skf2(elem!0))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[451, 4, 256])).
% 0.43/0.58 tff(713,plain,
% 0.43/0.58 (ssPv3(skf3(elem!0))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[119, 2, 4])).
% 0.43/0.58 tff(714,plain,
% 0.43/0.58 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(715,plain,
% 0.43/0.58 ((ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(716,plain,
% 0.43/0.58 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0)))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[715])).
% 0.43/0.58 tff(717,plain,
% 0.43/0.58 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0))),
% 0.43/0.58 inference(transitivity,[status(thm)],[716, 714])).
% 0.43/0.58 tff(718,plain,
% 0.43/0.58 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(719,plain,
% 0.43/0.58 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0)),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.43/0.58 tff(720,plain,
% 0.43/0.58 (ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0) | ssPv4(elem!0)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[719, 356, 13])).
% 0.43/0.58 tff(721,plain,
% 0.43/0.58 (ssPv2(elem!0)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[720, 1, 256, 2])).
% 0.43/0.58 tff(722,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(723,plain,
% 0.43/0.58 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(724,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[723])).
% 0.43/0.58 tff(725,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.43/0.58 inference(transitivity,[status(thm)],[724, 722])).
% 0.43/0.58 tff(726,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(727,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.43/0.58 tff(728,plain,
% 0.43/0.58 (ssPv1(skf2(elem!0)) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[727, 132, 76])).
% 0.43/0.58 tff(729,plain,
% 0.43/0.58 (ssPv1(skf2(elem!0))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[728, 721, 2, 284])).
% 0.43/0.58 tff(730,assumption,(ssPv3(skf3(elem!0))), introduced(assumption)).
% 0.43/0.58 tff(731,plain,
% 0.43/0.58 (~ssPv3(skf2(elem!0))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[419, 1, 730, 2])).
% 0.43/0.58 tff(732,assumption,(ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.43/0.58 tff(733,assumption,(ssPv4(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.43/0.58 tff(734,plain,
% 0.43/0.58 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(735,plain,
% 0.43/0.58 (ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[734, 74])).
% 0.43/0.58 tff(736,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(737,plain,
% 0.43/0.58 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(738,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[737])).
% 0.43/0.58 tff(739,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[738, 736])).
% 0.43/0.58 tff(740,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(741,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv2(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.43/0.58 tff(742,plain,
% 0.43/0.58 ((~ssPv1(skf2(elem!0))) | ssPv4(elem!0) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[741, 227, 76, 735])).
% 0.43/0.58 tff(743,plain,
% 0.43/0.58 (~ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[742, 733, 256, 732])).
% 0.43/0.58 tff(744,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(745,plain,
% 0.43/0.58 ((ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(746,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[745])).
% 0.43/0.58 tff(747,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[746, 744])).
% 0.43/0.58 tff(748,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(749,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(W) | (~ssRr(W, V)) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.43/0.58 tff(750,plain,
% 0.43/0.58 (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[749, 245, 735])).
% 0.43/0.58 tff(751,plain,
% 0.43/0.58 ($false),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[750, 743, 733, 346, 732])).
% 0.43/0.58 tff(752,plain,((~ssPv4(skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.58 tff(753,plain,
% 0.43/0.58 (~ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[752, 731, 729, 256])).
% 0.43/0.58 tff(754,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(755,plain,
% 0.43/0.58 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(756,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[755])).
% 0.43/0.58 tff(757,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[756, 754])).
% 0.43/0.58 tff(758,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(759,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.43/0.58 tff(760,plain,
% 0.43/0.58 (ssPv3(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[759, 171, 735])).
% 0.43/0.58 tff(761,plain,
% 0.43/0.58 (~ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[760, 753, 731, 729])).
% 0.43/0.58 tff(762,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(763,plain,
% 0.43/0.58 ((ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(764,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[763])).
% 0.43/0.58 tff(765,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[764, 762])).
% 0.43/0.58 tff(766,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(767,plain,
% 0.43/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.43/0.58 tff(768,plain,
% 0.43/0.58 ((~ssPv4(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[767, 152, 76, 735])).
% 0.43/0.58 tff(769,plain,
% 0.43/0.58 (ssPv3(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[768, 753, 284, 721])).
% 0.43/0.58 tff(770,assumption,(~ssPv4(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.43/0.58 tff(771,plain,
% 0.43/0.58 (~ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[760, 770, 346, 732])).
% 0.43/0.58 tff(772,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(773,plain,
% 0.43/0.58 ((ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(774,plain,
% 0.43/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[773])).
% 0.43/0.59 tff(775,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[774, 772])).
% 0.43/0.59 tff(776,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | (ssPv2(skf2(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(777,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(V, W)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[776, 775])).
% 0.43/0.59 tff(778,plain,
% 0.43/0.59 (ssPv3(skf2(elem!0)) | ssPv1(elem!0) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[777, 189, 76, 735])).
% 0.43/0.59 tff(779,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[778, 771, 770, 346, 472])).
% 0.43/0.59 tff(780,plain,(ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv1(skf2(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(781,plain,
% 0.43/0.59 (ssPv1(elem!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[780, 753, 731, 729])).
% 0.43/0.59 tff(782,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(783,plain,
% 0.43/0.59 ((ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(784,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[783])).
% 0.43/0.59 tff(785,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[784, 782])).
% 0.43/0.59 tff(786,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (ssPv2(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(787,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv1(V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.43/0.59 tff(788,plain,
% 0.43/0.59 ((~ssPv1(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[787, 207, 76, 735])).
% 0.43/0.59 tff(789,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[788, 781, 769, 729, 761])).
% 0.43/0.59 tff(790,plain,(ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(791,plain,
% 0.43/0.59 (ssPv4(skf3(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[790, 2, 256, 712, 713])).
% 0.43/0.59 tff(792,plain,
% 0.43/0.59 (~ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[429, 791, 256, 2])).
% 0.43/0.59 tff(793,plain,
% 0.43/0.59 (~ssPv1(skf3(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[449, 791, 4, 792])).
% 0.43/0.59 tff(794,plain,
% 0.43/0.59 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(795,plain,
% 0.43/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[794])).
% 0.43/0.59 tff(796,plain,
% 0.43/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(797,plain,
% 0.43/0.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U)) <=> (((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(U))) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(798,plain,
% 0.43/0.59 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[797])).
