TSTP Solution File: SYN755-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN755-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 23:57:12 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN755-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 07:03:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(ssPv4_type, type, (
% 0.19/0.44 ssPv4: $i > $o)).
% 0.19/0.44 tff(skf1_type, type, (
% 0.19/0.44 skf1: $i > $i)).
% 0.19/0.44 tff(elem_0_type, type, (
% 0.19/0.44 elem_0: $i)).
% 0.19/0.44 tff(ssPv1_type, type, (
% 0.19/0.44 ssPv1: $i > $o)).
% 0.19/0.44 tff(ssPv2_type, type, (
% 0.19/0.44 ssPv2: $i > $o)).
% 0.19/0.44 tff(ssPv3_type, type, (
% 0.19/0.44 ssPv3: $i > $o)).
% 0.19/0.44 tff(ssRr_type, type, (
% 0.19/0.44 ssRr: ( $i * $i ) > $o)).
% 0.19/0.44 tff(1,assumption,(~ssPv4(skf1(elem!0))), introduced(assumption)).
% 0.19/0.44 tff(2,assumption,(~ssPv2(skf1(elem!0))), introduced(assumption)).
% 0.19/0.44 tff(3,assumption,(~ssPv4(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.44 tff(4,assumption,(~ssPv3(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.44 tff(5,assumption,(~ssPv3(skf1(elem!0))), introduced(assumption)).
% 0.19/0.44 tff(6,assumption,(ssPv2(skf1(elem!0))), introduced(assumption)).
% 0.19/0.44 tff(7,assumption,(ssPv3(elem!0)), introduced(assumption)).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (^[U: $i] : refl(ssRr(U, skf1(U)) <=> ssRr(U, skf1(U)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (![U: $i] : ssRr(U, skf1(U)) <=> ![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (![U: $i] : ssRr(U, skf1(U)) <=> ![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(11,axiom,(![U: $i] : ssRr(U, skf1(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.44 tff(13,plain,(
% 0.19/0.44 ![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.44 inference(skolemize,[status(sab)],[12])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (![U: $i] : ssRr(U, skf1(U))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(elem!0, skf1(elem!0))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (ssRr(elem!0, skf1(elem!0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) <=> (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> (((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))))), rewrite((((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> (((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv3(U))))), rewrite((((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) <=> (((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(W)))), rewrite((((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(W)) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X)) <=> (((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) | ssPv3(X)))), rewrite((((~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W)) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.45 tff(22,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(W)) | ssPv3(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.45 tff(25,plain,(
% 0.19/0.45 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.45 inference(skolemize,[status(sab)],[24])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 ((ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0))) <=> ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[32, 26, 16])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (~ssPv2(skf1(elem!0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[33, 1, 7, 5])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(elem!0), skf1(skf1(elem!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (ssRr(skf1(elem!0), skf1(skf1(elem!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[35, 14])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv3(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.45 tff(42,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause11')).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.45 tff(45,plain,(
% 0.19/0.45 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(skolemize,[status(sab)],[44])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))) <=> (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[49, 47])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[52, 46, 36])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[53, 4, 1, 5])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) <=> (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssPv2(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv2(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> (((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))))), rewrite((((~ssPv2(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> ((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) <=> (((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv3(W)))), rewrite((((~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv3(W)) <=> ((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) <=> ((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) <=> (((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv1(X)))), rewrite((((~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) <=> (ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U)) <=> ((ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(U)))), rewrite(((ssPv1(X) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V))) | ssPv4(U)) <=> (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U)) <=> (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.46 tff(60,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | ssPv3(W)) | ssPv1(X)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.46 tff(63,plain,(
% 0.19/0.46 ![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[62])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 ((ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (ssPv4(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[70, 64, 36])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[71, 54, 1, 4])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 14])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (^[V: $i, U: $i] : refl((ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) <=> (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | ssPv1(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U)) <=> ((ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv3(U)))), rewrite(((ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V))) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.46 tff(80,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | ssPv1(U)) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.46 tff(83,plain,(
% 0.19/0.46 ![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[82])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 ((ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (ssPv1(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 84, 74])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[91, 72, 4, 54])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) <=> (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv4(V) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) <=> (((~ssRr(U, V)) | ssPv4(V) | (~ssRr(U, W))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | ssPv4(V) | (~ssRr(U, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv3(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W))) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U)) <=> (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.46 tff(98,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | ssPv4(V)) | ssPv1(W)) | ssPv2(U)) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.19/0.46 tff(101,plain,(
% 0.19/0.46 ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[100])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 ((ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[108, 102, 74])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[109, 92, 4, 72])).
% 0.19/0.47 tff(111,assumption,(ssPv1(skf1(elem!0))), introduced(assumption)).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv4(V)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) <=> ((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) | ssPv1(W)) <=> (((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) | ssPv1(W)) | ssPv4(U)) <=> (((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W))) | ssPv4(U)) <=> ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) | ssPv1(W)) | ssPv4(U)) <=> ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) | ssPv1(W)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.47 tff(117,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(V)) | ssPv1(W)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause9')).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.47 tff(120,plain,(
% 0.19/0.47 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[119])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.19/0.47 tff(122,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(124,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[124, 122])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | ssPv4(V) | (~ssPv1(U)) | ssPv1(W) | (~ssRr(U, W)))) | (~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[127, 121, 36])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[128, 54, 1, 111])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (^[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))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.47 tff(135,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv4(U))) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.19/0.47 tff(138,plain,(
% 0.19/0.47 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[137])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 ((ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[142, 140])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 ((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[145, 139, 74])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[146, 110, 4, 129])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (^[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)) | ssPv3(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv3(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W))) | ssPv3(U)) <=> (ssPv3(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)) | ssPv3(U)) <=> (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.47 tff(153,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | ssPv1(U)) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause29')).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.19/0.47 tff(156,plain,(
% 0.19/0.47 ![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[155])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 ((ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[160, 158])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[163, 157, 74])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[164, 110, 4, 54])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) <=> (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[166])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv4(U))))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) <=> ((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) <=> (((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv3(W)))), rewrite((((~ssPv4(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv3(W)) <=> ((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) <=> ((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X)) <=> (((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(X)))), rewrite((((~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X)) <=> (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(170,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[169])).
% 0.19/0.48 tff(171,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssRr(U, X))) | (~ssPv4(U))) | ssPv3(W)) | ssPv2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.19/0.48 tff(174,plain,(
% 0.19/0.48 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[173])).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 ((ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.48 tff(179,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[178, 176])).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(181,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.48 tff(182,plain,
% 0.19/0.48 ((~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[181, 175, 74])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[182, 165, 147, 129, 110])).
% 0.19/0.48 tff(184,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (~ssPv1(skf1(elem!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[184, 4, 1, 5])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) <=> (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[186])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(189,plain,
% 0.19/0.48 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv3(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V))) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(190,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.19/0.48 tff(191,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause15')).
% 0.19/0.48 tff(192,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.19/0.48 tff(193,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.19/0.48 tff(194,plain,(
% 0.19/0.48 ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[193])).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 ((ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))) <=> (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(201,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[201, 195, 36])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[202, 4, 2, 185])).
% 0.19/0.48 tff(204,plain,
% 0.19/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(205,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[204])).
