TSTP Solution File: SYN796-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN796-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:57:19 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN796-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.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 07:36:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(ssPv2_type, type, (
% 0.20/0.44 ssPv2: $i > $o)).
% 0.20/0.44 tff(skf2_type, type, (
% 0.20/0.44 skf2: $i > $i)).
% 0.20/0.44 tff(elem_0_type, type, (
% 0.20/0.44 elem_0: $i)).
% 0.20/0.44 tff(ssPv3_type, type, (
% 0.20/0.44 ssPv3: $i > $o)).
% 0.20/0.44 tff(skf3_type, type, (
% 0.20/0.44 skf3: $i > $i)).
% 0.20/0.44 tff(ssPv1_type, type, (
% 0.20/0.44 ssPv1: $i > $o)).
% 0.20/0.44 tff(ssPv4_type, type, (
% 0.20/0.44 ssPv4: $i > $o)).
% 0.20/0.44 tff(ssRr_type, type, (
% 0.20/0.44 ssRr: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,assumption,(~ssPv2(skf2(elem!0))), introduced(assumption)).
% 0.20/0.44 tff(2,assumption,(~ssPv1(elem!0)), introduced(assumption)).
% 0.20/0.44 tff(3,assumption,(~ssPv3(elem!0)), introduced(assumption)).
% 0.20/0.44 tff(4,assumption,(~ssPv2(elem!0)), introduced(assumption)).
% 0.20/0.44 tff(5,assumption,(ssPv2(skf2(elem!0))), introduced(assumption)).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (^[U: $i] : refl(ssRr(U, skf2(U)) <=> ssRr(U, skf2(U)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![U: $i] : ssRr(U, skf2(U)) <=> ![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(9,axiom,(![U: $i] : ssRr(U, skf2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.44 tff(11,plain,(
% 0.20/0.44 ![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.44 inference(skolemize,[status(sab)],[10])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (![U: $i] : ssRr(U, skf2(U))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(elem!0, skf2(elem!0))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (ssRr(elem!0, skf2(elem!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (^[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(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv2(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.45 tff(20,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv2(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.45 tff(23,plain,(
% 0.20/0.45 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[22])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 ((ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (ssPv1(elem!0) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))) | (~ssPv2(skf2(elem!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[30, 24, 14])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (~ssPv4(skf2(elem!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[31, 4, 5, 2])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (^[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))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv2(V))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.45 tff(38,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv2(V))) | ssPv2(U)) | ssPv1(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.45 tff(41,plain,(
% 0.20/0.45 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[40])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (ssPv1(skf2(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[48, 42, 14])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (ssPv1(skf2(elem!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[49, 4, 5, 32])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (^[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(W))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.45 tff(56,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.45 tff(59,plain,(
% 0.20/0.45 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[58])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 ((ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 ((~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[66, 60, 14])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[67, 50, 4, 3, 5])).
% 0.20/0.45 tff(69,plain,(ssPv2(elem!0) | ssPv3(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (~ssPv2(skf2(elem!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[69, 4, 2, 3])).
% 0.20/0.45 tff(71,assumption,(~ssPv3(skf3(elem!0))), introduced(assumption)).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (^[U: $i] : refl(ssRr(skf3(U), U) <=> ssRr(skf3(U), U))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![U: $i] : ssRr(skf3(U), U) <=> ![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(75,axiom,(![U: $i] : ssRr(skf3(U), U)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.45 tff(77,plain,(
% 0.20/0.45 ![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.45 inference(skolemize,[status(sab)],[76])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![U: $i] : ssRr(skf3(U), U)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(elem!0), elem!0)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (ssRr(skf3(elem!0), elem!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (^[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))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.46 tff(86,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv1(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.46 tff(89,plain,(
% 0.20/0.46 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[88])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | ssPv3(elem!0) | ssPv2(skf2(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[96, 90, 80, 14])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (~ssPv2(skf3(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 2, 3, 1])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (^[V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) <=> (((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | (~ssPv4(U))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U)) <=> (((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.46 tff(104,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(U))) | ssPv1(V)) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.46 tff(107,plain,(
% 0.20/0.46 ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[106])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[114, 108, 80])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (~ssPv4(skf3(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[115, 98, 2, 71])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (^[V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) <=> ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (^[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)) | ssPv1(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V)) <=> ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.46 tff(122,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(U)) | ssPv1(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.46 tff(125,plain,(
% 0.20/0.46 ![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[124])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[129, 127])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv4(elem!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv3(elem!0) | (~ssPv4(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[132, 126, 80])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (~ssPv4(elem!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[133, 98, 3, 2])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (ssPv2(skf3(elem!0)) | ssPv1(elem!0) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[137, 42, 80])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (~ssPv2(elem!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[138, 134, 2, 98])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> ((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W))) | ssPv1(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W))) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V)) <=> ((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W))) | ssPv2(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W))) | ssPv2(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.46 tff(145,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.20/0.46 tff(148,plain,(
% 0.20/0.46 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[147])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (ssPv1(elem!0) | ssPv4(skf3(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[155, 149, 80, 14])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[156, 139, 116, 1, 2])).
% 0.20/0.46 tff(158,plain,(ssPv1(elem!0) | ssPv2(skf2(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (ssPv3(skf3(elem!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[158, 70, 2, 3])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (^[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)) | (~ssRr(V, W)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(U))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(U))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(U))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.46 tff(165,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(V, W))) | (~ssPv4(V))) | ssPv2(W)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.20/0.46 tff(168,plain,(
% 0.20/0.46 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[167])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[172, 170])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (ssPv3(elem!0) | (~ssPv3(skf3(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[175, 169, 80, 14])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (~ssPv4(elem!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[176, 159, 3, 70])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 (ssPv4(skf3(elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[156, 70, 4, 2])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[179])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (^[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))) | (~ssPv3(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv3(X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V)) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv1(V)))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv1(V)) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V)) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.47 tff(184,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv3(X))) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.20/0.47 tff(187,plain,(
% 0.20/0.47 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[186])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 (((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[190])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[191, 189])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 (ssPv1(elem!0) | (~ssPv3(skf2(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[194, 188, 80, 14])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 (~ssPv3(skf2(elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[195, 178, 2, 159])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (^[V: $i, U: $i] : refl((ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) <=> (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[197])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) <=> ((ssPv3(V) | (~ssRr(U, V))) | ssPv1(U)))), rewrite(((ssPv3(V) | (~ssRr(U, V))) | ssPv1(U)) <=> (ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) <=> (ssPv1(U) | ssPv3(V) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) <=> ((ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv3(U)))), rewrite(((ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv4(U)))), rewrite(((ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V))) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U)) <=> ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[200])).
% 0.20/0.47 tff(202,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | ssPv3(V)) | ssPv1(U)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.20/0.47 tff(205,plain,(
% 0.20/0.47 ![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[204])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 (![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 ((ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0))),
% 0.20/0.47 inference(transitivity,[status(thm)],[209, 207])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(elem!0) | ssPv3(elem!0) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(212,plain,
% 0.20/0.47 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.47 tff(213,plain,
% 0.20/0.47 (ssPv1(elem!0) | ssPv3(skf2(elem!0)) | ssPv3(elem!0) | ssPv4(elem!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[212, 206, 14])).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[213, 196, 177, 3, 2])).
% 0.20/0.47 tff(215,plain,(ssPv2(elem!0) | ssPv3(elem!0) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 (ssPv2(elem!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[215, 2, 3])).
% 0.20/0.47 tff(217,assumption,(ssPv2(elem!0)), introduced(assumption)).
% 0.20/0.47 tff(218,assumption,(~ssPv2(skf3(elem!0))), introduced(assumption)).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (~ssPv4(elem!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[133, 218, 3, 2])).
% 0.20/0.47 tff(220,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[138, 219, 218, 2, 217])).
% 0.20/0.47 tff(221,plain,(ssPv2(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (ssPv2(skf3(elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[221, 216, 2, 3])).
% 0.20/0.47 tff(223,plain,
% 0.20/0.47 (ssPv2(skf2(elem!0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[97, 222, 3, 2])).
% 0.20/0.47 tff(224,assumption,(~ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 ((~![U: $i] : ssRr(U, skf2(U))) | ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (ssRr(skf2(elem!0), skf2(skf2(elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[225, 12])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[227])).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 (^[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))) | (~ssPv2(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(V)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(231,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[230])).
% 0.20/0.47 tff(232,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.20/0.47 tff(235,plain,(
% 0.20/0.47 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[234])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.20/0.47 tff(237,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 ((ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[238])).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[239, 237])).
% 0.20/0.47 tff(241,plain,
% 0.20/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(242,plain,
% 0.20/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.20/0.47 tff(243,plain,
% 0.20/0.47 (ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[242, 236, 14, 226])).
% 0.20/0.47 tff(244,plain,
% 0.20/0.47 (~ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[243, 224, 2, 5])).
% 0.20/0.47 tff(245,plain,
% 0.20/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(246,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[245])).
% 0.20/0.47 tff(247,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(248,plain,
% 0.20/0.47 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv4(W)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W))) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) | ssPv1(V)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W)) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V)) <=> (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(249,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[248])).
% 0.20/0.47 tff(250,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(V))) | ssPv1(U)) | ssPv4(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.20/0.47 tff(251,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.47 tff(252,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.20/0.47 tff(253,plain,(
% 0.20/0.47 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(skolemize,[status(sab)],[252])).
% 0.20/0.47 tff(254,plain,
% 0.20/0.47 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.20/0.47 tff(255,plain,
% 0.20/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(256,plain,
% 0.20/0.47 ((ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[260, 254, 14, 226])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[261, 244, 224, 2, 5])).
% 0.20/0.48 tff(263,plain,(ssPv1(skf2(elem!0)) | ssPv1(elem!0) | (~ssPv2(skf2(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (ssPv1(skf2(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[263, 2, 223])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[265])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (^[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(W, V))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) <=> (((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv2(V))))), rewrite((((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W)) <=> (((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)))), rewrite((((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(W)) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W)) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[268])).