% 0.43/0.59 tff(799,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssPv4(U))) | ssPv1(V)) | ssPv1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.43/0.59 tff(800,plain,
% 0.43/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.43/0.59 tff(801,plain,
% 0.43/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[800, 796])).
% 0.43/0.59 tff(802,plain,(
% 0.43/0.59 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[801])).
% 0.43/0.59 tff(803,plain,
% 0.43/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[802, 795])).
% 0.43/0.59 tff(804,plain,
% 0.43/0.59 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(805,plain,
% 0.43/0.59 (((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(806,plain,
% 0.43/0.59 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[805])).
% 0.43/0.59 tff(807,plain,
% 0.43/0.59 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[806, 804])).
% 0.43/0.59 tff(808,plain,
% 0.43/0.59 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(809,plain,
% 0.43/0.59 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.43/0.59 tff(810,plain,
% 0.43/0.59 (ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[809, 803, 13])).
% 0.43/0.59 tff(811,plain,
% 0.43/0.59 (ssPv1(elem!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[810, 791, 713, 793])).
% 0.43/0.59 tff(812,plain,
% 0.43/0.59 (ssPv2(skf2(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[252, 161, 284, 2])).
% 0.43/0.59 tff(813,plain,
% 0.43/0.59 (ssPv2(elem!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[109, 346, 2, 812])).
% 0.43/0.59 tff(814,plain,
% 0.43/0.59 (ssPv1(skf2(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[728, 813, 2, 284])).
% 0.43/0.59 tff(815,plain,
% 0.43/0.59 (~ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[752, 814, 346, 256])).
% 0.43/0.59 tff(816,plain,
% 0.43/0.59 (ssPv3(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[768, 815, 284, 813])).
% 0.43/0.59 tff(817,plain,
% 0.43/0.59 (~ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[760, 815, 346, 814])).
% 0.43/0.59 tff(818,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[788, 817, 816, 161, 814])).
% 0.43/0.59 tff(819,plain,(ssPv3(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(820,plain,
% 0.43/0.59 (ssPv3(skf2(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[819, 811, 712, 256, 2])).
% 0.43/0.59 tff(821,plain,
% 0.43/0.59 (ssPv2(elem!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[93, 820, 791, 256])).
% 0.43/0.59 tff(822,plain,
% 0.43/0.59 (ssPv1(skf2(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[728, 821, 2, 712])).
% 0.43/0.59 tff(823,plain,
% 0.43/0.59 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(824,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[823])).
% 0.43/0.59 tff(825,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(826,plain,
% 0.43/0.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(827,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[826])).
% 0.43/0.59 tff(828,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv3(V))) | (~ssPv4(V))) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.43/0.59 tff(829,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.43/0.59 tff(830,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[829, 825])).
% 0.43/0.59 tff(831,plain,(
% 0.43/0.59 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[830])).
% 0.43/0.59 tff(832,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[831, 824])).
% 0.43/0.59 tff(833,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(834,plain,
% 0.43/0.59 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(835,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[834])).
% 0.43/0.59 tff(836,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[835, 833])).
% 0.43/0.59 tff(837,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(838,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[837, 836])).
% 0.43/0.59 tff(839,plain,
% 0.43/0.59 ((~ssPv3(skf2(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[838, 832, 76, 735])).
% 0.43/0.59 tff(840,plain,
% 0.43/0.59 (~ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[839, 820, 712, 2])).
% 0.43/0.59 tff(841,plain,
% 0.43/0.59 (ssPv3(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[768, 840, 712, 821])).
% 0.43/0.59 tff(842,plain,
% 0.43/0.59 (ssPv2(skf2(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[252, 811, 712, 2])).
% 0.43/0.59 tff(843,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(844,plain,
% 0.43/0.59 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(845,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[844])).
% 0.43/0.59 tff(846,plain,
% 0.43/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[845, 843])).
% 0.43/0.59 tff(847,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(848,plain,
% 0.43/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.43/0.59 tff(849,plain,
% 0.43/0.59 ((~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[848, 268, 735])).
% 0.43/0.59 tff(850,plain,
% 0.43/0.59 (~ssPv2(skf2(skf2(elem!0)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[849, 840, 712, 842])).
% 0.43/0.59 tff(851,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[788, 850, 841, 811, 822])).
% 0.43/0.59 tff(852,plain,(ssPv3(elem!0) | ssPv4(elem!0) | ssPv2(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(853,plain,
% 0.43/0.59 (ssPv2(skf3(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[852, 2, 256])).
% 0.43/0.59 tff(854,plain,
% 0.43/0.59 (ssPv4(skf3(elem!0))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[790, 2, 256, 711, 345])).
% 0.43/0.59 tff(855,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[304, 854, 853, 256, 711])).
% 0.43/0.59 tff(856,plain,(ssPv3(elem!0) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(857,plain,
% 0.43/0.59 (ssPv3(elem!0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[856, 256])).
% 0.43/0.59 tff(858,plain,
% 0.43/0.59 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(859,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[858])).
% 0.43/0.59 tff(860,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(861,plain,
% 0.43/0.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> (((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(862,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[861])).
% 0.43/0.59 tff(863,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv4(V))) | ssPv4(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 0.43/0.59 tff(864,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.43/0.59 tff(865,plain,
% 0.43/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[864, 860])).
% 0.43/0.59 tff(866,plain,(
% 0.43/0.59 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[865])).
% 0.43/0.60 tff(867,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[866, 859])).
% 0.43/0.60 tff(868,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(869,plain,
% 0.43/0.60 ((ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(870,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[869])).
% 0.43/0.60 tff(871,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))),
% 0.43/0.60 inference(transitivity,[status(thm)],[870, 868])).
% 0.43/0.60 tff(872,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(873,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.43/0.60 tff(874,plain,
% 0.43/0.60 (ssPv3(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[873, 867, 76])).
% 0.43/0.60 tff(875,plain,
% 0.43/0.60 (ssPv3(skf2(elem!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[874, 857, 711, 256])).
% 0.43/0.60 tff(876,plain,
% 0.43/0.60 (~ssPv2(skf2(elem!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[609, 857, 256, 875])).
% 0.43/0.60 tff(877,plain,
% 0.43/0.60 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) <=> (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(878,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[877])).
% 0.43/0.60 tff(879,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(880,plain,
% 0.43/0.60 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) <=> (((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(U)))), rewrite((((~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) <=> ((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)))), rewrite(((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) <=> (ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V)) <=> ((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) | ssPv4(V)))), rewrite(((ssPv4(U) | (~ssPv4(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V))) | ssPv4(V)) <=> (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V)) <=> (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(881,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[880])).