% 0.19/0.48 tff(206,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(207,plain,
% 0.19/0.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv1(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv2(U)))), rewrite(((ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(208,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.48 tff(209,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | ssPv3(W)) | ssPv1(U)) | ssPv2(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause16')).
% 0.19/0.48 tff(210,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.19/0.48 tff(211,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.19/0.48 tff(212,plain,(
% 0.19/0.48 ![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(skolemize,[status(sab)],[211])).
% 0.19/0.48 tff(213,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.19/0.48 tff(214,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(215,plain,
% 0.19/0.48 ((ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))) <=> (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(216,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[215])).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[216, 214])).
% 0.19/0.48 tff(218,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W))) | ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (ssPv1(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[219, 213, 36])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[220, 4, 2, 185])).
% 0.19/0.48 tff(222,plain,
% 0.19/0.48 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[91, 203, 4, 221])).
% 0.19/0.48 tff(223,plain,
% 0.19/0.48 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[109, 222, 4, 203])).
% 0.19/0.48 tff(224,assumption,(~ssPv1(skf1(elem!0))), introduced(assumption)).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[220, 2, 224, 4])).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(227,plain,
% 0.19/0.48 ((ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[227])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[228, 226])).
% 0.19/0.48 tff(230,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[231, 102, 36])).
% 0.19/0.48 tff(233,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[232, 225, 2, 3, 5])).
% 0.19/0.48 tff(234,plain,(ssPv2(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[234, 4, 5, 2, 185])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[146, 223, 4, 235])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[164, 223, 4, 221])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[182, 237, 236, 235, 223])).
% 0.19/0.48 tff(239,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 (ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[239, 34, 5, 1])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[241])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 (^[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))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv4(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[244])).
% 0.19/0.48 tff(246,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | ssPv2(U)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause24')).
% 0.19/0.48 tff(247,plain,
% 0.19/0.48 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.19/0.49 tff(248,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.19/0.49 tff(249,plain,(
% 0.19/0.49 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[248])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.19/0.49 tff(251,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(252,plain,
% 0.19/0.49 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[252])).
% 0.19/0.49 tff(254,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[253, 251])).
% 0.19/0.49 tff(255,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(256,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.49 tff(257,plain,
% 0.19/0.49 (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[256, 250, 36])).
% 0.19/0.49 tff(258,plain,
% 0.19/0.49 (~ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[257, 240, 1, 34])).
% 0.19/0.49 tff(259,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(260,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[259])).
% 0.19/0.49 tff(261,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(262,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(263,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[262])).
% 0.19/0.49 tff(264,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | ssPv4(W)) | ssPv2(U)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause12')).
% 0.19/0.49 tff(265,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.19/0.49 tff(266,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[265, 261])).
% 0.19/0.49 tff(267,plain,(
% 0.19/0.49 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(skolemize,[status(sab)],[266])).
% 0.19/0.49 tff(268,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[267, 260])).
% 0.19/0.49 tff(269,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(270,plain,
% 0.19/0.49 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))) <=> (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(271,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[270])).
% 0.19/0.49 tff(272,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[271, 269])).
% 0.19/0.49 tff(273,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(274,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.19/0.49 tff(275,plain,
% 0.19/0.49 (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[274, 268, 36])).
% 0.19/0.49 tff(276,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[275, 258, 240, 1, 34])).
% 0.19/0.49 tff(277,plain,(ssPv4(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(278,plain,
% 0.19/0.49 (~ssPv3(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[277, 1, 5])).
% 0.19/0.49 tff(279,assumption,(~ssPv2(elem!0)), introduced(assumption)).
% 0.19/0.49 tff(280,assumption,(~ssPv3(elem!0)), introduced(assumption)).
% 0.19/0.49 tff(281,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv1(skf1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv1(skf1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(282,plain,
% 0.19/0.49 ((ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0)))) <=> (ssPv1(skf1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(283,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv1(skf1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(elem!0)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[282])).
% 0.19/0.49 tff(284,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv1(skf1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(transitivity,[status(thm)],[283, 281])).
% 0.19/0.49 tff(285,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(elem!0) | ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(286,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv1(skf1(elem!0)) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv2(elem!0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.19/0.49 tff(287,plain,
% 0.19/0.49 (ssPv1(skf1(elem!0)) | ssPv3(elem!0) | ssPv4(skf1(elem!0)) | ssPv2(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[286, 102, 16])).
% 0.19/0.49 tff(288,plain,
% 0.19/0.49 (ssPv1(skf1(elem!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[287, 1, 280, 279])).
% 0.19/0.49 tff(289,plain,
% 0.19/0.49 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(290,plain,
% 0.19/0.49 ((ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(291,plain,
% 0.19/0.49 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[290])).
% 0.19/0.49 tff(292,plain,
% 0.19/0.49 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0))),
% 0.19/0.49 inference(transitivity,[status(thm)],[291, 289])).
% 0.19/0.49 tff(293,plain,
% 0.19/0.49 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(elem!0) | ssPv2(elem!0) | ssPv1(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(294,plain,
% 0.19/0.49 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.19/0.49 tff(295,plain,
% 0.19/0.49 (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv1(elem!0) | ssPv2(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[294, 84, 16])).
% 0.19/0.49 tff(296,plain,
% 0.19/0.49 (ssPv1(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[295, 288, 280, 279])).
% 0.19/0.49 tff(297,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(298,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[297])).
% 0.19/0.49 tff(299,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(300,plain,
% 0.19/0.49 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(301,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[300])).
% 0.19/0.49 tff(302,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv4(W)) | ssPv2(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause21')).
% 0.19/0.49 tff(303,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.19/0.49 tff(304,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.19/0.49 tff(305,plain,(
% 0.19/0.49 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[304])).
% 0.19/0.49 tff(306,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[305, 298])).
% 0.19/0.49 tff(307,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(308,plain,
% 0.19/0.49 ((ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(309,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[308])).
% 0.19/0.49 tff(310,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(transitivity,[status(thm)],[309, 307])).
% 0.19/0.49 tff(311,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(312,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.19/0.49 tff(313,plain,
% 0.19/0.49 ((~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[312, 306, 16])).
% 0.19/0.49 tff(314,plain,
% 0.19/0.49 (~ssPv2(skf1(elem!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[313, 296, 1, 279])).
% 0.19/0.49 tff(315,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(316,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[315])).
% 0.19/0.49 tff(317,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(318,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(319,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[318])).
% 0.19/0.49 tff(320,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(U))) | ssPv2(W)) | ssPv2(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 0.19/0.49 tff(321,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.19/0.49 tff(322,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[321, 317])).
% 0.19/0.49 tff(323,plain,(
% 0.19/0.49 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(skolemize,[status(sab)],[322])).
% 0.19/0.49 tff(324,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[323, 316])).
% 0.19/0.49 tff(325,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(326,plain,
% 0.19/0.49 ((ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0))) <=> ((~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(327,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[326])).
% 0.19/0.49 tff(328,plain,
% 0.19/0.49 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0))),
% 0.19/0.49 inference(transitivity,[status(thm)],[327, 325])).
% 0.19/0.49 tff(329,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(330,plain,
% 0.19/0.49 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.49 tff(331,plain,
% 0.19/0.49 (ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv1(elem!0)) | ssPv2(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[330, 324, 16])).