% 0.20/0.48 tff(270,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv2(V))) | ssPv3(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.20/0.48 tff(273,plain,(
% 0.20/0.48 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(skolemize,[status(sab)],[272])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[276])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[277, 275])).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.48 tff(281,plain,
% 0.20/0.48 ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[280, 274, 80, 14])).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 (ssPv3(skf3(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[281, 264, 222, 216])).
% 0.20/0.48 tff(283,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(284,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[283])).
% 0.20/0.48 tff(285,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(286,plain,
% 0.20/0.48 (^[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)) | (~ssPv1(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(287,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[286])).
% 0.20/0.48 tff(288,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv3(U))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.20/0.48 tff(289,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.48 tff(290,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.20/0.48 tff(291,plain,(
% 0.20/0.48 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[290])).
% 0.20/0.48 tff(292,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[291, 284])).
% 0.20/0.48 tff(293,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(294,plain,
% 0.20/0.48 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(295,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[294])).
% 0.20/0.48 tff(296,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[295, 293])).
% 0.20/0.48 tff(297,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(298,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.48 tff(299,plain,
% 0.20/0.48 (ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[298, 292, 80])).
% 0.20/0.48 tff(300,plain,
% 0.20/0.48 (~ssPv1(skf3(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[299, 282, 2, 216])).
% 0.20/0.48 tff(301,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(302,plain,
% 0.20/0.48 ((ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(303,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[302])).
% 0.20/0.48 tff(304,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[303, 301])).
% 0.20/0.48 tff(305,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(306,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.20/0.48 tff(307,plain,
% 0.20/0.48 (ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[306, 236, 80, 14])).
% 0.20/0.48 tff(308,plain,
% 0.20/0.48 (~ssPv4(skf2(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[307, 300, 2, 216])).
% 0.20/0.48 tff(309,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(310,plain,
% 0.20/0.48 ((ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(311,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[310])).
% 0.20/0.48 tff(312,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[311, 309])).
% 0.20/0.48 tff(313,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(314,plain,
% 0.20/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv2(V)) | (~ssRr(V, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.48 tff(315,plain,
% 0.20/0.48 (ssPv1(skf3(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(elem!0))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[314, 254, 80, 14])).
% 0.20/0.48 tff(316,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[315, 308, 300, 2, 216])).
% 0.20/0.48 tff(317,plain,(ssPv1(elem!0) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(318,plain,
% 0.20/0.48 (ssPv1(elem!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[317, 3])).
% 0.20/0.48 tff(319,plain,
% 0.20/0.48 (ssPv1(elem!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[158, 1, 71, 3])).
% 0.20/0.48 tff(320,plain,
% 0.20/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(321,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[320])).
% 0.20/0.48 tff(322,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(323,plain,
% 0.20/0.48 (^[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))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V)) <=> (((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U))) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(324,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[323])).
% 0.20/0.48 tff(325,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | ssPv2(W)) | ssPv2(V)) | ssPv3(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause12')).
% 0.20/0.48 tff(326,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.20/0.48 tff(327,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.20/0.48 tff(328,plain,(
% 0.20/0.48 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[327])).
% 0.20/0.48 tff(329,plain,
% 0.20/0.48 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[328, 321])).
% 0.20/0.48 tff(330,plain,
% 0.20/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(331,plain,
% 0.20/0.49 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(332,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[331])).
% 0.20/0.49 tff(333,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[332, 330])).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf3(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(335,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.20/0.49 tff(336,plain,
% 0.20/0.49 ((~ssPv2(skf3(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv2(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[335, 329, 80, 14])).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 (~ssPv2(skf3(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[336, 4, 3, 1])).
% 0.20/0.49 tff(338,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(339,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[338])).
% 0.20/0.49 tff(340,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(341,plain,
% 0.20/0.49 (^[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))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) | ssPv2(W)) <=> ((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv2(W)))), rewrite(((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv2(W)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) | ssPv2(W)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) | ssPv2(W)) | ssPv4(X)) <=> ((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(X)))), rewrite(((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(X)) <=> (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) | ssPv2(W)) | ssPv4(X)) <=> (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(342,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) | ssPv2(W)) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[341])).
% 0.20/0.49 tff(343,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(U)) | ssPv2(W)) | ssPv4(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.20/0.49 tff(344,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.20/0.49 tff(345,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[344, 340])).
% 0.20/0.49 tff(346,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[345])).
% 0.20/0.49 tff(347,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[346, 339])).
% 0.20/0.49 tff(348,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(349,plain,
% 0.20/0.49 ((ssPv4(skf2(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(elem!0, 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(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(350,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf2(elem!0))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[349])).
% 0.20/0.49 tff(351,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf2(elem!0)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[350, 348])).
% 0.20/0.49 tff(352,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf3(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(353,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(V, X)) | (~ssRr(W, V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.20/0.49 tff(354,plain,
% 0.20/0.49 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv4(skf2(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[353, 347, 80, 14])).
% 0.20/0.49 tff(355,plain,
% 0.20/0.49 (ssPv4(skf2(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[354, 337, 71, 319])).
% 0.20/0.49 tff(356,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(357,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[356])).
% 0.20/0.49 tff(358,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(359,plain,
% 0.20/0.49 (^[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))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv4(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(360,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[359])).
% 0.20/0.49 tff(361,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv4(W))) | (~ssPv1(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 0.20/0.49 tff(362,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.20/0.49 tff(363,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[362, 358])).
% 0.20/0.49 tff(364,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[363])).
% 0.20/0.49 tff(365,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[364, 357])).
% 0.20/0.49 tff(366,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(367,plain,
% 0.20/0.49 (((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(368,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.49 tff(369,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[368, 366])).
% 0.20/0.49 tff(370,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(371,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.20/0.49 tff(372,plain,
% 0.20/0.49 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[371, 365, 80, 14])).
% 0.20/0.49 tff(373,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[372, 355, 337, 319, 4])).
% 0.20/0.49 tff(374,plain,(ssPv2(elem!0) | ssPv3(skf3(elem!0)) | ssPv3(elem!0) | ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(375,plain,
% 0.20/0.49 (ssPv3(skf3(elem!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[374, 1, 3, 4])).
% 0.20/0.49 tff(376,plain,
% 0.20/0.49 (~ssPv4(elem!0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[176, 1, 3, 375])).
% 0.20/0.49 tff(377,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(378,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[377])).
% 0.20/0.49 tff(379,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(380,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)) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> (((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) <=> (((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V)) <=> (((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)))), rewrite((((~ssPv4(X)) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V)) <=> ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(381,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[380])).
% 0.20/0.49 tff(382,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv4(X))) | ssPv4(W)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.20/0.49 tff(383,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.20/0.49 tff(384,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.20/0.49 tff(385,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(skolemize,[status(sab)],[384])).
% 0.20/0.49 tff(386,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[385, 378])).
% 0.20/0.49 tff(387,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(388,plain,
% 0.20/0.49 (((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0)) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(389,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[388])).
% 0.20/0.49 tff(390,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[389, 387])).
% 0.20/0.49 tff(391,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssPv4(skf2(skf2(elem!0)))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(392,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(X)) | (~ssPv1(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.20/0.49 tff(393,plain,
% 0.20/0.49 ((~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[392, 386, 14, 226])).
% 0.20/0.49 tff(394,plain,
% 0.20/0.49 (~ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[393, 376, 318, 1])).
% 0.20/0.49 tff(395,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) <=> (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(396,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[395])).
% 0.20/0.49 tff(397,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(398,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W))) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(399,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[398])).
% 0.20/0.50 tff(400,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv2(W)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause11')).
% 0.20/0.50 tff(401,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.20/0.50 tff(402,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[401, 397])).
% 0.20/0.50 tff(403,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[402])).
% 0.20/0.50 tff(404,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[403, 396])).
% 0.20/0.50 tff(405,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(406,plain,
% 0.20/0.50 ((ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(407,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[406])).
% 0.20/0.50 tff(408,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0))),
% 0.20/0.50 inference(transitivity,[status(thm)],[407, 405])).
% 0.20/0.50 tff(409,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(elem!0) | ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(410,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.20/0.50 tff(411,plain,
% 0.20/0.50 ((~ssPv1(skf2(elem!0))) | ssPv3(elem!0) | ssPv2(skf2(elem!0)) | ssPv4(elem!0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[410, 404, 14])).
% 0.20/0.50 tff(412,plain,
% 0.20/0.50 (~ssPv1(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[411, 376, 3, 1])).
% 0.20/0.50 tff(413,plain,
% 0.20/0.50 (~ssPv2(skf3(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[336, 1, 3, 4])).
% 0.20/0.50 tff(414,plain,
% 0.20/0.50 (~ssPv4(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[372, 413, 318, 4])).
% 0.20/0.50 tff(415,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(416,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[415])).
% 0.20/0.50 tff(417,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(418,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)) <=> (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U)) <=> (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(419,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[418])).
% 0.20/0.50 tff(420,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv1(U)) | ssPv4(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause16')).
% 0.20/0.50 tff(421,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.20/0.50 tff(422,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[421, 417])).
% 0.20/0.50 tff(423,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(skolemize,[status(sab)],[422])).
% 0.20/0.50 tff(424,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[423, 416])).
% 0.20/0.50 tff(425,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(426,plain,
% 0.20/0.50 ((ssPv4(skf2(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))) <=> (ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(427,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf2(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[426])).
% 0.20/0.50 tff(428,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf2(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[427, 425])).
% 0.20/0.50 tff(429,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf2(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(430,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.20/0.50 tff(431,plain,
% 0.20/0.50 (ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[430, 424, 226])).
% 0.20/0.50 tff(432,plain,
% 0.20/0.50 (~ssPv1(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[431, 414, 412, 394])).
% 0.20/0.50 tff(433,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(434,plain,
% 0.20/0.50 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(435,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[434])).
% 0.20/0.50 tff(436,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[435, 433])).
% 0.20/0.50 tff(437,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(438,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(V) | ssPv2(W) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.20/0.50 tff(439,plain,
% 0.20/0.50 (ssPv1(skf2(elem!0)) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | ssPv2(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[438, 149, 14, 226])).
% 0.20/0.50 tff(440,plain,
% 0.20/0.50 (ssPv2(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[439, 412, 1, 376])).