% 0.43/0.60 tff(882,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(U)) | ssPv3(W)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.43/0.60 tff(883,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.43/0.60 tff(884,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[883, 879])).
% 0.43/0.60 tff(885,plain,(
% 0.43/0.60 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[884])).
% 0.43/0.60 tff(886,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[885, 878])).
% 0.43/0.60 tff(887,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(888,plain,
% 0.43/0.60 ((ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(889,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[888])).
% 0.43/0.60 tff(890,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0))),
% 0.43/0.60 inference(transitivity,[status(thm)],[889, 887])).
% 0.43/0.60 tff(891,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(892,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv4(X)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | ssPv3(W) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.43/0.60 tff(893,plain,
% 0.43/0.60 (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[892, 886, 13, 76])).
% 0.43/0.60 tff(894,plain,
% 0.43/0.60 (ssPv3(skf3(elem!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[893, 1, 256, 284])).
% 0.43/0.60 tff(895,plain,
% 0.43/0.60 (ssPv3(skf2(elem!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[874, 473, 284, 256])).
% 0.43/0.60 tff(896,plain,
% 0.43/0.60 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(897,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[896])).
% 0.43/0.60 tff(898,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(899,plain,
% 0.43/0.60 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) <=> (((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv4(U)))), rewrite((((~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V)) <=> ((ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)))), rewrite(((ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V)) <=> (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(900,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[899])).
% 0.43/0.60 tff(901,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv4(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.43/0.60 tff(902,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.43/0.60 tff(903,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[902, 898])).
% 0.43/0.60 tff(904,plain,(
% 0.43/0.60 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[903])).
% 0.43/0.60 tff(905,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[904, 897])).
% 0.43/0.60 tff(906,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(907,plain,
% 0.43/0.60 ((ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(908,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[907])).
% 0.43/0.60 tff(909,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0))),
% 0.43/0.60 inference(transitivity,[status(thm)],[908, 906])).
% 0.43/0.60 tff(910,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(911,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.43/0.60 tff(912,plain,
% 0.43/0.60 ((~ssPv3(skf2(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[911, 905, 13, 76])).
% 0.43/0.60 tff(913,plain,
% 0.43/0.60 (ssPv2(elem!0)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[912, 1, 284, 895])).
% 0.43/0.60 tff(914,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(915,plain,
% 0.43/0.60 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(916,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[915])).
% 0.43/0.60 tff(917,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[916, 914])).
% 0.43/0.60 tff(918,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(919,plain,
% 0.43/0.60 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.43/0.60 tff(920,plain,
% 0.43/0.60 (ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[919, 602, 13])).
% 0.43/0.60 tff(921,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[920, 913, 894, 473, 1])).
% 0.43/0.60 tff(922,plain,(ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(923,plain,
% 0.43/0.60 (ssPv4(skf3(elem!0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[922, 857, 711, 256])).
% 0.43/0.60 tff(924,plain,
% 0.43/0.60 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(925,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[924])).
% 0.43/0.60 tff(926,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(927,plain,
% 0.43/0.60 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(928,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[927])).
% 0.43/0.60 tff(929,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssPv3(V))) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 0.43/0.60 tff(930,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.43/0.60 tff(931,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[930, 926])).
% 0.43/0.60 tff(932,plain,(
% 0.43/0.60 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[931])).
% 0.43/0.60 tff(933,plain,
% 0.43/0.60 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[932, 925])).
% 0.43/0.60 tff(934,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(935,plain,
% 0.43/0.60 (((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(936,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[935])).
% 0.43/0.60 tff(937,plain,
% 0.43/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[936, 934])).
% 0.43/0.61 tff(938,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(939,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.43/0.61 tff(940,plain,
% 0.43/0.61 ((~ssPv3(skf2(elem!0))) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv3(elem!0))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[939, 933, 13, 76])).
% 0.43/0.61 tff(941,plain,
% 0.43/0.61 (ssPv1(elem!0)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[940, 923, 875, 857])).
% 0.43/0.61 tff(942,plain,
% 0.43/0.61 (~ssPv1(skf3(elem!0))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[214, 941, 876, 875])).
% 0.43/0.61 tff(943,plain,
% 0.43/0.61 (~ssPv2(skf3(elem!0))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[304, 923, 256, 711])).
% 0.43/0.61 tff(944,plain,
% 0.43/0.61 (ssPv2(elem!0)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[93, 923, 875, 256])).
% 0.43/0.61 tff(945,plain,
% 0.43/0.61 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(946,plain,
% 0.43/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[945])).
% 0.43/0.61 tff(947,plain,
% 0.43/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(948,plain,
% 0.43/0.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> (((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W))) | (~ssPv2(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(949,plain,
% 0.43/0.61 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[948])).
% 0.43/0.61 tff(950,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv2(V))) | (~ssPv3(V))) | ssPv2(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.43/0.61 tff(951,plain,
% 0.43/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.43/0.61 tff(952,plain,
% 0.43/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[951, 947])).
% 0.43/0.61 tff(953,plain,(
% 0.43/0.61 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(skolemize,[status(sab)],[952])).
% 0.43/0.61 tff(954,plain,
% 0.43/0.61 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[953, 946])).
% 0.43/0.61 tff(955,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(956,plain,
% 0.43/0.61 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(957,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[956])).
% 0.43/0.61 tff(958,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[957, 955])).
% 0.43/0.61 tff(959,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(960,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.43/0.61 tff(961,plain,
% 0.43/0.61 (ssPv2(skf2(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(elem!0))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[960, 954, 13, 76])).
% 0.43/0.61 tff(962,plain,
% 0.43/0.61 (~ssPv3(skf3(elem!0))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[961, 944, 857, 876])).
% 0.43/0.61 tff(963,plain,
% 0.43/0.61 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(964,plain,
% 0.43/0.61 ((ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0)))) <=> (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(965,plain,
% 0.43/0.61 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[964])).
% 0.43/0.61 tff(966,plain,
% 0.43/0.61 (((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[965, 963])).
% 0.43/0.61 tff(967,plain,
% 0.43/0.61 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(968,plain,
% 0.43/0.61 ((~![V: $i, U: $i] : (ssPv3(V) | ssPv2(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)))) | ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.43/0.61 tff(969,plain,
% 0.43/0.61 (ssPv2(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[968, 41, 422])).