% 0.19/0.49 tff(332,plain,
% 0.19/0.49 (~ssPv3(skf1(elem!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[331, 314, 296, 279])).
% 0.19/0.49 tff(333,plain,
% 0.19/0.49 (ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[184, 1, 288, 332])).
% 0.19/0.49 tff(334,plain,
% 0.19/0.49 (~ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[257, 333, 1, 314])).
% 0.19/0.49 tff(335,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[275, 334, 333, 1, 314])).
% 0.19/0.49 tff(336,plain,(ssPv4(skf1(elem!0)) | ssPv2(elem!0) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(337,plain,
% 0.19/0.49 (ssPv2(elem!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[336, 278, 1])).
% 0.19/0.49 tff(338,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(339,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[338])).
% 0.19/0.49 tff(340,plain,
% 0.19/0.49 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(341,plain,
% 0.19/0.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv3(V)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv3(V)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(342,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[341])).
% 0.19/0.50 tff(343,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv3(V)) | ssPv2(W)) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 0.19/0.50 tff(344,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.19/0.50 tff(345,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[344, 340])).
% 0.19/0.50 tff(346,plain,(
% 0.19/0.50 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.50 inference(skolemize,[status(sab)],[345])).
% 0.19/0.50 tff(347,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[346, 339])).
% 0.19/0.50 tff(348,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(349,plain,
% 0.19/0.50 ((ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(350,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[349])).
% 0.19/0.50 tff(351,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[350, 348])).
% 0.19/0.50 tff(352,plain,
% 0.19/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(353,plain,
% 0.19/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.19/0.50 tff(354,plain,
% 0.19/0.50 (ssPv3(elem!0) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[353, 347, 16])).
% 0.19/0.50 tff(355,plain,
% 0.19/0.50 (ssPv2(skf1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[354, 337, 5, 278])).
% 0.19/0.50 tff(356,plain,
% 0.19/0.50 (^[V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(357,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[356])).
% 0.19/0.50 tff(358,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(359,plain,
% 0.19/0.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V))) | ssPv4(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(360,plain,
% 0.19/0.50 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[359])).
% 0.19/0.50 tff(361,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.19/0.50 tff(362,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.19/0.50 tff(363,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[362, 358])).
% 0.19/0.50 tff(364,plain,(
% 0.19/0.50 ![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[363])).
% 0.19/0.50 tff(365,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[364, 357])).
% 0.19/0.50 tff(366,plain,
% 0.19/0.50 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(367,plain,
% 0.19/0.50 ((ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(368,plain,
% 0.19/0.50 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[367])).
% 0.19/0.50 tff(369,plain,
% 0.19/0.50 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[368, 366])).
% 0.19/0.50 tff(370,plain,
% 0.19/0.50 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(371,plain,
% 0.19/0.50 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv3(V)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.19/0.50 tff(372,plain,
% 0.19/0.50 ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[371, 365, 36])).
% 0.19/0.50 tff(373,plain,
% 0.19/0.50 (~ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[372, 355, 5, 1])).
% 0.19/0.50 tff(374,plain,
% 0.19/0.50 (^[V: $i, U: $i] : refl((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(375,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[374])).
% 0.19/0.50 tff(376,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U))) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(377,plain,
% 0.19/0.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv3(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv4(U)))), rewrite(((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(378,plain,
% 0.19/0.50 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U)) <=> ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[377])).
% 0.19/0.50 tff(379,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | ssPv3(U)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.19/0.50 tff(380,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.19/0.50 tff(381,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.19/0.50 tff(382,plain,(
% 0.19/0.50 ![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[381])).
% 0.19/0.50 tff(383,plain,
% 0.19/0.50 (![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.19/0.50 tff(384,plain,
% 0.19/0.50 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(385,plain,
% 0.19/0.50 ((ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(386,plain,
% 0.19/0.50 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[385])).
% 0.19/0.50 tff(387,plain,
% 0.19/0.50 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[386, 384])).
% 0.19/0.50 tff(388,plain,
% 0.19/0.50 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(389,plain,
% 0.19/0.50 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.19/0.50 tff(390,plain,
% 0.19/0.50 ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[389, 383, 36])).
% 0.19/0.50 tff(391,plain,
% 0.19/0.50 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[390, 355, 5, 1])).
% 0.19/0.50 tff(392,plain,
% 0.19/0.50 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[71, 391, 1, 373])).
% 0.19/0.50 tff(393,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(394,plain,
% 0.19/0.50 ((ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(395,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[394])).
% 0.19/0.50 tff(396,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[395, 393])).
% 0.19/0.50 tff(397,plain,
% 0.19/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(398,plain,
% 0.19/0.50 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv2(U)) | ssPv3(V) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.19/0.50 tff(399,plain,
% 0.19/0.50 ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[398, 347, 36])).
% 0.19/0.50 tff(400,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[399, 392, 373, 5, 355])).
% 0.19/0.50 tff(401,plain,(ssPv4(skf1(elem!0)) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(402,plain,
% 0.19/0.50 (ssPv4(skf1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[401, 5])).
% 0.19/0.50 tff(403,assumption,(ssPv4(skf1(elem!0))), introduced(assumption)).
% 0.19/0.50 tff(404,plain,
% 0.19/0.50 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(405,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[404])).
% 0.19/0.50 tff(406,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(407,plain,
% 0.19/0.50 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(U))))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X)) <=> (((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | ssPv3(X)))), rewrite((((~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X)) <=> (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(408,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[407])).
% 0.19/0.50 tff(409,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv3(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.19/0.50 tff(410,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.19/0.50 tff(411,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[410, 406])).
% 0.19/0.50 tff(412,plain,(
% 0.19/0.50 ![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[411])).
% 0.19/0.50 tff(413,plain,
% 0.19/0.50 (![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[412, 405])).
% 0.19/0.50 tff(414,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(415,plain,
% 0.19/0.50 ((ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(416,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[415])).
% 0.19/0.50 tff(417,plain,
% 0.19/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[416, 414])).
% 0.19/0.50 tff(418,plain,
% 0.19/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | (~ssPv1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(419,plain,
% 0.19/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.19/0.50 tff(420,plain,
% 0.19/0.50 ((~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[419, 413, 16])).
% 0.19/0.50 tff(421,plain,
% 0.19/0.50 (~ssPv1(elem!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[420, 6, 403, 5])).
% 0.19/0.51 tff(422,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(423,plain,
% 0.19/0.51 ((ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(424,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[423])).
% 0.19/0.51 tff(425,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0))),
% 0.19/0.51 inference(transitivity,[status(thm)],[424, 422])).
% 0.19/0.51 tff(426,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(427,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.19/0.51 tff(428,plain,
% 0.19/0.51 ((~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | ssPv1(elem!0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[427, 157, 16])).
% 0.19/0.51 tff(429,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[428, 421, 6, 280, 403])).
% 0.19/0.51 tff(430,plain,((~ssPv2(skf1(elem!0))) | ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(431,plain,
% 0.19/0.51 (~ssPv2(skf1(elem!0))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[430, 5, 403, 280])).
% 0.19/0.51 tff(432,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(433,plain,
% 0.19/0.51 ((ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0)))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(434,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[433])).
% 0.19/0.51 tff(435,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[434, 432])).