% 0.20/0.50 tff(441,plain,
% 0.20/0.50 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (ssPv2(skf2(elem!0)) | ssPv1(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] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(442,plain,
% 0.20/0.50 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))) <=> (ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(443,plain,
% 0.20/0.50 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | (ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[442])).
% 0.20/0.50 tff(444,plain,
% 0.20/0.50 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[443, 441])).
% 0.20/0.50 tff(445,plain,
% 0.20/0.50 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(446,plain,
% 0.20/0.50 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | ssPv4(V) | (~ssPv2(V)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.20/0.50 tff(447,plain,
% 0.20/0.50 (ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[446, 42, 226])).
% 0.20/0.50 tff(448,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[447, 440, 432, 1, 394])).
% 0.20/0.50 tff(449,plain,(ssPv2(skf2(elem!0)) | ssPv3(elem!0) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(450,plain,
% 0.20/0.50 (ssPv2(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[449, 4, 3])).
% 0.20/0.50 tff(451,plain,
% 0.20/0.50 (~ssPv1(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[67, 450, 3, 4])).
% 0.20/0.50 tff(452,plain,
% 0.20/0.50 (ssPv4(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[49, 451, 4, 450])).
% 0.20/0.50 tff(453,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(454,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[453])).
% 0.20/0.50 tff(455,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(456,plain,
% 0.20/0.50 (^[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)) | (~ssRr(U, W)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(457,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[456])).
% 0.20/0.50 tff(458,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv1(W)) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.20/0.50 tff(459,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.20/0.50 tff(460,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[459, 455])).
% 0.20/0.50 tff(461,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[460])).
% 0.20/0.50 tff(462,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[461, 454])).
% 0.20/0.50 tff(463,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(464,plain,
% 0.20/0.50 ((ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(465,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[464])).
% 0.20/0.50 tff(466,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0))),
% 0.20/0.50 inference(transitivity,[status(thm)],[465, 463])).
% 0.20/0.50 tff(467,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(468,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.20/0.50 tff(469,plain,
% 0.20/0.50 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv3(elem!0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[468, 462, 14])).
% 0.20/0.50 tff(470,plain,
% 0.20/0.50 (~ssPv3(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[469, 451, 318, 3])).
% 0.20/0.50 tff(471,plain,
% 0.20/0.50 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(472,plain,
% 0.20/0.50 ((ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(473,plain,
% 0.20/0.50 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[472])).
% 0.20/0.50 tff(474,plain,
% 0.20/0.50 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[473, 471])).
% 0.20/0.50 tff(475,plain,
% 0.20/0.50 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv1(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(476,plain,
% 0.20/0.50 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.20/0.50 tff(477,plain,
% 0.20/0.50 (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(elem!0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[476, 126, 14])).
% 0.20/0.50 tff(478,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[477, 470, 452, 4, 451])).
% 0.20/0.50 tff(479,plain,(ssPv2(elem!0) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(480,plain,
% 0.20/0.50 (ssPv2(elem!0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[479, 3])).
% 0.20/0.50 tff(481,plain,
% 0.20/0.50 (ssPv2(elem!0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[374, 1, 3, 71])).
% 0.20/0.50 tff(482,assumption,(~ssPv4(elem!0)), introduced(assumption)).
% 0.20/0.50 tff(483,plain,
% 0.20/0.50 (~ssPv1(skf2(elem!0))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[411, 482, 3, 1])).
% 0.20/0.50 tff(484,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i] : refl((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(485,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[484])).
% 0.20/0.50 tff(486,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(487,plain,
% 0.20/0.50 (^[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(W, V))) <=> (((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))))), rewrite((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V))) | ssPv3(W)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V)) <=> ((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv4(V)))), rewrite(((ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(W, V)) | ssPv3(W)) | ssPv4(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V)) <=> (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(488,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[487])).
% 0.20/0.50 tff(489,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | ssPv3(W)) | ssPv3(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.20/0.50 tff(490,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.20/0.50 tff(491,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[490, 486])).
% 0.20/0.50 tff(492,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(skolemize,[status(sab)],[491])).
% 0.20/0.50 tff(493,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[492, 485])).
% 0.20/0.50 tff(494,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(495,plain,
% 0.20/0.51 ((ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(496,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[495])).
% 0.20/0.51 tff(497,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0))),
% 0.20/0.51 inference(transitivity,[status(thm)],[496, 494])).
% 0.20/0.51 tff(498,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv4(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(skf3(elem!0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(499,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | (~ssPv4(U)) | ssPv4(V) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.20/0.51 tff(500,plain,
% 0.20/0.51 (ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv4(elem!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[499, 493, 80])).
% 0.20/0.51 tff(501,plain,
% 0.20/0.51 (~ssPv4(skf3(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[500, 482, 3, 71])).
% 0.20/0.51 tff(502,plain,
% 0.20/0.51 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(503,plain,
% 0.20/0.51 ((ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(504,plain,
% 0.20/0.51 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[503])).
% 0.20/0.51 tff(505,plain,
% 0.20/0.51 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[504, 502])).
% 0.20/0.51 tff(506,plain,
% 0.20/0.51 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(507,plain,
% 0.20/0.51 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.20/0.51 tff(508,plain,
% 0.20/0.51 (ssPv1(skf3(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(elem!0) | ssPv3(skf3(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[507, 206, 80])).
% 0.20/0.51 tff(509,plain,
% 0.20/0.51 (ssPv1(skf3(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[508, 501, 3, 71])).
% 0.20/0.51 tff(510,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(511,plain,
% 0.20/0.51 ((ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(512,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[511])).
% 0.20/0.51 tff(513,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0))),
% 0.20/0.51 inference(transitivity,[status(thm)],[512, 510])).
% 0.20/0.51 tff(514,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(515,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | ssPv2(W) | (~ssRr(U, W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.20/0.51 tff(516,plain,
% 0.20/0.51 ((~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[515, 404, 80])).
% 0.20/0.51 tff(517,plain,
% 0.20/0.51 (ssPv2(elem!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[516, 501, 71, 319])).
% 0.20/0.51 tff(518,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(519,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[518])).
% 0.20/0.51 tff(520,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(521,plain,
% 0.20/0.51 (^[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)) | (~ssRr(U, W)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv3(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(522,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[521])).
% 0.20/0.51 tff(523,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | (~ssPv2(U))) | ssPv1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.20/0.51 tff(524,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.20/0.51 tff(525,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[524, 520])).
% 0.20/0.51 tff(526,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[525])).
% 0.20/0.51 tff(527,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[526, 519])).
% 0.20/0.51 tff(528,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(529,plain,
% 0.20/0.51 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(530,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[529])).
% 0.20/0.51 tff(531,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[530, 528])).
% 0.20/0.51 tff(532,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf2(elem!0))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(533,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.20/0.51 tff(534,plain,
% 0.20/0.51 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[533, 527, 14])).
% 0.20/0.51 tff(535,plain,
% 0.20/0.51 (~ssPv3(skf2(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[534, 483, 319, 517])).
% 0.20/0.51 tff(536,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) <=> (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(537,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[536])).
% 0.20/0.51 tff(538,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(539,plain,
% 0.20/0.51 (^[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))) | (~ssRr(V, X))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv1(V))))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(W)))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W))) | ssPv3(W)) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) <=> ((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X)) <=> (((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) | ssPv1(X)))), rewrite((((~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W)) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))), ((((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(540,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[539])).
% 0.20/0.51 tff(541,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssRr(V, W))) | (~ssRr(V, X))) | (~ssPv1(V))) | ssPv3(W)) | ssPv1(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.20/0.51 tff(542,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.20/0.51 tff(543,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[542, 538])).
% 0.20/0.51 tff(544,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(skolemize,[status(sab)],[543])).
% 0.20/0.51 tff(545,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[544, 537])).
% 0.20/0.51 tff(546,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(547,plain,
% 0.20/0.51 ((ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(548,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[547])).
% 0.20/0.51 tff(549,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[548, 546])).
% 0.20/0.51 tff(550,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(skf2(elem!0)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(551,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.20/0.51 tff(552,plain,
% 0.20/0.51 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv3(skf2(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[551, 545, 80, 14])).
% 0.20/0.51 tff(553,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[552, 535, 509, 319, 483])).
% 0.20/0.51 tff(554,plain,(ssPv4(elem!0) | ssPv3(elem!0) | ssPv3(skf3(elem!0)) | ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(555,plain,
% 0.20/0.51 (ssPv4(elem!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[554, 1, 71, 3])).
% 0.20/0.51 tff(556,assumption,(~ssPv4(skf3(elem!0))), introduced(assumption)).
% 0.20/0.51 tff(557,plain,
% 0.20/0.51 (ssPv1(skf3(elem!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[508, 556, 3, 71])).
% 0.20/0.51 tff(558,assumption,(ssPv1(elem!0)), introduced(assumption)).
% 0.20/0.51 tff(559,plain,
% 0.20/0.51 (ssPv2(elem!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[516, 556, 71, 558])).
% 0.20/0.51 tff(560,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(561,plain,
% 0.20/0.52 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(562,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[561])).
% 0.20/0.52 tff(563,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[562, 560])).
% 0.20/0.52 tff(564,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv2(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(565,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.20/0.52 tff(566,plain,
% 0.20/0.52 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | (~ssPv2(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[565, 60, 80])).
% 0.20/0.52 tff(567,plain,
% 0.20/0.52 (ssPv2(skf3(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[566, 559, 71, 558])).
% 0.20/0.52 tff(568,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(569,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[568])).
% 0.20/0.52 tff(570,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(571,plain,
% 0.20/0.52 (^[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(W, V))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> (((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(V))))), rewrite((((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(572,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[571])).
% 0.20/0.52 tff(573,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssPv1(W))) | (~ssRr(V, X))) | (~ssPv1(X))) | (~ssPv1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.20/0.52 tff(574,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.20/0.52 tff(575,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.20/0.52 tff(576,plain,(
% 0.20/0.52 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[575])).
% 0.20/0.52 tff(577,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[576, 569])).