% 0.43/0.61 tff(970,plain,
% 0.43/0.61 (ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[969, 962, 943, 923])).
% 0.43/0.61 tff(971,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(972,plain,
% 0.43/0.61 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(973,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[972])).
% 0.43/0.61 tff(974,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[973, 971])).
% 0.43/0.61 tff(975,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(976,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssRr(U, W)) | ssPv1(W) | (~ssPv2(U)))) | (~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.43/0.61 tff(977,plain,
% 0.43/0.61 ((~ssPv4(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[976, 132, 422])).
% 0.43/0.61 tff(978,plain,
% 0.43/0.61 (ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[977, 970, 923, 942])).
% 0.43/0.61 tff(979,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(980,plain,
% 0.43/0.61 (((~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(981,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[980])).
% 0.43/0.61 tff(982,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[981, 979])).
% 0.43/0.61 tff(983,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(984,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(X)) | (~ssPv3(U)) | ssPv3(V) | (~ssRr(U, V)) | ssPv4(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.43/0.61 tff(985,plain,
% 0.43/0.61 (ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[984, 412, 13, 422])).
% 0.43/0.61 tff(986,plain,
% 0.43/0.61 (ssPv4(skf3(skf3(elem!0)))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[985, 978, 857, 962])).
% 0.43/0.61 tff(987,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(988,plain,
% 0.43/0.61 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(989,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0)))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[988])).
% 0.43/0.61 tff(990,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[989, 987])).
% 0.43/0.61 tff(991,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(992,plain,
% 0.43/0.61 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[991, 990])).
% 0.43/0.61 tff(993,plain,
% 0.43/0.61 (ssPv2(skf3(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[992, 954, 422, 500])).
% 0.43/0.61 tff(994,plain,
% 0.43/0.61 (~ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[993, 978, 943, 970])).
% 0.43/0.61 tff(995,plain,
% 0.43/0.61 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(996,plain,
% 0.43/0.61 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0)))) <=> ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(997,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[996])).
% 0.43/0.62 tff(998,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[997, 995])).
% 0.43/0.62 tff(999,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(1000,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.43/0.62 tff(1001,plain,
% 0.43/0.62 ((~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1000, 832, 422, 500])).
% 0.43/0.62 tff(1002,plain,
% 0.43/0.62 ($false),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1001, 994, 986, 923, 978])).
% 0.43/0.62 tff(1003,plain,(ssPv4(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.62 tff(1004,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1005,plain,
% 0.43/0.62 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1006,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[1005])).
% 0.43/0.62 tff(1007,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.43/0.62 tff(1008,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(1009,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.43/0.62 tff(1010,plain,
% 0.43/0.62 (ssPv4(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv3(elem!0) | (~ssPv4(elem!0))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1009, 867, 13])).
% 0.43/0.62 tff(1011,plain,
% 0.43/0.62 (ssPv4(skf3(elem!0))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1010, 2, 1003, 345])).
% 0.43/0.62 tff(1012,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1013,plain,
% 0.43/0.62 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1014,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[1013])).
% 0.43/0.62 tff(1015,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[1014, 1012])).
% 0.43/0.62 tff(1016,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(1017,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 0.43/0.62 tff(1018,plain,
% 0.43/0.62 ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv4(elem!0)) | ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1017, 832, 13, 422])).
% 0.43/0.62 tff(1019,plain,
% 0.43/0.62 (ssPv3(skf3(skf3(elem!0)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1018, 1011, 1003, 345])).
% 0.43/0.62 tff(1020,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1021,plain,
% 0.43/0.62 ((ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1022,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[1021])).
% 0.43/0.62 tff(1023,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[1022, 1020])).
% 0.43/0.62 tff(1024,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv3(elem!0) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(1025,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv2(U)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.43/0.62 tff(1026,plain,
% 0.43/0.62 (ssPv2(skf3(elem!0)) | ssPv3(elem!0) | (~ssPv4(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1025, 294, 13, 422])).
% 0.43/0.62 tff(1027,plain,
% 0.43/0.62 (~ssPv2(skf3(skf3(elem!0)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1026, 4, 1003, 2])).
% 0.43/0.62 tff(1028,plain,
% 0.43/0.62 (~ssPv1(skf3(elem!0))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[449, 1027, 4, 1011])).
% 0.43/0.62 tff(1029,plain,
% 0.43/0.62 (ssPv1(elem!0)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[810, 1028, 1011, 345])).
% 0.43/0.62 tff(1030,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1031,plain,
% 0.43/0.62 ((ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0)))) <=> ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1032,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[1031])).
% 0.43/0.62 tff(1033,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[1032, 1030])).
% 0.43/0.62 tff(1034,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(1035,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.43/0.62 tff(1036,plain,
% 0.43/0.62 ((~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1035, 905, 422, 500])).
% 0.43/0.62 tff(1037,plain,
% 0.43/0.62 (ssPv4(skf3(skf3(skf3(elem!0))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1036, 1027, 1011, 345])).
% 0.43/0.62 tff(1038,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1039,plain,
% 0.43/0.62 (((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv1(skf3(skf3(elem!0))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0)))) <=> ((~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(1040,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv1(skf3(skf3(elem!0))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[1039])).
% 0.43/0.62 tff(1041,plain,
% 0.43/0.62 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv1(skf3(skf3(elem!0))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[1040, 1038])).
% 0.43/0.62 tff(1042,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0)))) | ssPv1(skf3(skf3(elem!0))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(1043,plain,
% 0.43/0.62 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0))))) | (~ssRr(skf3(skf3(skf3(elem!0))), skf3(skf3(elem!0))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.43/0.62 tff(1044,plain,
% 0.43/0.62 ((~ssPv3(skf3(elem!0))) | ssPv1(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(skf3(elem!0)))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1043, 933, 422, 500])).
% 0.43/0.62 tff(1045,plain,
% 0.43/0.62 (ssPv1(skf3(skf3(elem!0)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[1044, 1037, 345, 1019])).
% 0.43/0.62 tff(1046,plain,
% 0.43/0.62 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(1047,plain,
% 0.43/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[1046])).
% 0.43/0.63 tff(1048,plain,
% 0.43/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(1049,plain,
% 0.43/0.63 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> (((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> (((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv3(V))))), rewrite((((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv3(V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(1050,plain,
% 0.43/0.63 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[1049])).