% 0.19/0.51 tff(436,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(elem!0)) | (~ssPv4(elem!0)) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(437,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.19/0.51 tff(438,plain,
% 0.19/0.51 ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv4(elem!0))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[437, 175, 16])).
% 0.19/0.51 tff(439,plain,
% 0.19/0.51 (~ssPv4(elem!0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[438, 431, 403, 5])).
% 0.19/0.51 tff(440,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(441,plain,
% 0.19/0.51 ((ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(442,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[441])).
% 0.19/0.51 tff(443,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))),
% 0.19/0.51 inference(transitivity,[status(thm)],[442, 440])).
% 0.19/0.51 tff(444,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(445,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.19/0.51 tff(446,plain,
% 0.19/0.51 (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[445, 46, 16])).
% 0.19/0.51 tff(447,plain,
% 0.19/0.51 (~ssPv1(skf1(elem!0))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[446, 439, 280, 5])).
% 0.19/0.51 tff(448,plain,
% 0.19/0.51 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(449,plain,
% 0.19/0.51 ((ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))) <=> (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(450,plain,
% 0.19/0.51 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[449])).
% 0.19/0.51 tff(451,plain,
% 0.19/0.51 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[450, 448])).
% 0.19/0.51 tff(452,plain,
% 0.19/0.51 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(453,plain,
% 0.19/0.51 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.19/0.51 tff(454,plain,
% 0.19/0.51 (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[453, 84, 36])).
% 0.19/0.51 tff(455,plain,
% 0.19/0.51 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[454, 447, 5, 431])).
% 0.19/0.51 tff(456,plain,
% 0.19/0.51 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[232, 455, 431, 5])).
% 0.19/0.51 tff(457,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(458,plain,
% 0.19/0.51 ((ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(459,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[458])).
% 0.19/0.51 tff(460,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[459, 457])).
% 0.19/0.51 tff(461,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(462,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.19/0.51 tff(463,plain,
% 0.19/0.51 ((~ssPv4(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[462, 139, 36])).
% 0.19/0.51 tff(464,plain,
% 0.19/0.51 (~ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[463, 456, 403, 5])).
% 0.19/0.51 tff(465,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(466,plain,
% 0.19/0.51 ((ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(467,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[466])).
% 0.19/0.51 tff(468,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[467, 465])).
% 0.19/0.51 tff(469,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(470,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.19/0.51 tff(471,plain,
% 0.19/0.51 (ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[470, 157, 36])).
% 0.19/0.51 tff(472,plain,
% 0.19/0.51 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[471, 456, 5, 447])).
% 0.19/0.51 tff(473,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(474,plain,
% 0.19/0.51 ((ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(475,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[474])).
% 0.19/0.51 tff(476,plain,
% 0.19/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[475, 473])).
% 0.19/0.51 tff(477,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(478,plain,
% 0.19/0.51 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.19/0.51 tff(479,plain,
% 0.19/0.51 ((~ssPv4(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[478, 175, 36])).
% 0.19/0.51 tff(480,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[479, 472, 464, 403, 456])).
% 0.19/0.51 tff(481,plain,(ssPv3(skf1(elem!0)) | (~ssPv4(skf1(elem!0))) | ssPv3(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(482,plain,
% 0.19/0.51 (ssPv3(elem!0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[481, 402, 5])).
% 0.19/0.51 tff(483,plain,
% 0.19/0.51 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(484,plain,
% 0.19/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[483])).
% 0.19/0.51 tff(485,plain,
% 0.19/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(486,plain,
% 0.19/0.51 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(X))))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) <=> ((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U))) <=> (((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv3(U))))), rewrite((((~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(487,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[486])).
% 0.19/0.52 tff(488,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(X))) | (~ssPv3(U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.19/0.52 tff(489,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.19/0.52 tff(490,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[489, 485])).
% 0.19/0.52 tff(491,plain,(
% 0.19/0.52 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[490])).
% 0.19/0.52 tff(492,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[491, 484])).
% 0.19/0.52 tff(493,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(494,plain,
% 0.19/0.52 (((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(495,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[494])).
% 0.19/0.52 tff(496,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[495, 493])).
% 0.19/0.52 tff(497,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(elem!0)) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(498,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.19/0.52 tff(499,plain,
% 0.19/0.52 ((~ssPv2(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[498, 492, 16])).
% 0.19/0.52 tff(500,plain,
% 0.19/0.52 (~ssPv1(skf1(elem!0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[499, 6, 402, 482])).
% 0.19/0.52 tff(501,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(502,plain,
% 0.19/0.52 ((ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(503,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[502])).
% 0.19/0.52 tff(504,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0))),
% 0.19/0.52 inference(transitivity,[status(thm)],[503, 501])).
% 0.19/0.52 tff(505,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (ssPv1(skf1(elem!0)) | ssPv4(elem!0) | (~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(506,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv1(X) | ssPv4(U) | (~ssPv2(V)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv4(elem!0)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.19/0.52 tff(507,plain,
% 0.19/0.52 ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | ssPv3(skf1(elem!0)) | ssPv4(elem!0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[506, 64, 16])).
% 0.19/0.52 tff(508,plain,
% 0.19/0.52 (ssPv4(elem!0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[507, 500, 5, 6])).
% 0.19/0.52 tff(509,plain,
% 0.19/0.52 (~ssPv1(elem!0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[420, 6, 402, 5])).
% 0.19/0.52 tff(510,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(511,plain,
% 0.19/0.52 ((ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(512,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[511])).
% 0.19/0.52 tff(513,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0))),
% 0.19/0.52 inference(transitivity,[status(thm)],[512, 510])).
% 0.19/0.52 tff(514,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (ssPv2(elem!0) | ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(515,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssRr(U, W)) | ssPv3(W) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.19/0.52 tff(516,plain,
% 0.19/0.52 ((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0)) | ssPv1(elem!0) | ssPv2(elem!0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[515, 195, 16])).
% 0.19/0.52 tff(517,plain,
% 0.19/0.52 (ssPv2(elem!0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[516, 509, 5, 6])).
% 0.19/0.52 tff(518,plain,
% 0.19/0.52 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(519,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[518])).
% 0.19/0.52 tff(520,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(521,plain,
% 0.19/0.52 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(522,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[521])).
% 0.19/0.52 tff(523,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | (~ssPv4(U))) | ssPv1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 0.19/0.52 tff(524,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.19/0.52 tff(525,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[524, 520])).
% 0.19/0.52 tff(526,plain,(
% 0.19/0.52 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[525])).
% 0.19/0.52 tff(527,plain,
% 0.19/0.52 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[526, 519])).
% 0.19/0.52 tff(528,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(529,plain,
% 0.19/0.52 (((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(530,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[529])).
% 0.19/0.52 tff(531,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[530, 528])).
% 0.19/0.52 tff(532,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(533,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.19/0.52 tff(534,plain,
% 0.19/0.52 ((~ssPv2(skf1(elem!0))) | ssPv1(skf1(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[533, 527, 16])).
% 0.19/0.52 tff(535,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[534, 517, 508, 500, 6])).
% 0.19/0.52 tff(536,plain,((~ssPv2(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(537,plain,
% 0.19/0.52 (~ssPv2(skf1(elem!0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[536, 5])).
% 0.19/0.52 tff(538,assumption,(ssPv4(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.52 tff(539,plain,
% 0.19/0.52 (ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[479, 538, 402, 4])).