% 0.20/0.52 tff(578,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(579,plain,
% 0.20/0.52 (((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(580,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(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] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[579])).
% 0.20/0.52 tff(581,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(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] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[580, 578])).
% 0.20/0.52 tff(582,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(583,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.20/0.52 tff(584,plain,
% 0.20/0.52 ((~ssPv2(skf3(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv1(skf3(elem!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[583, 577, 80, 14])).
% 0.20/0.52 tff(585,plain,
% 0.20/0.52 (~ssPv1(skf2(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[584, 567, 558, 557])).
% 0.20/0.52 tff(586,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(587,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[586])).
% 0.20/0.52 tff(588,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(589,plain,
% 0.20/0.52 (^[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))) | (~ssPv3(W))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv2(V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W))) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(590,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[589])).
% 0.20/0.52 tff(591,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(V, W))) | (~ssPv3(W))) | (~ssRr(V, X))) | (~ssPv2(V))) | ssPv1(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.20/0.52 tff(592,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.20/0.52 tff(593,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.20/0.52 tff(594,plain,(
% 0.20/0.52 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[593])).
% 0.20/0.52 tff(595,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[594, 587])).
% 0.20/0.52 tff(596,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(597,plain,
% 0.20/0.52 ((ssPv1(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))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(598,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[597])).
% 0.20/0.52 tff(599,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[598, 596])).
% 0.20/0.52 tff(600,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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))) | (~ssPv3(skf2(elem!0))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(601,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.20/0.52 tff(602,plain,
% 0.20/0.52 ((~ssPv2(skf3(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | (~ssPv2(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[601, 595, 80, 14])).
% 0.20/0.52 tff(603,plain,
% 0.20/0.52 (~ssPv3(skf2(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[602, 567, 585, 559])).
% 0.20/0.52 tff(604,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[552, 603, 585, 558, 557])).
% 0.20/0.52 tff(605,plain,(ssPv4(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(606,plain,
% 0.20/0.52 (ssPv4(skf3(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[605, 319, 71, 3])).
% 0.20/0.52 tff(607,plain,
% 0.20/0.52 (ssPv2(skf3(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[566, 481, 71, 319])).
% 0.20/0.52 tff(608,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) <=> (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(609,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[608])).
% 0.20/0.52 tff(610,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(611,plain,
% 0.20/0.52 (^[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))) | (~ssPv4(V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv4(V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | (~ssPv4(V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X)) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv3(X)))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(612,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[611])).
% 0.20/0.52 tff(613,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv2(W))) | (~ssRr(V, X))) | (~ssPv4(V))) | ssPv3(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.20/0.52 tff(614,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.20/0.52 tff(615,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[614, 610])).
% 0.20/0.52 tff(616,plain,(
% 0.20/0.52 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[615])).
% 0.20/0.52 tff(617,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[616, 609])).
% 0.20/0.52 tff(618,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(619,plain,
% 0.20/0.52 ((ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(620,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[619])).
% 0.20/0.52 tff(621,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[620, 618])).
% 0.20/0.52 tff(622,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(623,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.20/0.52 tff(624,plain,
% 0.20/0.52 ((~ssPv2(skf3(elem!0))) | ssPv3(skf2(elem!0)) | (~ssPv4(skf3(elem!0))) | (~ssPv4(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[623, 617, 80, 14])).
% 0.20/0.52 tff(625,plain,
% 0.20/0.52 (ssPv3(skf2(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[624, 607, 606, 555])).
% 0.20/0.52 tff(626,plain,
% 0.20/0.52 (~ssPv1(skf2(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[281, 607, 71, 481])).
% 0.20/0.52 tff(627,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[534, 626, 625, 319, 481])).
% 0.20/0.52 tff(628,plain,(ssPv2(skf2(elem!0)) | ssPv3(skf3(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(629,plain,
% 0.20/0.52 (ssPv3(skf3(elem!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[628, 1, 3])).
% 0.20/0.52 tff(630,plain,
% 0.20/0.52 (~ssPv4(elem!0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[176, 1, 3, 629])).
% 0.20/0.52 tff(631,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(632,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[631])).
% 0.20/0.52 tff(633,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(634,plain,
% 0.20/0.52 (^[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(W, V))) <=> (((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V)))), ((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) <=> ((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) <=> (((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv4(X)))), rewrite((((~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V)) <=> ((ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)))), rewrite(((ssPv4(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W)) | ssPv2(V)) <=> (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V)) <=> (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(635,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[634])).
% 0.20/0.53 tff(636,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(U))) | (~ssRr(W, V))) | (~ssRr(V, X))) | ssPv4(W)) | ssPv4(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.20/0.53 tff(637,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.20/0.53 tff(638,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[637, 633])).
% 0.20/0.53 tff(639,plain,(
% 0.20/0.53 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.53 inference(skolemize,[status(sab)],[638])).
% 0.20/0.53 tff(640,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[639, 632])).
% 0.20/0.53 tff(641,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(642,plain,
% 0.20/0.53 ((ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0)) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(643,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[642])).
% 0.20/0.53 tff(644,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[643, 641])).
% 0.20/0.53 tff(645,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(646,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.20/0.53 tff(647,plain,
% 0.20/0.53 (ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv2(elem!0)) | ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[646, 640, 14, 226])).
% 0.20/0.53 tff(648,plain,
% 0.20/0.53 (ssPv4(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[647, 630, 480, 1])).
% 0.20/0.53 tff(649,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[393, 648, 630, 318, 1])).
% 0.20/0.53 tff(650,plain,(ssPv2(skf2(elem!0)) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(651,plain,
% 0.20/0.53 (ssPv2(skf2(elem!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[650, 3])).
% 0.20/0.53 tff(652,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(653,plain,
% 0.20/0.53 (((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0)) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(654,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[653])).
% 0.20/0.53 tff(655,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[654, 652])).
% 0.20/0.53 tff(656,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(657,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.20/0.53 tff(658,plain,
% 0.20/0.53 (ssPv3(elem!0) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[657, 274, 14, 226])).
% 0.20/0.53 tff(659,plain,
% 0.20/0.53 (~ssPv1(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[658, 651, 3, 480])).
% 0.20/0.53 tff(660,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(661,plain,
% 0.20/0.53 ((ssPv1(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(662,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[661])).
% 0.20/0.53 tff(663,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[662, 660])).
% 0.20/0.53 tff(664,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(skf2(skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(665,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.20/0.53 tff(666,plain,
% 0.20/0.53 ((~ssPv2(elem!0)) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[665, 595, 14, 226])).
% 0.20/0.53 tff(667,plain,
% 0.20/0.53 (~ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[666, 659, 480, 651])).
% 0.20/0.53 tff(668,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(669,plain,
% 0.20/0.53 ((ssPv1(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(670,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[669])).
% 0.20/0.53 tff(671,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[670, 668])).
% 0.20/0.53 tff(672,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (ssPv1(skf2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(673,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv1(U)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | ssPv3(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.20/0.53 tff(674,plain,
% 0.20/0.53 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[673, 545, 14, 226])).
% 0.20/0.53 tff(675,plain,
% 0.20/0.53 (~ssPv1(skf2(elem!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[674, 667, 318, 659])).
% 0.20/0.53 tff(676,plain,
% 0.20/0.53 (~ssPv3(skf2(elem!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[469, 675, 318, 3])).
% 0.20/0.53 tff(677,plain,
% 0.20/0.53 (~ssPv1(skf3(elem!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[552, 676, 318, 675])).
% 0.20/0.53 tff(678,plain,
% 0.20/0.53 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(679,plain,
% 0.20/0.53 ((ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(680,plain,
% 0.20/0.53 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[679])).
% 0.20/0.53 tff(681,plain,
% 0.20/0.53 (((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[680, 678])).
% 0.20/0.53 tff(682,plain,
% 0.20/0.53 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | (ssPv4(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv1(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(683,plain,
% 0.20/0.53 ((~![V: $i, U: $i] : (ssPv4(U) | ssPv3(U) | ssPv1(U) | ssPv3(V) | (~ssRr(U, V)))) | ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.20/0.53 tff(684,plain,
% 0.20/0.53 (ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv4(skf2(elem!0)) | ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[683, 206, 226])).
% 0.20/0.53 tff(685,plain,
% 0.20/0.53 (ssPv4(skf2(elem!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[684, 676, 667, 675])).
% 0.20/0.53 tff(686,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(687,plain,
% 0.20/0.53 ((ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(688,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[687])).
% 0.20/0.54 tff(689,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[688, 686])).
% 0.20/0.54 tff(690,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(skf2(skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(691,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.20/0.54 tff(692,plain,
% 0.20/0.54 ((~ssPv4(elem!0)) | (~ssPv2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[691, 617, 14, 226])).
% 0.20/0.54 tff(693,plain,
% 0.20/0.54 (~ssPv4(elem!0)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[692, 685, 480, 667])).
% 0.20/0.54 tff(694,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(695,plain,
% 0.20/0.54 ((ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0)) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(696,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[695])).
% 0.20/0.54 tff(697,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0))),
% 0.20/0.54 inference(transitivity,[status(thm)],[696, 694])).
% 0.20/0.54 tff(698,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(skf3(elem!0)) | ssPv1(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(elem!0))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(699,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.20/0.54 tff(700,plain,
% 0.20/0.54 (ssPv1(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(skf3(elem!0)) | ssPv4(elem!0)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[699, 424, 80])).
% 0.20/0.54 tff(701,plain,
% 0.20/0.54 (ssPv4(skf3(elem!0))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[700, 693, 318, 677])).
% 0.20/0.54 tff(702,plain,
% 0.20/0.54 (ssPv3(skf3(elem!0))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[500, 701, 3, 693])).
% 0.20/0.54 tff(703,plain,
% 0.20/0.54 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(704,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[703])).
% 0.20/0.54 tff(705,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(706,plain,
% 0.20/0.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(707,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[706])).
% 0.20/0.54 tff(708,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv3(U))) | ssPv4(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 0.20/0.54 tff(709,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.20/0.54 tff(710,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[709, 705])).
% 0.20/0.54 tff(711,plain,(
% 0.20/0.54 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[710])).