% 0.43/0.63 tff(1051,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv3(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.43/0.63 tff(1052,plain,
% 0.43/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 0.43/0.63 tff(1053,plain,
% 0.43/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[1052, 1048])).
% 0.43/0.63 tff(1054,plain,(
% 0.43/0.63 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(skolemize,[status(sab)],[1053])).
% 0.43/0.63 tff(1055,plain,
% 0.43/0.63 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[1054, 1047])).
% 0.43/0.63 tff(1056,plain,
% 0.43/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(1057,plain,
% 0.43/0.63 (((~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(1058,plain,
% 0.43/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[1057])).
% 0.43/0.63 tff(1059,plain,
% 0.43/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.43/0.63 inference(transitivity,[status(thm)],[1058, 1056])).
% 0.43/0.63 tff(1060,plain,
% 0.43/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.43/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(1061,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.53/0.63 tff(1062,plain,
% 0.53/0.63 ((~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1061, 1055, 13, 422])).
% 0.53/0.63 tff(1063,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1062, 1045, 1029, 345, 1019])).
% 0.53/0.63 tff(1064,plain,(ssPv2(skf3(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(1065,plain,
% 0.53/0.63 (ssPv2(skf3(elem!0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1064, 2])).
% 0.53/0.63 tff(1066,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1067,plain,
% 0.53/0.63 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0)) <=> ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1068,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[1067])).
% 0.53/0.63 tff(1069,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[1068, 1066])).
% 0.53/0.63 tff(1070,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(1071,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv2(W))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.53/0.63 tff(1072,plain,
% 0.53/0.63 ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1071, 954, 13, 422])).
% 0.53/0.63 tff(1073,plain,
% 0.53/0.63 (ssPv2(elem!0)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1072, 1065, 1019, 345])).
% 0.53/0.63 tff(1074,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1075,plain,
% 0.53/0.63 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1076,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[1075])).
% 0.53/0.63 tff(1077,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(transitivity,[status(thm)],[1076, 1074])).
% 0.53/0.63 tff(1078,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(1079,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 0.53/0.63 tff(1080,plain,
% 0.53/0.63 ((~ssPv2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1079, 268, 76])).
% 0.53/0.63 tff(1081,plain,
% 0.53/0.63 (~ssPv2(skf2(elem!0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1080, 121, 1003, 1073])).
% 0.53/0.63 tff(1082,plain,
% 0.53/0.63 (~ssPv1(elem!0)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[216, 121, 1003, 1065, 2])).
% 0.53/0.63 tff(1083,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1084,plain,
% 0.53/0.63 (((~ssPv4(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1085,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[1084])).
% 0.53/0.63 tff(1086,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(transitivity,[status(thm)],[1085, 1083])).
% 0.53/0.63 tff(1087,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssPv4(elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(1088,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | ssPv1(X) | (~ssRr(X, V)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 0.53/0.63 tff(1089,plain,
% 0.53/0.63 (ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1088, 576, 76])).
% 0.53/0.63 tff(1090,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1089, 1082, 1081, 1003, 1073])).
% 0.53/0.63 tff(1091,plain,(ssPv4(skf2(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(1092,plain,
% 0.53/0.63 (ssPv4(skf2(elem!0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1091, 2])).
% 0.53/0.63 tff(1093,plain,
% 0.53/0.63 (ssPv1(skf2(elem!0))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[728, 1092, 2, 1073])).
% 0.53/0.63 tff(1094,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1095,plain,
% 0.53/0.63 (((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1096,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[1095])).
% 0.53/0.63 tff(1097,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.53/0.63 tff(1098,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(elem!0))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(1099,plain,
% 0.53/0.63 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.53/0.63 tff(1100,plain,
% 0.53/0.63 ((~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1099, 639, 76, 735])).
% 0.53/0.63 tff(1101,plain,
% 0.53/0.63 (~ssPv3(skf2(skf2(elem!0)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[1100, 1093, 1003, 1073])).
% 0.53/0.63 tff(1102,plain,
% 0.53/0.63 (ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[768, 1101, 1092, 1073])).
% 0.53/0.63 tff(1103,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1104,plain,
% 0.53/0.63 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(1105,plain,
% 0.53/0.63 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[1104])).
% 0.53/0.64 tff(1106,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[1105, 1103])).
% 0.53/0.64 tff(1107,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(1108,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0)))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.53/0.64 tff(1109,plain,
% 0.53/0.64 ((~ssPv1(skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv1(skf2(skf2(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1108, 316, 76, 735])).
% 0.53/0.64 tff(1110,plain,
% 0.53/0.64 (ssPv1(skf2(skf2(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1109, 1093, 1003, 1092])).
% 0.53/0.64 tff(1111,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1112,plain,
% 0.53/0.64 (((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1113,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[1112])).
% 0.53/0.64 tff(1114,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[1113, 1111])).
% 0.53/0.64 tff(1115,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(1116,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.53/0.64 tff(1117,plain,
% 0.53/0.64 ((~ssPv1(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1116, 335, 76, 735])).
% 0.53/0.64 tff(1118,plain,
% 0.53/0.64 (~ssPv2(skf2(skf2(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1117, 1110, 1073, 1093])).
% 0.53/0.64 tff(1119,plain,
% 0.53/0.64 (~ssPv3(skf2(elem!0))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[839, 1102, 2, 1092])).
% 0.53/0.64 tff(1120,plain,
% 0.53/0.64 ($false),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[750, 1119, 1118, 1093, 1102])).
% 0.53/0.64 tff(1121,plain,(ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.64 tff(1122,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1123,plain,
% 0.53/0.64 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1124,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[1123])).
% 0.53/0.64 tff(1125,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0)))),
% 0.53/0.64 inference(transitivity,[status(thm)],[1124, 1122])).
% 0.53/0.64 tff(1126,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(1127,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv3(U) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.53/0.64 tff(1128,plain,
% 0.53/0.64 (ssPv3(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv4(elem!0))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1127, 832, 13, 76])).
% 0.53/0.64 tff(1129,plain,
% 0.53/0.64 (~ssPv4(skf2(elem!0))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1128, 3, 1003, 1121])).
% 0.53/0.64 tff(1130,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1131,plain,
% 0.53/0.64 ((ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1132,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[1131])).
% 0.53/0.64 tff(1133,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.53/0.64 tff(1134,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(1135,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(U) | (~ssPv3(X)) | (~ssRr(U, V)) | ssPv2(V) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.53/0.64 tff(1136,plain,
% 0.53/0.64 (ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | ssPv4(skf3(skf3(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1135, 905, 13, 422])).