% 0.19/0.52 tff(540,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(541,plain,
% 0.19/0.52 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(542,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[541])).
% 0.19/0.52 tff(543,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[542, 540])).
% 0.19/0.52 tff(544,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(545,plain,
% 0.19/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.19/0.52 tff(546,plain,
% 0.19/0.52 ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[545, 413, 36])).
% 0.19/0.52 tff(547,plain,
% 0.19/0.52 (~ssPv1(skf1(elem!0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[546, 539, 538, 4])).
% 0.19/0.52 tff(548,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[471, 547, 539, 5, 538])).
% 0.19/0.52 tff(549,plain,((~ssPv4(skf1(skf1(elem!0)))) | ssPv3(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(550,plain,
% 0.19/0.52 (~ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[549, 4, 5])).
% 0.19/0.52 tff(551,plain,
% 0.19/0.52 (ssPv1(skf1(elem!0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[234, 3, 5, 4, 2])).
% 0.19/0.52 tff(552,plain,
% 0.19/0.52 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(553,plain,
% 0.19/0.53 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(554,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[553])).
% 0.19/0.53 tff(555,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[554, 552])).
% 0.19/0.53 tff(556,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(557,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv4(W) | (~ssPv2(V)))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.19/0.53 tff(558,plain,
% 0.19/0.53 ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[557, 306, 36])).
% 0.19/0.53 tff(559,plain,
% 0.19/0.53 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[558, 551, 3, 2])).
% 0.19/0.53 tff(560,assumption,(~ssPv2(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.53 tff(561,assumption,(~ssPv4(skf1(skf1(skf1(elem!0))))), introduced(assumption)).
% 0.19/0.53 tff(562,plain,
% 0.19/0.53 (ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[109, 561, 4, 560])).
% 0.19/0.53 tff(563,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(564,plain,
% 0.19/0.53 ((ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(565,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[564])).
% 0.19/0.53 tff(566,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[565, 563])).
% 0.19/0.53 tff(567,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(568,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.19/0.53 tff(569,plain,
% 0.19/0.53 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[568, 268, 74])).
% 0.19/0.53 tff(570,plain,
% 0.19/0.53 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[569, 561, 3, 560])).
% 0.19/0.53 tff(571,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(572,plain,
% 0.19/0.53 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0))))) <=> (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(573,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[572])).
% 0.19/0.53 tff(574,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[573, 571])).
% 0.19/0.53 tff(575,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(576,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssRr(U, W)) | ssPv3(W))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.19/0.53 tff(577,plain,
% 0.19/0.53 (ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[576, 46, 74])).
% 0.19/0.53 tff(578,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[577, 570, 562, 4, 3])).
% 0.19/0.53 tff(579,plain,(ssPv4(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(580,plain,
% 0.19/0.53 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[579, 559, 4, 3])).
% 0.19/0.53 tff(581,plain,
% 0.19/0.53 (ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[232, 3, 2, 5])).
% 0.19/0.53 tff(582,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(583,plain,
% 0.19/0.53 ((ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(584,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[583])).
% 0.19/0.53 tff(585,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[584, 582])).
% 0.19/0.53 tff(586,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(587,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.19/0.53 tff(588,plain,
% 0.19/0.53 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv3(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[587, 250, 74])).
% 0.19/0.53 tff(589,plain,
% 0.19/0.53 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[588, 580, 3, 559])).
% 0.19/0.53 tff(590,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(591,plain,
% 0.19/0.53 ((ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(592,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[591])).
% 0.19/0.53 tff(593,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[592, 590])).
% 0.19/0.53 tff(594,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(595,plain,
% 0.19/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv1(U)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.19/0.53 tff(596,plain,
% 0.19/0.53 ((~ssPv1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[595, 413, 74])).
% 0.19/0.53 tff(597,plain,
% 0.19/0.53 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[596, 589, 581, 580])).
% 0.19/0.53 tff(598,plain,
% 0.19/0.53 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[577, 589, 4, 3])).
% 0.19/0.53 tff(599,plain,
% 0.19/0.53 ((~![U: $i] : ssRr(U, skf1(U))) | ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(600,plain,
% 0.19/0.53 (ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[599, 14])).
% 0.19/0.53 tff(601,plain,
% 0.19/0.53 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(602,plain,
% 0.19/0.53 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(603,plain,
% 0.19/0.53 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[602])).
% 0.19/0.53 tff(604,plain,
% 0.19/0.53 (((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[603, 601])).
% 0.19/0.53 tff(605,plain,
% 0.19/0.53 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(606,plain,
% 0.19/0.53 ((~![V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | ssPv1(U) | (~ssPv1(V)) | (~ssRr(U, V)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.19/0.53 tff(607,plain,
% 0.19/0.53 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[606, 84, 600])).
% 0.19/0.53 tff(608,plain,
% 0.19/0.53 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[607, 597, 589, 598])).
% 0.19/0.53 tff(609,plain,
% 0.19/0.53 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(610,plain,
% 0.19/0.53 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(611,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[610])).
% 0.19/0.54 tff(612,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[611, 609])).
% 0.19/0.54 tff(613,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(614,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv2(U) | (~ssRr(U, V)) | ssPv4(V) | ssPv1(W) | (~ssRr(U, W)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.19/0.54 tff(615,plain,
% 0.19/0.54 (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[614, 102, 600])).
% 0.19/0.54 tff(616,plain,
% 0.19/0.54 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[615, 608, 589, 597])).
% 0.19/0.54 tff(617,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(618,plain,
% 0.19/0.54 ((ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(619,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[618])).
% 0.19/0.54 tff(620,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[619, 617])).
% 0.19/0.54 tff(621,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(622,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.19/0.54 tff(623,plain,
% 0.19/0.54 ((~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[622, 139, 600])).
% 0.19/0.54 tff(624,plain,
% 0.19/0.54 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[623, 616, 580, 589])).
% 0.19/0.54 tff(625,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(626,plain,
% 0.19/0.54 ((ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0))))))) <=> (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(627,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[626])).
% 0.19/0.54 tff(628,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[627, 625])).
% 0.19/0.54 tff(629,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | (ssPv3(skf1(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(630,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv2(W)))) | ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.19/0.54 tff(631,plain,
% 0.19/0.54 (ssPv1(skf1(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[630, 157, 600])).
% 0.19/0.54 tff(632,plain,
% 0.19/0.54 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[631, 616, 589, 598])).
% 0.19/0.54 tff(633,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(634,plain,
% 0.19/0.54 ((ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0))))))) <=> ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(635,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[634])).
% 0.19/0.54 tff(636,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[635, 633])).
% 0.19/0.54 tff(637,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(638,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | (~ssPv4(U)) | ssPv3(W) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)))) | (~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | (~ssRr(skf1(skf1(skf1(elem!0))), skf1(skf1(skf1(skf1(elem!0)))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.19/0.54 tff(639,plain,
% 0.19/0.54 ((~ssPv4(skf1(skf1(skf1(elem!0))))) | (~ssPv4(skf1(skf1(skf1(skf1(elem!0)))))) | ssPv2(skf1(skf1(skf1(skf1(elem!0))))) | ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[638, 175, 600])).
% 0.19/0.54 tff(640,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[639, 632, 624, 580, 616])).