% 0.20/0.54 tff(712,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[711, 704])).
% 0.20/0.54 tff(713,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(714,plain,
% 0.20/0.54 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(715,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[714])).
% 0.20/0.54 tff(716,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0))),
% 0.20/0.54 inference(transitivity,[status(thm)],[715, 713])).
% 0.20/0.54 tff(717,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(elem!0) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(718,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | (~ssPv2(U)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.20/0.54 tff(719,plain,
% 0.20/0.54 ((~ssPv2(skf3(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv4(elem!0)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[718, 712, 80])).
% 0.20/0.54 tff(720,plain,
% 0.20/0.54 (~ssPv2(skf3(elem!0))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[719, 702, 318, 693])).
% 0.20/0.54 tff(721,plain,
% 0.20/0.54 ((~![U: $i] : ssRr(skf3(U), U)) | ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(722,plain,
% 0.20/0.54 (ssRr(skf3(skf3(elem!0)), skf3(elem!0))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[721, 78])).
% 0.20/0.54 tff(723,plain,
% 0.20/0.54 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(724,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[723])).
% 0.20/0.54 tff(725,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(726,plain,
% 0.20/0.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv2(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(727,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[726])).
% 0.20/0.54 tff(728,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv2(W))) | (~ssPv3(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause24')).
% 0.20/0.54 tff(729,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.20/0.54 tff(730,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[729, 725])).
% 0.20/0.54 tff(731,plain,(
% 0.20/0.54 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[730])).
% 0.20/0.54 tff(732,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[731, 724])).
% 0.20/0.54 tff(733,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(734,plain,
% 0.20/0.54 (((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(735,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[734])).
% 0.20/0.54 tff(736,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[735, 733])).
% 0.20/0.54 tff(737,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(738,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.20/0.54 tff(739,plain,
% 0.20/0.54 (ssPv2(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | (~ssPv2(elem!0)) | ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[738, 732, 80, 722])).
% 0.20/0.54 tff(740,plain,
% 0.20/0.54 (ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[739, 720, 480, 702])).
% 0.20/0.54 tff(741,plain,
% 0.20/0.54 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) <=> (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(742,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[741])).
% 0.20/0.54 tff(743,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(744,plain,
% 0.20/0.54 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv1(W)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> (((~ssRr(U, V)) | (~ssPv1(W)) | (~ssRr(V, W))) | (~ssRr(V, X))))), rewrite((((~ssRr(U, V)) | (~ssPv1(W)) | (~ssRr(V, W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) <=> ((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(X)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv4(X)) <=> (ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) <=> (ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V)) <=> ((ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv2(V)))), rewrite(((ssPv4(X) | ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W))) | ssPv2(V)) <=> (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))), ((((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V)) <=> (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(745,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[744])).
% 0.20/0.54 tff(746,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssRr(V, X))) | ssPv4(U)) | ssPv4(X)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.20/0.54 tff(747,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.20/0.54 tff(748,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[747, 743])).
% 0.20/0.54 tff(749,plain,(
% 0.20/0.54 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[748])).
% 0.20/0.54 tff(750,plain,
% 0.20/0.54 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[749, 742])).
% 0.20/0.54 tff(751,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(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(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(752,plain,
% 0.20/0.54 ((ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(753,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[752])).
% 0.20/0.54 tff(754,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[753, 751])).
% 0.20/0.54 tff(755,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | ssPv2(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(skf3(elem!0), elem!0)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(756,plain,
% 0.20/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.20/0.54 tff(757,plain,
% 0.20/0.54 (ssPv2(skf3(elem!0)) | (~ssPv1(elem!0)) | ssPv4(elem!0) | ssPv4(skf3(skf3(elem!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[756, 750, 80, 722])).
% 0.20/0.54 tff(758,plain,
% 0.20/0.54 (ssPv4(skf3(skf3(elem!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[757, 720, 318, 693])).
% 0.20/0.54 tff(759,plain,
% 0.20/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(760,plain,
% 0.20/0.55 ((ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(761,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[760])).
% 0.20/0.55 tff(762,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[761, 759])).
% 0.20/0.55 tff(763,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (ssPv3(elem!0) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(764,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv4(U)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv2(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.20/0.55 tff(765,plain,
% 0.20/0.55 (ssPv3(elem!0) | (~ssPv4(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[764, 617, 80, 722])).
% 0.20/0.55 tff(766,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[765, 758, 740, 3, 701])).
% 0.20/0.55 tff(767,plain,(ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(768,plain,
% 0.20/0.55 (^[W: $i, V: $i, U: $i] : refl((ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(769,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[768])).
% 0.20/0.55 tff(770,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(771,plain,
% 0.20/0.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> ((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv2(W)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> ((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv1(V)))), rewrite(((ssPv4(U) | (~ssRr(U, V)) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V))) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(772,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[771])).
% 0.20/0.55 tff(773,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv3(V))) | ssPv4(U)) | ssPv2(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 0.20/0.55 tff(774,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.20/0.55 tff(775,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[774, 770])).
% 0.20/0.55 tff(776,plain,(
% 0.20/0.55 ![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[775])).
% 0.20/0.55 tff(777,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[776, 769])).
% 0.20/0.55 tff(778,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(779,plain,
% 0.20/0.55 ((ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(780,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[779])).
% 0.20/0.55 tff(781,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[780, 778])).
% 0.20/0.55 tff(782,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(783,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.20/0.55 tff(784,plain,
% 0.20/0.55 (ssPv1(elem!0) | ssPv4(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[783, 777, 80, 14])).
% 0.20/0.55 tff(785,plain,
% 0.20/0.55 (ssPv4(skf3(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[784, 1, 767, 2])).
% 0.20/0.55 tff(786,assumption,(ssPv4(skf3(elem!0))), introduced(assumption)).
% 0.20/0.55 tff(787,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(788,plain,
% 0.20/0.55 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(789,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[788])).
% 0.20/0.55 tff(790,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[789, 787])).
% 0.20/0.55 tff(791,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(elem!0)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(792,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.20/0.55 tff(793,plain,
% 0.20/0.55 (ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[792, 462, 80])).
% 0.20/0.55 tff(794,plain,
% 0.20/0.55 (~ssPv1(skf3(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[793, 71, 767, 2])).
% 0.20/0.55 tff(795,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(796,plain,
% 0.20/0.55 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(797,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[796])).
% 0.20/0.55 tff(798,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[797, 795])).
% 0.20/0.55 tff(799,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(800,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv2(U)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.20/0.55 tff(801,plain,
% 0.20/0.55 (ssPv1(skf3(elem!0)) | ssPv3(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[800, 90, 80, 722])).
% 0.20/0.55 tff(802,plain,
% 0.20/0.55 (~ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[801, 794, 4, 71])).
% 0.20/0.55 tff(803,plain,
% 0.20/0.55 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv1(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) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(804,plain,
% 0.20/0.55 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0)))) <=> (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(805,plain,
% 0.20/0.55 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[804])).
% 0.20/0.55 tff(806,plain,
% 0.20/0.55 (((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[805, 803])).
% 0.20/0.55 tff(807,plain,
% 0.20/0.55 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(808,plain,
% 0.20/0.55 ((~![V: $i, U: $i] : (ssPv3(V) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(V)))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.20/0.55 tff(809,plain,
% 0.20/0.55 (ssPv1(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv3(skf3(elem!0)) | ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[808, 126, 722])).
% 0.20/0.55 tff(810,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[809, 802, 794, 71, 786])).
% 0.20/0.55 tff(811,plain,(ssPv3(skf3(elem!0)) | (~ssPv4(skf3(elem!0))) | ssPv2(elem!0) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(812,plain,
% 0.20/0.55 (ssPv3(skf3(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[811, 785, 4, 2])).
% 0.20/0.55 tff(813,plain,
% 0.20/0.55 (~ssPv3(skf2(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[195, 812, 2, 785])).
% 0.20/0.55 tff(814,plain,
% 0.20/0.55 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(815,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[814])).
% 0.20/0.55 tff(816,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(817,plain,
% 0.20/0.55 (^[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))) | (~ssPv3(W))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(X, V))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) <=> ((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) <=> (((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv1(X))))), rewrite((((~ssPv4(U)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | (~ssPv1(X))) <=> ((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) <=> ((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V)) <=> (((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv2(V)))), rewrite((((~ssPv4(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W))) | ssPv2(V)) <=> ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V)) <=> ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(818,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[817])).
% 0.20/0.55 tff(819,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(U))) | (~ssRr(W, V))) | (~ssPv3(W))) | (~ssRr(X, V))) | (~ssPv1(X))) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.20/0.55 tff(820,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.20/0.55 tff(821,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[820, 816])).
% 0.20/0.55 tff(822,plain,(
% 0.20/0.55 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[821])).
% 0.20/0.55 tff(823,plain,
% 0.20/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[822, 815])).
% 0.20/0.55 tff(824,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(825,plain,
% 0.20/0.55 (((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(826,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[825])).
% 0.20/0.55 tff(827,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0))),
% 0.20/0.55 inference(transitivity,[status(thm)],[826, 824])).
% 0.20/0.55 tff(828,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(elem!0))) | (~ssPv1(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(829,plain,
% 0.20/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.20/0.55 tff(830,plain,
% 0.20/0.55 ((~ssPv1(skf3(elem!0))) | (~ssPv4(skf3(elem!0))) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[829, 823, 80])).
% 0.20/0.55 tff(831,plain,
% 0.20/0.55 (~ssPv1(skf3(elem!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[830, 812, 4, 785])).
% 0.20/0.55 tff(832,plain,
% 0.20/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(833,plain,
% 0.20/0.56 ((ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0)))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(834,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[833])).
% 0.20/0.56 tff(835,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[834, 832])).
% 0.20/0.56 tff(836,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv3(skf3(elem!0))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(837,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.20/0.56 tff(838,plain,
% 0.20/0.56 (ssPv1(skf3(elem!0)) | (~ssPv3(skf3(elem!0))) | ssPv2(elem!0) | ssPv4(skf3(skf3(elem!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[837, 777, 80, 722])).