% 0.53/0.64 tff(1137,plain,
% 0.53/0.64 (ssPv4(skf3(skf3(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1136, 4, 1003, 1121])).
% 0.53/0.64 tff(1138,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1139,plain,
% 0.53/0.64 ((ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0))) <=> (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1140,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[1139])).
% 0.53/0.64 tff(1141,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[1140, 1138])).
% 0.53/0.64 tff(1142,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv4(skf3(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(1143,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | ssPv2(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.53/0.64 tff(1144,plain,
% 0.53/0.64 (ssPv2(skf3(elem!0)) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1143, 86, 13, 422])).
% 0.53/0.64 tff(1145,plain,
% 0.53/0.64 (ssPv4(skf3(elem!0))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1144, 1137, 4, 1121])).
% 0.53/0.64 tff(1146,assumption,(ssPv2(skf3(skf3(elem!0)))), introduced(assumption)).
% 0.53/0.64 tff(1147,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1148,plain,
% 0.53/0.64 (((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.64 inference(rewrite,[status(thm)],[])).
% 0.53/0.64 tff(1149,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))))),
% 0.53/0.64 inference(monotonicity,[status(thm)],[1148])).
% 0.53/0.64 tff(1150,plain,
% 0.53/0.64 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.64 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.53/0.64 tff(1151,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv1(skf3(elem!0))))),
% 0.53/0.64 inference(quant_inst,[status(thm)],[])).
% 0.53/0.64 tff(1152,plain,
% 0.53/0.64 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv3(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)) | (~ssPv1(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.64 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.53/0.64 tff(1153,plain,
% 0.53/0.64 ((~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1152, 639, 13, 422])).
% 0.53/0.64 tff(1154,plain,
% 0.53/0.64 (~ssPv1(skf3(elem!0))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1153, 1146, 1121, 1137])).
% 0.53/0.64 tff(1155,plain,
% 0.53/0.64 (ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[977, 1154, 1145, 1146])).
% 0.53/0.64 tff(1156,plain,
% 0.53/0.64 (~ssPv3(skf3(skf3(skf3(elem!0))))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[993, 1155, 4, 1146])).
% 0.53/0.64 tff(1157,plain,
% 0.53/0.64 ($false),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1001, 1156, 1155, 1145, 1137])).
% 0.53/0.64 tff(1158,plain,((~ssPv2(skf3(skf3(elem!0)))) | ssPv2(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.64 tff(1159,plain,
% 0.53/0.64 (~ssPv2(skf3(skf3(elem!0)))),
% 0.53/0.64 inference(unit_resolution,[status(thm)],[1158, 4])).
% 0.53/0.65 tff(1160,plain,
% 0.53/0.65 (~ssPv1(skf3(elem!0))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[449, 1159, 4, 1145])).
% 0.53/0.65 tff(1161,plain,
% 0.53/0.65 (ssPv3(skf3(elem!0))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[969, 1159, 4, 1145])).
% 0.53/0.65 tff(1162,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1163,plain,
% 0.53/0.65 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1164,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1163])).
% 0.53/0.65 tff(1165,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.65 inference(transitivity,[status(thm)],[1164, 1162])).
% 0.53/0.65 tff(1166,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1167,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.53/0.65 tff(1168,plain,
% 0.53/0.65 ((~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1167, 933, 13, 422])).
% 0.53/0.65 tff(1169,plain,
% 0.53/0.65 ($false),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1168, 1161, 1160, 1121, 1137])).
% 0.53/0.65 tff(1170,plain,(ssPv2(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.65 tff(1171,plain,
% 0.53/0.65 (ssPv3(skf2(elem!0))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[159, 1129, 1003, 1170])).
% 0.53/0.65 tff(1172,plain,
% 0.53/0.65 (ssPv1(elem!0)),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[139, 3, 1003, 1170])).
% 0.53/0.65 tff(1173,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1174,plain,
% 0.53/0.65 (((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1175,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1174])).
% 0.53/0.65 tff(1176,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(transitivity,[status(thm)],[1175, 1173])).
% 0.53/0.65 tff(1177,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1178,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 0.53/0.65 tff(1179,plain,
% 0.53/0.65 ((~ssPv3(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv1(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1178, 1055, 76, 735])).
% 0.53/0.65 tff(1180,plain,
% 0.53/0.65 (~ssPv1(skf2(skf2(elem!0)))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1179, 1172, 1121, 1171])).
% 0.53/0.65 tff(1181,plain,
% 0.53/0.65 (ssPv3(skf2(elem!0))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[159, 121, 1003, 1170])).
% 0.53/0.65 tff(1182,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1183,plain,
% 0.53/0.65 ((ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1184,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1183])).
% 0.53/0.65 tff(1185,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(transitivity,[status(thm)],[1184, 1182])).
% 0.53/0.65 tff(1186,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1187,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | ssPv4(W) | (~ssRr(W, V)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 0.53/0.65 tff(1188,plain,
% 0.53/0.65 ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1187, 867, 735])).
% 0.53/0.65 tff(1189,plain,
% 0.53/0.65 (ssPv3(skf2(skf2(elem!0)))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1188, 733, 121, 1181])).
% 0.53/0.65 tff(1190,assumption,(~ssPv1(skf2(skf2(elem!0)))), introduced(assumption)).
% 0.53/0.65 tff(1191,plain,
% 0.53/0.65 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1192,plain,
% 0.53/0.65 (ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1191, 74])).
% 0.53/0.65 tff(1193,plain,
% 0.53/0.65 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1194,plain,
% 0.53/0.65 (((~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1195,plain,
% 0.53/0.65 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1194])).
% 0.53/0.65 tff(1196,plain,
% 0.53/0.65 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(transitivity,[status(thm)],[1195, 1193])).
% 0.53/0.65 tff(1197,plain,
% 0.53/0.65 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1198,plain,
% 0.53/0.65 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | ssPv1(skf2(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.53/0.65 tff(1199,plain,
% 0.53/0.65 ((~ssPv3(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1198, 803, 1192])).
% 0.53/0.65 tff(1200,plain,
% 0.53/0.65 (ssPv1(skf2(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1199, 1189, 1190, 733])).
% 0.53/0.65 tff(1201,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1202,plain,
% 0.53/0.65 (((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1203,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1202])).
% 0.53/0.65 tff(1204,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(transitivity,[status(thm)],[1203, 1201])).