% 0.19/0.54 tff(641,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(642,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[641, 550, 4, 537, 5])).
% 0.19/0.54 tff(643,plain,(ssPv3(skf1(skf1(elem!0))) | ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(644,plain,
% 0.19/0.54 (ssPv3(skf1(skf1(elem!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[643, 5])).
% 0.19/0.54 tff(645,plain,
% 0.19/0.54 (~ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[463, 644, 402, 5])).
% 0.19/0.54 tff(646,plain,
% 0.19/0.54 (ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[232, 645, 537, 5])).
% 0.19/0.54 tff(647,plain,
% 0.19/0.54 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(648,plain,
% 0.19/0.54 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[647])).
% 0.19/0.54 tff(649,plain,
% 0.19/0.54 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(650,plain,
% 0.19/0.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv2(V))) <=> ((~ssRr(U, V)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv2(U)) <=> (((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(651,plain,
% 0.19/0.54 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv2(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[650])).
% 0.19/0.54 tff(652,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv2(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.19/0.54 tff(653,plain,
% 0.19/0.54 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.19/0.54 tff(654,plain,
% 0.19/0.54 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[653, 649])).
% 0.19/0.54 tff(655,plain,(
% 0.19/0.54 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(skolemize,[status(sab)],[654])).
% 0.19/0.54 tff(656,plain,
% 0.19/0.54 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[655, 648])).
% 0.19/0.54 tff(657,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(658,plain,
% 0.19/0.54 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(659,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | ((~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[658])).
% 0.19/0.54 tff(660,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[659, 657])).
% 0.19/0.54 tff(661,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(662,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv2(V)) | (~ssPv1(W)))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.19/0.54 tff(663,plain,
% 0.19/0.54 ((~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[662, 656, 36])).
% 0.19/0.54 tff(664,plain,
% 0.19/0.54 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[663, 646, 402, 537])).
% 0.19/0.54 tff(665,plain,
% 0.19/0.54 (ssPv1(skf1(elem!0))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[454, 646, 5, 537])).
% 0.19/0.54 tff(666,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(667,plain,
% 0.19/0.54 ((ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))) <=> ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(668,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[667])).
% 0.19/0.54 tff(669,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[668, 666])).
% 0.19/0.54 tff(670,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv2(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(671,plain,
% 0.19/0.54 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv1(U)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.19/0.54 tff(672,plain,
% 0.19/0.54 ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[671, 324, 36])).
% 0.19/0.54 tff(673,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[672, 665, 664, 644, 537])).
% 0.19/0.54 tff(674,plain,(ssPv3(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(675,plain,
% 0.19/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | ((~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(676,plain,
% 0.19/0.54 ((ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))) <=> ((~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(677,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | ((~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[676])).
% 0.19/0.55 tff(678,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[677, 675])).
% 0.19/0.55 tff(679,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (ssPv3(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(680,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv3(X) | (~ssPv3(U)) | (~ssPv2(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | ssPv4(W))) | (~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.19/0.55 tff(681,plain,
% 0.19/0.55 ((~ssPv3(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv3(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[680, 26, 36])).
% 0.19/0.55 tff(682,plain,
% 0.19/0.55 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[681, 3, 674, 4])).
% 0.19/0.55 tff(683,plain,
% 0.19/0.55 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[579, 682, 4, 3])).
% 0.19/0.55 tff(684,plain,
% 0.19/0.55 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[588, 683, 3, 682])).
% 0.19/0.55 tff(685,plain,
% 0.19/0.55 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[577, 684, 4, 3])).
% 0.19/0.55 tff(686,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i] : refl((ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(687,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[686])).
% 0.19/0.55 tff(688,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(689,plain,
% 0.19/0.55 (^[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)) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) <=> (((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)))), rewrite((((~ssRr(U, V)) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) <=> ((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) <=> (((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv2(U)))), rewrite((((~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U)) <=> ((ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(U)))), rewrite(((ssPv2(U) | (~ssRr(U, V)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V))) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))), (((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U)) <=> (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(690,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[689])).
% 0.19/0.55 tff(691,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv2(V))) | (~ssRr(U, W))) | ssPv1(W)) | ssPv2(U)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause13')).
% 0.19/0.55 tff(692,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.19/0.55 tff(693,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[692, 688])).
% 0.19/0.55 tff(694,plain,(
% 0.19/0.55 ![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[693])).
% 0.19/0.55 tff(695,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[694, 687])).
% 0.19/0.55 tff(696,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(697,plain,
% 0.19/0.55 ((ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))) <=> (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(698,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[697])).
% 0.19/0.55 tff(699,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[698, 696])).
% 0.19/0.55 tff(700,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(701,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssRr(skf1(skf1(elem!0)), skf1(skf1(skf1(elem!0))))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.19/0.55 tff(702,plain,
% 0.19/0.55 (ssPv2(skf1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | ssPv1(skf1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[701, 695, 74])).
% 0.19/0.55 tff(703,plain,
% 0.19/0.55 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[702, 685, 3, 682])).
% 0.19/0.55 tff(704,plain,
% 0.19/0.55 (~ssPv1(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[607, 703, 684, 685])).
% 0.19/0.55 tff(705,plain,
% 0.19/0.55 (ssPv4(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[615, 704, 684, 703])).
% 0.19/0.55 tff(706,plain,
% 0.19/0.55 (~ssPv3(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[623, 705, 683, 684])).
% 0.19/0.55 tff(707,plain,
% 0.19/0.55 (~ssPv2(skf1(skf1(skf1(skf1(elem!0)))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[631, 705, 684, 685])).
% 0.19/0.55 tff(708,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[639, 707, 706, 683, 705])).
% 0.19/0.55 tff(709,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(710,plain,
% 0.19/0.55 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[709, 4])).
% 0.19/0.55 tff(711,plain,
% 0.19/0.55 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[220, 224, 4, 2])).
% 0.19/0.55 tff(712,plain,
% 0.19/0.55 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[202, 224, 4, 2])).
% 0.19/0.55 tff(713,assumption,(~ssPv1(skf1(skf1(elem!0)))), introduced(assumption)).
% 0.19/0.55 tff(714,plain,
% 0.19/0.55 (~ssPv1(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[91, 713, 4, 560])).
% 0.19/0.55 tff(715,plain,
% 0.19/0.55 (ssPv4(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[109, 714, 4, 560])).
% 0.19/0.55 tff(716,plain,
% 0.19/0.55 (~ssPv3(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[146, 715, 4, 710])).
% 0.19/0.55 tff(717,plain,
% 0.19/0.55 (~ssPv2(skf1(skf1(skf1(elem!0))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[164, 715, 4, 713])).
% 0.19/0.55 tff(718,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[182, 717, 716, 710, 715])).
% 0.19/0.55 tff(719,plain,(ssPv1(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(720,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[719, 712, 711, 4])).
% 0.19/0.55 tff(721,plain,(ssPv1(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(722,plain,
% 0.19/0.55 (ssPv1(skf1(elem!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[721, 2, 4])).
% 0.19/0.55 tff(723,plain,
% 0.19/0.55 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[546, 722, 710, 4])).
% 0.19/0.55 tff(724,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(725,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[724])).