% 0.20/0.56 tff(839,plain,
% 0.20/0.56 (ssPv4(skf3(skf3(elem!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[838, 812, 4, 831])).
% 0.20/0.56 tff(840,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(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)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(841,plain,
% 0.20/0.56 (((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0))))) <=> ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(842,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[841])).
% 0.20/0.56 tff(843,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[842, 840])).
% 0.20/0.56 tff(844,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv3(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(845,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.20/0.56 tff(846,plain,
% 0.20/0.56 (ssPv1(skf3(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf3(skf3(elem!0)))) | (~ssPv4(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[845, 188, 80, 722])).
% 0.20/0.56 tff(847,plain,
% 0.20/0.56 (~ssPv3(skf3(skf3(elem!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[846, 839, 767, 831])).
% 0.20/0.56 tff(848,plain,
% 0.20/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(849,plain,
% 0.20/0.56 ((ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0))))) <=> (ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(850,plain,
% 0.20/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[849])).
% 0.20/0.56 tff(851,plain,
% 0.20/0.56 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[850, 848])).
% 0.20/0.56 tff(852,plain,
% 0.20/0.56 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | ssPv2(skf3(skf3(elem!0))) | ssPv1(skf3(elem!0)) | (~ssPv4(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(853,plain,
% 0.20/0.56 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.20/0.56 tff(854,plain,
% 0.20/0.56 (ssPv1(skf3(elem!0)) | ssPv3(skf3(skf3(elem!0))) | (~ssPv4(skf3(skf3(elem!0)))) | ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[853, 108, 722])).
% 0.20/0.56 tff(855,plain,
% 0.20/0.56 (ssPv2(skf3(skf3(elem!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[854, 847, 831, 839])).
% 0.20/0.56 tff(856,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(857,plain,
% 0.20/0.56 ((ssPv1(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)) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(858,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[857])).
% 0.20/0.56 tff(859,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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)) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[858, 856])).
% 0.20/0.56 tff(860,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (ssPv1(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)) | (~ssPv3(elem!0)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(861,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | (~ssPv2(U)) | (~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(V, X)) | (~ssRr(V, W)) | (~ssPv3(W)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssRr(skf3(skf3(elem!0)), skf3(elem!0))) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.20/0.56 tff(862,plain,
% 0.20/0.56 ((~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv3(elem!0)) | (~ssPv2(skf3(skf3(elem!0))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[861, 595, 80, 722])).
% 0.20/0.56 tff(863,plain,
% 0.20/0.56 (~ssPv2(skf3(elem!0))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[862, 855, 767, 2])).
% 0.20/0.56 tff(864,assumption,(~ssPv3(skf2(elem!0))), introduced(assumption)).
% 0.20/0.56 tff(865,plain,
% 0.20/0.56 (~ssPv4(skf2(elem!0))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[477, 224, 4, 864])).
% 0.20/0.56 tff(866,plain,
% 0.20/0.56 (ssPv3(skf2(skf2(elem!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[684, 865, 864, 224])).
% 0.20/0.56 tff(867,plain,
% 0.20/0.56 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(868,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[867])).
% 0.20/0.56 tff(869,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(870,plain,
% 0.20/0.56 (^[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)) | (~ssRr(W, V)) | (~ssPv3(U)))), ((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(U))))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(U))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(W, V)) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) <=> (((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv1(V)))), rewrite((((~ssRr(U, V)) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V)) <=> (((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | ssPv1(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))), (((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(871,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[870])).
% 0.20/0.56 tff(872,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(U))) | (~ssRr(W, V))) | ssPv4(W)) | ssPv1(V)) | ssPv4(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 0.20/0.56 tff(873,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.20/0.56 tff(874,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[873, 869])).
% 0.20/0.56 tff(875,plain,(
% 0.20/0.56 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(skolemize,[status(sab)],[874])).
% 0.20/0.56 tff(876,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[875, 868])).
% 0.20/0.56 tff(877,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(878,plain,
% 0.20/0.56 (((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(879,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[878])).
% 0.20/0.56 tff(880,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[879, 877])).
% 0.20/0.56 tff(881,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv4(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(elem!0) | (~ssPv3(elem!0)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(882,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.20/0.56 tff(883,plain,
% 0.20/0.56 (ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[882, 876, 14])).
% 0.20/0.56 tff(884,plain,
% 0.20/0.56 (ssPv4(elem!0)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[883, 865, 767, 224])).
% 0.20/0.56 tff(885,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(886,plain,
% 0.20/0.56 (((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(887,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[886])).
% 0.20/0.56 tff(888,plain,
% 0.20/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[887, 885])).
% 0.20/0.56 tff(889,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(890,plain,
% 0.20/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssRr(U, V)) | ssPv1(V) | (~ssPv3(X)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.20/0.56 tff(891,plain,
% 0.20/0.56 (ssPv1(skf2(elem!0)) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[890, 188, 14, 226])).
% 0.20/0.56 tff(892,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[891, 884, 866, 767, 224])).
% 0.20/0.56 tff(893,plain,(ssPv1(skf2(elem!0)) | ssPv3(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(894,plain,
% 0.20/0.56 (ssPv1(skf2(elem!0))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[893, 813, 4])).
% 0.20/0.56 tff(895,plain,
% 0.20/0.56 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(896,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[895])).
% 0.20/0.56 tff(897,plain,
% 0.20/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(898,plain,
% 0.20/0.57 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) <=> ((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> (((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | ssPv2(U) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(899,plain,
% 0.20/0.57 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[898])).
% 0.20/0.57 tff(900,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv4(V))) | ssPv2(U)) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause23')).
% 0.20/0.57 tff(901,plain,
% 0.20/0.57 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[900, 899])).
% 0.20/0.57 tff(902,plain,
% 0.20/0.57 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[901, 897])).
% 0.20/0.57 tff(903,plain,(
% 0.20/0.57 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.57 inference(skolemize,[status(sab)],[902])).
% 0.20/0.57 tff(904,plain,
% 0.20/0.57 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[903, 896])).
% 0.20/0.57 tff(905,plain,
% 0.20/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(906,plain,
% 0.20/0.57 (((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(907,plain,
% 0.20/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)))),
% 0.44/0.57 inference(monotonicity,[status(thm)],[906])).
% 0.44/0.57 tff(908,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0))),
% 0.44/0.57 inference(transitivity,[status(thm)],[907, 905])).
% 0.44/0.57 tff(909,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(910,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv4(V)) | (~ssRr(V, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.44/0.57 tff(911,plain,
% 0.44/0.57 (ssPv2(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv4(elem!0)) | ssPv2(elem!0)),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[910, 904, 80, 14])).
% 0.44/0.57 tff(912,plain,
% 0.44/0.57 (~ssPv4(elem!0)),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[911, 894, 863, 4])).
% 0.44/0.57 tff(913,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(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] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(914,plain,
% 0.44/0.57 (((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(915,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(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)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))))),
% 0.44/0.57 inference(monotonicity,[status(thm)],[914])).
% 0.44/0.57 tff(916,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(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)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(transitivity,[status(thm)],[915, 913])).
% 0.44/0.57 tff(917,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(918,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv4(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[917, 916])).
% 0.44/0.57 tff(919,plain,
% 0.44/0.57 ((~ssPv1(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv4(skf2(skf2(elem!0))))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[918, 365, 14, 226])).
% 0.44/0.57 tff(920,plain,
% 0.44/0.57 (~ssPv4(skf2(skf2(elem!0)))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[919, 894, 4, 1])).
% 0.44/0.57 tff(921,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(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] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(922,plain,
% 0.44/0.57 ((ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(923,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(monotonicity,[status(thm)],[922])).
% 0.44/0.57 tff(924,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.44/0.57 inference(transitivity,[status(thm)],[923, 921])).
% 0.44/0.57 tff(925,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (ssPv4(skf2(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(926,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | ssPv4(U) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssPv1(W)) | (~ssRr(V, W)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.44/0.57 tff(927,plain,
% 0.44/0.57 (ssPv2(skf2(elem!0)) | ssPv4(elem!0) | (~ssPv1(skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[926, 750, 14, 226])).
% 0.44/0.57 tff(928,plain,
% 0.44/0.57 (~ssPv1(skf2(skf2(elem!0)))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[927, 920, 1, 912])).
% 0.44/0.57 tff(929,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(930,plain,
% 0.44/0.57 ((ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(931,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))))),
% 0.44/0.57 inference(monotonicity,[status(thm)],[930])).
% 0.44/0.57 tff(932,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0)))),
% 0.44/0.57 inference(transitivity,[status(thm)],[931, 929])).
% 0.44/0.57 tff(933,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv4(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv4(skf2(elem!0)))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(934,plain,
% 0.44/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.44/0.57 tff(935,plain,
% 0.44/0.57 ((~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv4(elem!0) | ssPv4(skf2(elem!0))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[934, 424, 14])).
% 0.44/0.57 tff(936,plain,
% 0.44/0.57 (ssPv4(skf2(elem!0))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[935, 912, 2, 894])).
% 0.44/0.57 tff(937,plain,
% 0.44/0.57 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(938,plain,
% 0.44/0.57 ((ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0)))) <=> (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(939,plain,
% 0.44/0.57 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.44/0.57 inference(monotonicity,[status(thm)],[938])).
% 0.44/0.57 tff(940,plain,
% 0.44/0.57 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.44/0.57 inference(transitivity,[status(thm)],[939, 937])).
% 0.44/0.57 tff(941,plain,
% 0.44/0.57 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv4(skf2(elem!0))))),
% 0.44/0.57 inference(quant_inst,[status(thm)],[])).
% 0.44/0.57 tff(942,plain,
% 0.44/0.57 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv2(U) | ssPv1(V) | (~ssPv4(U)))) | ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.44/0.57 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.44/0.57 tff(943,plain,
% 0.44/0.57 (ssPv3(skf2(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0)))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[942, 108, 226])).
% 0.44/0.57 tff(944,plain,
% 0.44/0.57 ($false),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[943, 936, 928, 1, 813])).
% 0.44/0.57 tff(945,plain,(ssPv2(skf2(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.57 tff(946,plain,
% 0.44/0.57 (ssPv2(skf2(elem!0))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[945, 4, 2])).