% 0.53/0.65 tff(1205,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1206,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.53/0.65 tff(1207,plain,
% 0.53/0.65 ((~ssPv3(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1206, 933, 76, 735])).
% 0.53/0.65 tff(1208,plain,
% 0.53/0.65 (ssPv1(skf2(elem!0))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1207, 1189, 1003, 1181])).
% 0.53/0.65 tff(1209,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv1(skf2(skf2(skf2(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv1(skf2(skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1210,plain,
% 0.53/0.65 (((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv1(skf2(skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1211,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv1(skf2(skf2(skf2(elem!0)))))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1210])).
% 0.53/0.65 tff(1212,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv1(skf2(skf2(skf2(elem!0))))))),
% 0.53/0.65 inference(transitivity,[status(thm)],[1211, 1209])).
% 0.53/0.65 tff(1213,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(skf2(elem!0))))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))))),
% 0.53/0.65 inference(quant_inst,[status(thm)],[])).
% 0.53/0.65 tff(1214,plain,
% 0.53/0.65 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(skf2(elem!0)), skf2(skf2(skf2(elem!0))))) | (~ssPv1(skf2(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.53/0.65 tff(1215,plain,
% 0.53/0.65 ((~ssPv3(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1214, 1055, 735, 1192])).
% 0.53/0.65 tff(1216,plain,
% 0.53/0.65 ($false),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1215, 1208, 1200, 1181, 1189])).
% 0.53/0.65 tff(1217,plain,((~ssPv4(skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.65 tff(1218,plain,
% 0.53/0.65 (~ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.65 inference(unit_resolution,[status(thm)],[1217, 1180, 1129])).
% 0.53/0.65 tff(1219,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1220,plain,
% 0.53/0.65 ((ssPv4(skf2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.65 inference(rewrite,[status(thm)],[])).
% 0.53/0.65 tff(1221,plain,
% 0.53/0.65 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.53/0.65 inference(monotonicity,[status(thm)],[1220])).
% 0.53/0.66 tff(1222,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1221, 1219])).
% 0.53/0.66 tff(1223,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1224,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | ssPv4(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 0.53/0.66 tff(1225,plain,
% 0.53/0.66 ((~ssPv3(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1224, 374, 76, 735])).
% 0.53/0.66 tff(1226,plain,
% 0.53/0.66 (~ssPv2(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1225, 1218, 1129, 1121])).
% 0.53/0.66 tff(1227,plain,
% 0.53/0.66 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1228,plain,
% 0.53/0.66 ((ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1229,plain,
% 0.53/0.66 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[1228])).
% 0.53/0.66 tff(1230,plain,
% 0.53/0.66 (((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1229, 1227])).
% 0.53/0.66 tff(1231,plain,
% 0.53/0.66 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1232,plain,
% 0.53/0.66 ((~![V: $i, U: $i] : (ssPv4(V) | ssPv3(V) | ssPv2(V) | ssPv4(U) | (~ssRr(U, V)))) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.53/0.66 tff(1233,plain,
% 0.53/0.66 (ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | ssPv2(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1232, 356, 735])).
% 0.53/0.66 tff(1234,plain,
% 0.53/0.66 (ssPv3(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1233, 1226, 1129, 1218])).
% 0.53/0.66 tff(1235,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1236,plain,
% 0.53/0.66 ((ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1237,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[1236])).
% 0.53/0.66 tff(1238,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1237, 1235])).
% 0.53/0.66 tff(1239,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1240,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i] : (ssPv4(V) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv3(V)) | ssPv4(W) | (~ssRr(V, W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.53/0.66 tff(1241,plain,
% 0.53/0.66 ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1240, 392, 76, 735])).
% 0.53/0.66 tff(1242,plain,
% 0.53/0.66 (ssPv2(elem!0)),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1241, 1218, 1129, 1171])).
% 0.53/0.66 tff(1243,plain,
% 0.53/0.66 (~ssPv1(skf2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[788, 1226, 1172, 1234])).
% 0.53/0.66 tff(1244,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1245,plain,
% 0.53/0.66 (((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1246,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[1245])).
% 0.53/0.66 tff(1247,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.53/0.66 tff(1248,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1249,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | (~ssPv3(V)) | (~ssRr(V, W)) | (~ssPv2(U)) | (~ssPv3(W)))) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.53/0.66 tff(1250,plain,
% 0.53/0.66 ((~ssPv3(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1249, 620, 76, 735])).
% 0.53/0.66 tff(1251,plain,
% 0.53/0.66 ($false),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1250, 1243, 1242, 1171, 1234])).
% 0.53/0.66 tff(1252,plain,(ssPv3(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.66 tff(1253,plain,
% 0.53/0.66 (ssPv4(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[920, 1121, 1252])).
% 0.53/0.66 tff(1254,plain,
% 0.53/0.66 (~ssPv2(elem!0)),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1253, 1])).
% 0.53/0.66 tff(1255,plain,
% 0.53/0.66 (ssPv2(elem!0) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1072, 1170, 1252])).
% 0.53/0.66 tff(1256,plain,
% 0.53/0.66 (~ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1255, 1254])).
% 0.53/0.66 tff(1257,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1258,plain,
% 0.53/0.66 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0))))) <=> ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1259,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[1258])).
% 0.53/0.66 tff(1260,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1259, 1257])).
% 0.53/0.66 tff(1261,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv3(skf3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1262,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv3(U) | (~ssPv2(V)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv1(U)))) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.53/0.66 tff(1263,plain,
% 0.53/0.66 ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1262, 171, 422])).
% 0.53/0.66 tff(1264,plain,
% 0.53/0.66 (ssPv4(skf3(elem!0)) | (~ssPv1(skf3(skf3(elem!0)))) | ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1263, 1170])).
% 0.53/0.66 tff(1265,plain,
% 0.53/0.66 (~ssPv1(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1264, 1256, 1])).
% 0.53/0.66 tff(1266,plain,
% 0.53/0.66 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1267,plain,
% 0.53/0.66 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1268,plain,
% 0.53/0.66 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[1267])).
% 0.53/0.66 tff(1269,plain,
% 0.53/0.66 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1268, 1266])).
% 0.53/0.66 tff(1270,plain,
% 0.53/0.66 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(skf3(elem!0))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1271,plain,
% 0.53/0.66 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv1(U) | (~ssPv3(V)) | (~ssPv2(V)))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 0.53/0.66 tff(1272,plain,
% 0.53/0.66 ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1271, 554, 422])).