% 0.19/0.55 tff(726,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(727,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv1(W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv1(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssRr(U, X))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> (((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) <=> ((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X)) <=> (((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(X)))), rewrite((((~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X)) <=> (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(728,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[727])).
% 0.19/0.55 tff(729,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssRr(U, X))) | (~ssPv3(U))) | ssPv4(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.19/0.55 tff(730,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.19/0.55 tff(731,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[730, 726])).
% 0.19/0.55 tff(732,plain,(
% 0.19/0.55 ![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[731])).
% 0.19/0.55 tff(733,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[732, 725])).
% 0.19/0.55 tff(734,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(735,plain,
% 0.19/0.55 ((ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(736,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[735])).
% 0.19/0.55 tff(737,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[736, 734])).
% 0.19/0.55 tff(738,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(elem!0)) | (~ssPv3(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(739,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.19/0.55 tff(740,plain,
% 0.19/0.55 ((~ssPv1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[739, 733, 16])).
% 0.19/0.55 tff(741,plain,
% 0.19/0.55 (~ssPv3(elem!0)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[740, 111, 674, 1])).
% 0.19/0.55 tff(742,plain,
% 0.19/0.55 (ssPv2(elem!0)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[336, 741, 1])).
% 0.19/0.55 tff(743,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(744,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[743])).
% 0.19/0.55 tff(745,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(746,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U)) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U)) <=> (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(747,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[746])).
% 0.19/0.55 tff(748,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause19')).
% 0.19/0.55 tff(749,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.19/0.55 tff(750,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[749, 745])).
% 0.19/0.55 tff(751,plain,(
% 0.19/0.55 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(skolemize,[status(sab)],[750])).
% 0.19/0.55 tff(752,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[751, 744])).
% 0.19/0.55 tff(753,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(754,plain,
% 0.19/0.55 ((ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(755,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[754])).
% 0.19/0.55 tff(756,plain,
% 0.19/0.55 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[755, 753])).
% 0.19/0.55 tff(757,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | ssPv2(skf1(elem!0)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(758,plain,
% 0.19/0.55 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssRr(U, W)) | ssPv2(W))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.19/0.55 tff(759,plain,
% 0.19/0.55 (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv2(elem!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[758, 752, 16])).
% 0.19/0.55 tff(760,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[759, 742, 741, 2, 111])).
% 0.19/0.55 tff(761,plain,((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(762,plain,
% 0.19/0.55 (ssPv4(skf1(elem!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[761, 722, 2])).
% 0.19/0.55 tff(763,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[479, 762, 723, 710, 4])).
% 0.19/0.55 tff(764,plain,(ssPv2(skf1(elem!0)) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.55 tff(765,plain,
% 0.19/0.55 (ssPv2(skf1(elem!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[764, 4])).
% 0.19/0.55 tff(766,plain,
% 0.19/0.55 (~ssPv4(skf1(elem!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[479, 560, 710, 4])).
% 0.19/0.55 tff(767,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i] : refl(((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)) <=> ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(768,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[767])).
% 0.19/0.55 tff(769,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(770,plain,
% 0.19/0.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv4(V))) <=> ((~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W))) | ssPv2(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv4(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv4(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W)) | ssPv4(U)) <=> ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv4(U)) <=> ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(771,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[770])).
% 0.19/0.55 tff(772,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv2(W)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause17')).
% 0.19/0.55 tff(773,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.19/0.55 tff(774,plain,
% 0.19/0.55 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[773, 769])).
% 0.19/0.56 tff(775,plain,(
% 0.19/0.56 ![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.56 inference(skolemize,[status(sab)],[774])).
% 0.19/0.56 tff(776,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[775, 768])).
% 0.19/0.56 tff(777,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(778,plain,
% 0.19/0.56 (((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(779,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[778])).
% 0.19/0.56 tff(780,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[779, 777])).
% 0.19/0.56 tff(781,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(elem!0)) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(782,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)) | (~ssPv4(V)) | (~ssRr(U, W)) | ssPv2(W))) | (~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.19/0.56 tff(783,plain,
% 0.19/0.56 ((~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0)))) | ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[782, 776, 36])).
% 0.19/0.56 tff(784,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[783, 766, 560, 710, 765])).
% 0.19/0.56 tff(785,plain,(ssPv2(skf1(skf1(elem!0))) | ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(786,plain,
% 0.19/0.56 (ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[785, 4])).
% 0.19/0.56 tff(787,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(788,plain,
% 0.19/0.56 (((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(789,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[788])).
% 0.19/0.56 tff(790,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[789, 787])).
% 0.19/0.56 tff(791,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(792,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv3(U)) | (~ssPv1(X)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv2(W)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[791, 790])).
% 0.19/0.56 tff(793,plain,
% 0.19/0.56 ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[792, 492, 36])).
% 0.19/0.56 tff(794,plain,
% 0.19/0.56 (~ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[793, 786, 674, 710])).
% 0.19/0.56 tff(795,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(796,plain,
% 0.19/0.56 (((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(797,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[796])).
% 0.19/0.56 tff(798,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[797, 795])).
% 0.19/0.56 tff(799,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | ((~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(800,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | ssPv1(W) | (~ssRr(U, W)) | (~ssPv2(V)))) | (~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.19/0.56 tff(801,plain,
% 0.19/0.56 ((~ssPv2(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv1(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[800, 527, 36])).
% 0.19/0.56 tff(802,plain,
% 0.19/0.56 (~ssPv4(skf1(elem!0))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[801, 794, 786, 765])).
% 0.19/0.56 tff(803,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[71, 802, 794, 786, 4])).
% 0.19/0.56 tff(804,plain,(ssPv3(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(805,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(806,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[805])).
% 0.19/0.56 tff(807,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(808,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(809,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[808])).
% 0.19/0.56 tff(810,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv3(U))) | ssPv4(W)) | ssPv1(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause27')).
% 0.19/0.56 tff(811,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.19/0.56 tff(812,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[811, 807])).
% 0.19/0.56 tff(813,plain,(
% 0.19/0.56 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(skolemize,[status(sab)],[812])).
% 0.19/0.56 tff(814,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[813, 806])).
% 0.19/0.56 tff(815,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(816,plain,
% 0.19/0.56 ((ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))) <=> (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(817,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[816])).
% 0.19/0.56 tff(818,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[817, 815])).
% 0.19/0.56 tff(819,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(820,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv3(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | ssPv4(W))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.19/0.56 tff(821,plain,
% 0.19/0.56 (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[820, 814, 36])).
% 0.19/0.56 tff(822,plain,
% 0.19/0.56 (ssPv1(skf1(elem!0)) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[821, 674, 804])).
% 0.19/0.56 tff(823,plain,
% 0.19/0.56 (ssPv1(skf1(elem!0))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[822, 3])).
% 0.19/0.56 tff(824,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(825,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[824])).
% 0.19/0.56 tff(826,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(827,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssPv3(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv2(W))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V))) | (~ssPv2(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) <=> ((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> (((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssRr(U, X))))), rewrite((((~ssPv3(V)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) <=> ((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> (((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssPv1(U))))), rewrite((((~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) <=> ((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X)) <=> (((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | ssPv4(X)))), rewrite((((~ssPv1(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W))) | ssPv4(X)) <=> ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))), ((((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X)) <=> ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(828,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[827])).