% 0.44/0.57 tff(947,plain,
% 0.44/0.57 (~ssPv4(skf2(elem!0))),
% 0.44/0.57 inference(unit_resolution,[status(thm)],[31, 946, 2, 4])).
% 0.44/0.57 tff(948,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(949,plain,
% 0.44/0.57 (((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.57 inference(rewrite,[status(thm)],[])).
% 0.44/0.57 tff(950,plain,
% 0.44/0.57 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[949])).
% 0.44/0.58 tff(951,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.58 inference(transitivity,[status(thm)],[950, 948])).
% 0.44/0.58 tff(952,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | ssPv2(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(953,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.44/0.58 tff(954,plain,
% 0.44/0.58 (ssPv2(skf3(elem!0)) | (~ssPv3(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(elem!0)))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[953, 732, 80, 14])).
% 0.44/0.58 tff(955,plain,
% 0.44/0.58 (ssPv2(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[954, 946, 767, 4])).
% 0.44/0.58 tff(956,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(957,plain,
% 0.44/0.58 ((ssPv4(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(958,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[957])).
% 0.44/0.58 tff(959,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0)))),
% 0.44/0.58 inference(transitivity,[status(thm)],[958, 956])).
% 0.44/0.58 tff(960,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (ssPv4(skf2(elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv2(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv4(skf3(elem!0)))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(961,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv2(U)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv4(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.44/0.58 tff(962,plain,
% 0.44/0.58 ((~ssPv2(skf3(elem!0))) | ssPv4(skf3(elem!0)) | ssPv2(elem!0) | ssPv4(skf2(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[961, 640, 80, 14])).
% 0.44/0.58 tff(963,plain,
% 0.44/0.58 (ssPv4(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[962, 955, 4, 947])).
% 0.44/0.58 tff(964,plain,
% 0.44/0.58 (ssPv1(skf2(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[263, 946, 2])).
% 0.44/0.58 tff(965,plain,
% 0.44/0.58 (ssPv4(elem!0)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[935, 947, 2, 964])).
% 0.44/0.58 tff(966,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(967,plain,
% 0.44/0.58 (((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(968,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[967])).
% 0.44/0.58 tff(969,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.44/0.58 inference(transitivity,[status(thm)],[968, 966])).
% 0.44/0.58 tff(970,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf3(elem!0))) | ssPv1(elem!0) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | (~ssPv3(elem!0)))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(971,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.44/0.58 tff(972,plain,
% 0.44/0.58 ((~ssPv2(skf3(elem!0))) | ssPv1(elem!0) | (~ssPv1(skf3(elem!0))) | (~ssPv3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[971, 527, 80])).
% 0.44/0.58 tff(973,plain,
% 0.44/0.58 (~ssPv1(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[972, 955, 767, 2])).
% 0.44/0.58 tff(974,plain,
% 0.44/0.58 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)))),
% 0.44/0.58 inference(bind,[status(th)],[])).
% 0.44/0.58 tff(975,plain,
% 0.44/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(quant_intro,[status(thm)],[974])).
% 0.44/0.58 tff(976,plain,
% 0.44/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(977,plain,
% 0.44/0.58 (^[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))) | (~ssPv1(X))) <=> (((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), (((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) <=> (((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(U)))), rewrite((((~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)))), ((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) <=> ((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv1(W)))), rewrite(((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V))) | ssPv1(W)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))), (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V)) <=> ((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) | ssPv1(V)))), rewrite(((ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W)) | ssPv1(V)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))), ((((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V)) <=> (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))))),
% 0.44/0.58 inference(bind,[status(th)],[])).
% 0.44/0.58 tff(978,plain,
% 0.44/0.58 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(quant_intro,[status(thm)],[977])).
% 0.44/0.58 tff(979,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssRr(W, V))) | (~ssRr(V, X))) | (~ssPv1(X))) | ssPv3(U)) | ssPv1(W)) | ssPv1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.44/0.58 tff(980,plain,
% 0.44/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.44/0.58 tff(981,plain,
% 0.44/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[980, 976])).
% 0.44/0.58 tff(982,plain,(
% 0.44/0.58 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(skolemize,[status(sab)],[981])).
% 0.44/0.58 tff(983,plain,
% 0.44/0.58 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[982, 975])).
% 0.44/0.58 tff(984,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(985,plain,
% 0.44/0.58 ((ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(986,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(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) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[985])).
% 0.44/0.58 tff(987,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(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) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0)))),
% 0.44/0.58 inference(transitivity,[status(thm)],[986, 984])).
% 0.44/0.58 tff(988,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (ssPv3(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(989,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(U) | (~ssPv1(X)) | (~ssRr(U, V)) | ssPv1(V) | (~ssRr(V, X)) | (~ssRr(W, V)) | ssPv1(W))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.44/0.58 tff(990,plain,
% 0.44/0.58 (ssPv1(skf3(elem!0)) | (~ssPv1(skf2(elem!0))) | ssPv1(elem!0) | ssPv3(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[989, 983, 80, 14])).
% 0.44/0.58 tff(991,plain,
% 0.44/0.58 (ssPv3(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[990, 964, 2, 973])).
% 0.44/0.58 tff(992,plain,
% 0.44/0.58 (~ssPv3(skf2(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[195, 991, 2, 963])).
% 0.44/0.58 tff(993,plain,
% 0.44/0.58 ($false),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[624, 992, 965, 955, 963])).
% 0.44/0.58 tff(994,plain,(ssPv2(elem!0) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.58 tff(995,plain,
% 0.44/0.58 (ssPv2(elem!0)),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[994, 2])).
% 0.44/0.58 tff(996,assumption,(~ssPv1(skf3(elem!0))), introduced(assumption)).
% 0.44/0.58 tff(997,plain,
% 0.44/0.58 (~ssPv4(skf2(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[307, 996, 2, 995])).
% 0.44/0.58 tff(998,plain,
% 0.44/0.58 ($false),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[315, 997, 996, 2, 995])).
% 0.44/0.58 tff(999,plain,(ssPv1(skf3(elem!0)) | ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.58 tff(1000,plain,
% 0.44/0.58 (ssPv1(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[999, 2])).
% 0.44/0.58 tff(1001,plain,
% 0.44/0.58 (~ssPv3(skf3(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[299, 1000, 2, 995])).
% 0.44/0.58 tff(1002,plain,
% 0.44/0.58 ($false),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[793, 1001, 1000, 767, 2])).
% 0.44/0.58 tff(1003,plain,(ssPv1(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.58 tff(1004,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(1005,plain,
% 0.44/0.58 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(1006,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[1005])).
% 0.44/0.58 tff(1007,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.44/0.58 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.44/0.58 tff(1008,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv1(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(1009,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.44/0.58 tff(1010,plain,
% 0.44/0.58 (ssPv1(skf2(elem!0)) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[1009, 292, 14])).
% 0.44/0.58 tff(1011,plain,
% 0.44/0.58 (~ssPv2(skf2(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[1010, 224, 767, 1003])).
% 0.44/0.58 tff(1012,plain,
% 0.44/0.58 (ssPv3(skf2(elem!0))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[893, 224, 4])).
% 0.44/0.58 tff(1013,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(1014,plain,
% 0.44/0.58 (((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0))))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(1015,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))))),
% 0.44/0.58 inference(monotonicity,[status(thm)],[1014])).
% 0.44/0.58 tff(1016,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.44/0.58 inference(transitivity,[status(thm)],[1015, 1013])).
% 0.44/0.58 tff(1017,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(elem!0) | ssPv2(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))) | (~ssPv2(skf2(skf2(elem!0)))))),
% 0.44/0.58 inference(quant_inst,[status(thm)],[])).
% 0.44/0.58 tff(1018,plain,
% 0.44/0.58 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(U) | ssPv2(V) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv2(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.44/0.58 tff(1019,plain,
% 0.44/0.58 ((~ssPv3(skf2(elem!0))) | ssPv2(skf2(elem!0)) | ssPv2(elem!0) | (~ssPv2(skf2(skf2(elem!0))))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[1018, 732, 14, 226])).
% 0.44/0.58 tff(1020,plain,
% 0.44/0.58 (~ssPv2(skf2(skf2(elem!0)))),
% 0.44/0.58 inference(unit_resolution,[status(thm)],[1019, 1012, 4, 1011])).
% 0.44/0.58 tff(1021,plain,
% 0.44/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(1022,plain,
% 0.44/0.58 (((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(1023,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[1022])).
% 0.46/0.58 tff(1024,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[1023, 1021])).
% 0.46/0.58 tff(1025,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | ((~ssPv4(elem!0)) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(1026,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv4(U)) | (~ssPv1(X)) | ssPv2(V) | (~ssRr(U, V)) | (~ssRr(X, V)) | (~ssRr(W, V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 0.46/0.58 tff(1027,plain,
% 0.46/0.58 ((~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[1026, 823, 14])).
% 0.46/0.58 tff(1028,plain,
% 0.46/0.58 (~ssPv4(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[1027, 1011, 767, 1003])).
% 0.46/0.58 tff(1029,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(1030,plain,
% 0.46/0.58 ((ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(1031,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[1030])).
% 0.46/0.59 tff(1032,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[1031, 1029])).
% 0.46/0.59 tff(1033,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (ssPv4(elem!0) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | ssPv2(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(elem!0))))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(1034,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv4(U) | (~ssRr(U, V)) | ssPv1(V) | ssPv2(W) | (~ssRr(V, W)) | (~ssPv3(V)))) | (~ssRr(elem!0, skf2(elem!0))) | ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv2(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 0.46/0.59 tff(1035,plain,
% 0.46/0.59 (ssPv1(skf2(elem!0)) | (~ssPv3(skf2(elem!0))) | ssPv4(elem!0) | ssPv2(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1034, 777, 14, 226])).
% 0.46/0.59 tff(1036,plain,
% 0.46/0.59 ($false),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1035, 1028, 1012, 224, 1020])).
% 0.46/0.59 tff(1037,plain,(ssPv1(skf2(elem!0)) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.59 tff(1038,plain,
% 0.46/0.59 (ssPv1(skf2(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1037, 4])).