% 0.53/0.66 tff(1273,plain,
% 0.53/0.66 (ssPv1(skf3(elem!0)) | ssPv1(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1272, 1170, 1252])).
% 0.53/0.66 tff(1274,plain,
% 0.53/0.66 (ssPv1(skf3(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1273, 1265])).
% 0.53/0.66 tff(1275,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1276,plain,
% 0.53/0.66 (((~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.53/0.66 inference(rewrite,[status(thm)],[])).
% 0.53/0.66 tff(1277,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0)))))),
% 0.53/0.66 inference(monotonicity,[status(thm)],[1276])).
% 0.53/0.66 tff(1278,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.53/0.66 inference(transitivity,[status(thm)],[1277, 1275])).
% 0.53/0.66 tff(1279,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv3(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.53/0.66 inference(quant_inst,[status(thm)],[])).
% 0.53/0.66 tff(1280,plain,
% 0.53/0.66 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssRr(U, V)) | (~ssPv1(X)) | (~ssPv3(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.53/0.66 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.53/0.66 tff(1281,plain,
% 0.53/0.66 ((~ssPv1(skf2(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1280, 1055, 13, 76])).
% 0.53/0.66 tff(1282,plain,
% 0.53/0.66 ((~ssPv1(skf2(elem!0))) | (~ssPv1(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1281, 1121, 1252])).
% 0.53/0.66 tff(1283,plain,
% 0.53/0.66 (~ssPv1(skf2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1282, 1274])).
% 0.53/0.66 tff(1284,plain,
% 0.53/0.66 (ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[159, 1003, 1170])).
% 0.53/0.66 tff(1285,plain,
% 0.53/0.66 (ssPv3(skf2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1284, 121])).
% 0.53/0.66 tff(1286,plain,
% 0.53/0.66 (ssPv4(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1241, 121, 474, 1285])).
% 0.53/0.66 tff(1287,assumption,(~ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.53/0.66 tff(1288,plain,
% 0.53/0.66 ((~ssPv3(skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1207, 1003])).
% 0.53/0.66 tff(1289,plain,
% 0.53/0.66 (~ssPv3(skf2(skf2(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1288, 1285, 1287])).
% 0.53/0.66 tff(1290,plain,
% 0.53/0.66 ($false),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1188, 1289, 1286, 121, 1285])).
% 0.53/0.66 tff(1291,plain,(ssPv4(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.66 tff(1292,plain,
% 0.53/0.66 (ssPv4(skf2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1291, 1283, 1254])).
% 0.53/0.66 tff(1293,plain,
% 0.53/0.66 (ssPv3(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv2(elem!0)),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[301, 1170])).
% 0.53/0.66 tff(1294,plain,
% 0.53/0.66 (ssPv3(skf2(elem!0))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1293, 1292, 1254])).
% 0.53/0.66 tff(1295,plain,
% 0.53/0.66 ($false),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[912, 1294, 1292, 1, 1254])).
% 0.53/0.66 tff(1296,plain,(ssPv4(skf3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.66 tff(1297,plain,
% 0.53/0.66 ((~ssPv4(skf3(elem!0))) | ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1018, 1003, 1252])).
% 0.53/0.66 tff(1298,plain,
% 0.53/0.66 (ssPv3(skf3(skf3(elem!0)))),
% 0.53/0.66 inference(unit_resolution,[status(thm)],[1297, 1296])).
% 0.53/0.66 tff(1299,plain,
% 0.53/0.66 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(1300,plain,
% 0.53/0.67 ((ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0)))) <=> ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(1301,plain,
% 0.53/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))))),
% 0.53/0.67 inference(monotonicity,[status(thm)],[1300])).
% 0.53/0.67 tff(1302,plain,
% 0.53/0.67 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.53/0.67 inference(transitivity,[status(thm)],[1301, 1299])).
% 0.53/0.67 tff(1303,plain,
% 0.53/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(elem!0))))),
% 0.53/0.67 inference(quant_inst,[status(thm)],[])).
% 0.53/0.67 tff(1304,plain,
% 0.53/0.67 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.67 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 0.53/0.67 tff(1305,plain,
% 0.53/0.67 ((~ssPv2(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1304, 602, 422])).
% 0.53/0.67 tff(1306,plain,
% 0.53/0.67 (ssPv4(skf3(skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1305, 1170, 1252])).
% 0.53/0.67 tff(1307,plain,
% 0.53/0.67 (ssPv4(skf3(skf3(elem!0)))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1306, 1298])).
% 0.53/0.67 tff(1308,plain,
% 0.53/0.67 (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1168, 1121, 1252])).
% 0.53/0.67 tff(1309,plain,
% 0.53/0.67 (ssPv1(skf3(elem!0))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1308, 1307])).
% 0.53/0.67 tff(1310,plain,
% 0.53/0.67 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(1311,plain,
% 0.53/0.67 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0)) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(1312,plain,
% 0.53/0.67 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))))),
% 0.53/0.67 inference(monotonicity,[status(thm)],[1311])).
% 0.53/0.67 tff(1313,plain,
% 0.53/0.67 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.53/0.67 inference(transitivity,[status(thm)],[1312, 1310])).
% 0.53/0.67 tff(1314,plain,
% 0.53/0.67 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0))),
% 0.53/0.67 inference(quant_inst,[status(thm)],[])).
% 0.53/0.67 tff(1315,plain,
% 0.53/0.67 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv4(U)) | (~ssRr(V, W)) | ssPv1(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.67 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.53/0.67 tff(1316,plain,
% 0.53/0.67 (ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1315, 316, 13, 422])).
% 0.53/0.67 tff(1317,plain,
% 0.53/0.67 (ssPv1(elem!0)),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1316, 1307, 1296, 1309])).
% 0.53/0.67 tff(1318,plain,
% 0.53/0.67 (~ssPv1(skf2(elem!0))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1282, 1309])).
% 0.53/0.67 tff(1319,plain,
% 0.53/0.67 ((~ssPv1(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv1(skf2(elem!0))),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[323, 1003])).
% 0.53/0.67 tff(1320,plain,
% 0.53/0.67 ($false),
% 0.53/0.67 inference(unit_resolution,[status(thm)],[1319, 1318, 1317, 1296])).
% 0.53/0.67 % SZS output end Proof
%------------------------------------------------------------------------------