% 0.46/0.59 tff(1039,plain,
% 0.46/0.59 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(1040,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[1039])).
% 0.46/0.59 tff(1041,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1042,plain,
% 0.46/0.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv3(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv1(W))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(1043,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[1042])).
% 0.46/0.59 tff(1044,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(V, W))) | (~ssPv1(W))) | (~ssPv1(V))) | (~ssPv3(V))) | ssPv3(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.46/0.59 tff(1045,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 0.46/0.59 tff(1046,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1045, 1041])).
% 0.46/0.59 tff(1047,plain,(
% 0.46/0.59 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(skolemize,[status(sab)],[1046])).
% 0.46/0.59 tff(1048,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1047, 1040])).
% 0.46/0.59 tff(1049,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1050,plain,
% 0.46/0.59 ((ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1051,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[1050])).
% 0.46/0.59 tff(1052,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0)))),
% 0.46/0.59 inference(transitivity,[status(thm)],[1051, 1049])).
% 0.46/0.59 tff(1053,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (ssPv3(skf3(elem!0)) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv3(elem!0)) | (~ssPv1(skf2(elem!0))))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(1054,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, W)) | (~ssPv3(V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssRr(skf3(elem!0), elem!0)) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.46/0.59 tff(1055,plain,
% 0.46/0.59 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv3(elem!0)) | ssPv3(skf3(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1054, 1048, 80, 14])).
% 0.46/0.59 tff(1056,plain,
% 0.46/0.59 (ssPv3(skf3(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1055, 1038, 767, 1003])).
% 0.46/0.59 tff(1057,assumption,(ssPv1(skf2(elem!0))), introduced(assumption)).
% 0.46/0.59 tff(1058,plain,
% 0.46/0.59 (~ssPv4(elem!0)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1027, 1, 767, 1003])).
% 0.46/0.59 tff(1059,plain,
% 0.46/0.59 (~ssPv4(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[393, 1, 1003, 1058])).
% 0.46/0.59 tff(1060,plain,
% 0.46/0.59 (~ssPv1(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[927, 1059, 1, 1058])).
% 0.46/0.59 tff(1061,plain,
% 0.46/0.59 (^[V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(1062,plain,
% 0.46/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[1061])).
% 0.46/0.59 tff(1063,plain,
% 0.46/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1064,plain,
% 0.46/0.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) <=> (((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U)))), ((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) <=> ((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U))))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) <=> (((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U))) | (~ssPv4(V))))), rewrite((((~ssRr(U, V)) | (~ssPv1(V)) | (~ssPv1(U))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))), (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) | ssPv2(V)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))), ((((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V)) <=> ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(1065,plain,
% 0.46/0.59 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V)) <=> ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[1064])).
% 0.46/0.59 tff(1066,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(U))) | (~ssPv1(V))) | (~ssPv4(V))) | ssPv2(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.46/0.59 tff(1067,plain,
% 0.46/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.46/0.59 tff(1068,plain,
% 0.46/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1067, 1063])).
% 0.46/0.59 tff(1069,plain,(
% 0.46/0.59 ![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(skolemize,[status(sab)],[1068])).
% 0.46/0.59 tff(1070,plain,
% 0.46/0.59 (![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1069, 1062])).
% 0.46/0.59 tff(1071,plain,
% 0.46/0.59 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1072,plain,
% 0.46/0.59 (((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1073,plain,
% 0.46/0.59 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[1072])).
% 0.46/0.59 tff(1074,plain,
% 0.46/0.59 (((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[1073, 1071])).
% 0.46/0.59 tff(1075,plain,
% 0.46/0.59 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | ((~ssRr(elem!0, skf2(elem!0))) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(1076,plain,
% 0.46/0.59 ((~![V: $i, U: $i] : ((~ssRr(U, V)) | ssPv2(V) | (~ssPv4(V)) | (~ssPv1(V)) | (~ssPv1(U)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 0.46/0.59 tff(1077,plain,
% 0.46/0.59 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | ssPv2(skf2(elem!0)) | (~ssPv4(skf2(elem!0)))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1076, 1070, 14])).
% 0.46/0.59 tff(1078,plain,
% 0.46/0.59 (~ssPv4(skf2(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1077, 1, 1003, 1057])).
% 0.46/0.59 tff(1079,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(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)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1080,plain,
% 0.46/0.59 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssPv3(skf2(elem!0)))) <=> ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1081,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[1080])).
% 0.46/0.59 tff(1082,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssPv3(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[1081, 1079])).
% 0.46/0.59 tff(1083,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(elem!0)) | (~ssPv3(skf2(elem!0))))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(1084,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv1(V) | ssPv4(V) | (~ssRr(W, V)) | ssPv4(W) | (~ssPv3(U)))) | (~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | ssPv4(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.46/0.59 tff(1085,plain,
% 0.46/0.59 ((~ssPv3(skf2(elem!0))) | ssPv4(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | ssPv4(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1084, 876, 226])).
% 0.46/0.59 tff(1086,plain,
% 0.46/0.59 (~ssPv3(skf2(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1085, 1060, 1078, 1059])).
% 0.46/0.59 tff(1087,plain,
% 0.46/0.59 (ssPv3(skf2(skf2(elem!0)))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[674, 1060, 1003, 1057])).
% 0.46/0.59 tff(1088,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1089,plain,
% 0.46/0.59 ((ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1090,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | ((~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[1089])).
% 0.46/0.59 tff(1091,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[1090, 1088])).
% 0.46/0.59 tff(1092,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (ssPv3(skf2(elem!0)) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(1093,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv3(V)))) | (~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.46/0.59 tff(1094,plain,
% 0.46/0.59 ((~ssPv1(skf2(elem!0))) | ssPv3(skf2(elem!0)) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1093, 462, 226])).
% 0.46/0.59 tff(1095,plain,
% 0.46/0.59 ($false),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1094, 1087, 1086, 1060, 1057])).
% 0.46/0.59 tff(1096,plain,(ssPv2(skf2(elem!0)) | (~ssPv1(skf2(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.59 tff(1097,plain,
% 0.46/0.59 (ssPv2(skf2(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[1096, 1038])).
% 0.46/0.59 tff(1098,plain,
% 0.46/0.59 (ssPv2(skf3(elem!0))),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[954, 1097, 767, 4])).
% 0.46/0.59 tff(1099,plain,
% 0.46/0.59 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(1100,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[1099])).
% 0.46/0.59 tff(1101,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1102,plain,
% 0.46/0.59 (^[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(W))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))))),
% 0.46/0.59 inference(bind,[status(th)],[])).
% 0.46/0.59 tff(1103,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(quant_intro,[status(thm)],[1102])).
% 0.46/0.59 tff(1104,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv1(U))) | (~ssPv4(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.46/0.59 tff(1105,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.46/0.59 tff(1106,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1105, 1101])).
% 0.46/0.59 tff(1107,plain,(
% 0.46/0.59 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(skolemize,[status(sab)],[1106])).
% 0.46/0.59 tff(1108,plain,
% 0.46/0.59 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[1107, 1100])).
% 0.46/0.59 tff(1109,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1110,plain,
% 0.46/0.59 (((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0)))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(1111,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0)))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[1110])).
% 0.46/0.59 tff(1112,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[1111, 1109])).
% 0.46/0.59 tff(1113,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(1114,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssPv2(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 0.46/0.60 tff(1115,plain,
% 0.46/0.60 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(skf2(elem!0)))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1114, 1108, 14])).
% 0.46/0.60 tff(1116,plain,
% 0.46/0.60 (~ssPv4(elem!0)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1115, 1097, 1003, 1038])).
% 0.46/0.60 tff(1117,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[719, 1116, 1098, 1003, 1056])).
% 0.46/0.60 tff(1118,plain,(ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.60 tff(1119,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[647, 1059, 1058, 1118, 1])).
% 0.46/0.60 tff(1120,plain,(ssPv2(skf2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.60 tff(1121,plain,
% 0.46/0.60 (ssPv1(skf2(elem!0))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1010, 1120, 767, 1003])).
% 0.46/0.60 tff(1122,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(1123,plain,
% 0.46/0.60 (((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0))) <=> ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(1124,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(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] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[1123])).
% 0.46/0.60 tff(1125,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(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] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[1124, 1122])).
% 0.46/0.60 tff(1126,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | ((~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(elem!0)))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(1127,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv2(U)) | (~ssPv1(X)) | (~ssRr(U, V)) | (~ssPv1(V)) | (~ssRr(V, X)) | (~ssRr(W, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf2(elem!0))) | (~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0)))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0))))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.46/0.60 tff(1128,plain,
% 0.46/0.60 ((~ssPv1(skf2(elem!0))) | (~ssPv1(elem!0)) | (~ssPv2(elem!0)) | (~ssPv1(skf2(skf2(elem!0))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1127, 577, 14, 226])).
% 0.46/0.60 tff(1129,plain,
% 0.46/0.60 (~ssPv1(skf2(skf2(elem!0)))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1128, 1121, 1003, 1118])).
% 0.46/0.60 tff(1130,plain,
% 0.46/0.60 (ssPv3(skf2(skf2(elem!0)))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[674, 1129, 1003, 1121])).
% 0.46/0.60 tff(1131,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(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(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(1132,plain,
% 0.46/0.60 (((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))) <=> ((~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(1133,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[1132])).
% 0.46/0.60 tff(1134,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[1133, 1131])).
% 0.46/0.60 tff(1135,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv1(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0)))))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(1136,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssRr(skf2(elem!0), skf2(skf2(elem!0)))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.46/0.60 tff(1137,plain,
% 0.46/0.60 ((~ssPv1(skf2(elem!0))) | (~ssPv2(skf2(elem!0))) | ssPv1(skf2(skf2(elem!0))) | (~ssPv3(skf2(skf2(elem!0))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1136, 527, 226])).
% 0.46/0.60 tff(1138,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[1137, 1130, 1129, 1121, 1120])).
% 0.46/0.60 % SZS output end Proof
%------------------------------------------------------------------------------