% 0.19/0.56 tff(829,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(W))) | (~ssRr(U, X))) | (~ssPv1(U))) | ssPv4(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.19/0.56 tff(830,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.19/0.56 tff(831,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[830, 826])).
% 0.19/0.56 tff(832,plain,(
% 0.19/0.56 ![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[831])).
% 0.19/0.56 tff(833,plain,
% 0.19/0.56 (![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[832, 825])).
% 0.19/0.56 tff(834,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(835,plain,
% 0.19/0.56 (((~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0))))) <=> ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(836,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[835])).
% 0.19/0.56 tff(837,plain,
% 0.19/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[836, 834])).
% 0.19/0.56 tff(838,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(skf1(elem!0))) | ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv2(skf1(skf1(elem!0)))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(839,plain,
% 0.19/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.19/0.56 tff(840,plain,
% 0.19/0.56 ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[839, 833, 36])).
% 0.19/0.56 tff(841,plain,
% 0.19/0.56 ((~ssPv1(skf1(elem!0))) | (~ssPv2(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[840, 804])).
% 0.19/0.56 tff(842,plain,
% 0.19/0.56 (~ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[841, 823, 3])).
% 0.19/0.56 tff(843,plain,
% 0.19/0.56 ((~ssPv1(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv2(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[672, 804])).
% 0.19/0.56 tff(844,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[843, 842, 823, 2])).
% 0.19/0.56 tff(845,plain,(ssPv4(skf1(skf1(elem!0))) | ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(846,plain,
% 0.19/0.56 (ssPv4(skf1(skf1(elem!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[845, 2])).
% 0.19/0.56 tff(847,plain,
% 0.19/0.56 (ssPv2(skf1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[257, 804])).
% 0.19/0.56 tff(848,plain,
% 0.19/0.56 (ssPv4(skf1(elem!0))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[847, 846, 2])).
% 0.19/0.56 tff(849,plain,
% 0.19/0.56 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(850,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[849])).
% 0.19/0.57 tff(851,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(852,plain,
% 0.19/0.57 (^[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))) | (~ssPv3(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv3(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(853,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[852])).
% 0.19/0.57 tff(854,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssPv3(U))) | ssPv1(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.19/0.57 tff(855,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.19/0.57 tff(856,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[855, 851])).
% 0.19/0.57 tff(857,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[856])).
% 0.19/0.57 tff(858,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[857, 850])).
% 0.19/0.57 tff(859,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(860,plain,
% 0.19/0.57 ((ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0))))) <=> (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(861,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[860])).
% 0.19/0.57 tff(862,plain,
% 0.19/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[861, 859])).
% 0.19/0.57 tff(863,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(skf1(elem!0)) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssPv3(skf1(elem!0))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(864,plain,
% 0.19/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.19/0.57 tff(865,plain,
% 0.19/0.57 (ssPv1(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[864, 858, 36])).
% 0.19/0.57 tff(866,plain,
% 0.19/0.57 (ssPv1(skf1(elem!0)) | (~ssPv4(skf1(skf1(elem!0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[865, 674, 804])).
% 0.19/0.57 tff(867,plain,
% 0.19/0.57 (ssPv1(skf1(elem!0))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[866, 846])).
% 0.19/0.57 tff(868,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i, X: $i] : refl((ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) <=> (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(869,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[868])).
% 0.19/0.57 tff(870,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(871,plain,
% 0.19/0.57 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(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, W)) | (~ssRr(U, V)) | (~ssPv4(V)))), ((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv3(W))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V))) | (~ssPv3(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) <=> ((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) <=> (((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | (~ssRr(U, X))))), rewrite((((~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) <=> ((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) <=> (((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv2(X)))), rewrite((((~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv2(X)) <=> (ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) <=> (ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U)) <=> ((ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv4(U)))), rewrite(((ssPv2(X) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W))) | ssPv4(U)) <=> (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))), ((((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U)) <=> (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(872,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U)) <=> ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[871])).
% 0.19/0.57 tff(873,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv3(W))) | (~ssRr(U, X))) | ssPv2(X)) | ssPv4(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.19/0.57 tff(874,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.19/0.57 tff(875,plain,
% 0.19/0.57 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[874, 870])).
% 0.19/0.57 tff(876,plain,(
% 0.19/0.57 ![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[875])).
% 0.46/0.57 tff(877,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[876, 869])).
% 0.46/0.57 tff(878,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(879,plain,
% 0.46/0.57 ((ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(880,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[879])).
% 0.46/0.57 tff(881,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0))),
% 0.46/0.57 inference(transitivity,[status(thm)],[880, 878])).
% 0.46/0.57 tff(882,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (ssPv2(skf1(elem!0)) | ssPv4(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(883,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv2(X) | ssPv4(U) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.46/0.57 tff(884,plain,
% 0.46/0.57 ((~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[883, 877, 16])).
% 0.46/0.57 tff(885,plain,
% 0.46/0.57 ((~ssPv4(skf1(elem!0))) | ssPv2(skf1(elem!0)) | ssPv4(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[884, 674])).
% 0.46/0.57 tff(886,plain,
% 0.46/0.57 (ssPv4(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[885, 848, 2])).
% 0.46/0.57 tff(887,plain,
% 0.46/0.57 (^[W: $i, V: $i, U: $i] : refl((ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))))),
% 0.46/0.57 inference(bind,[status(th)],[])).
% 0.46/0.57 tff(888,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(quant_intro,[status(thm)],[887])).
% 0.46/0.57 tff(889,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(890,plain,
% 0.46/0.57 (^[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))) | (~ssPv1(W))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv1(W))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv1(W))))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv4(U))))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv1(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))), ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) <=> ((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv3(U)) <=> (((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv3(U)))), rewrite((((~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))), (((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv3(U)) <=> (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))))),
% 0.46/0.57 inference(bind,[status(th)],[])).
% 0.46/0.57 tff(891,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv3(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(quant_intro,[status(thm)],[890])).
% 0.46/0.57 tff(892,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv4(V))) | (~ssRr(U, W))) | (~ssPv1(W))) | (~ssPv4(U))) | ssPv3(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.46/0.57 tff(893,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.46/0.57 tff(894,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[893, 889])).
% 0.46/0.57 tff(895,plain,(
% 0.46/0.57 ![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(skolemize,[status(sab)],[894])).
% 0.46/0.57 tff(896,plain,
% 0.46/0.57 (![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[895, 888])).
% 0.46/0.57 tff(897,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(898,plain,
% 0.46/0.57 ((ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0)))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(899,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0))))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[898])).
% 0.46/0.57 tff(900,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.57 inference(transitivity,[status(thm)],[899, 897])).
% 0.46/0.57 tff(901,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(902,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv1(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.46/0.57 tff(903,plain,
% 0.46/0.57 (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[902, 896, 16])).
% 0.46/0.57 tff(904,plain,
% 0.46/0.57 (ssPv3(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[903, 886, 848, 867])).
% 0.46/0.57 tff(905,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(906,plain,
% 0.46/0.57 ((ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(907,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[906])).
% 0.46/0.57 tff(908,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0))),
% 0.46/0.57 inference(transitivity,[status(thm)],[907, 905])).
% 0.46/0.57 tff(909,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(910,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv3(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.46/0.57 tff(911,plain,
% 0.46/0.57 ((~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[910, 858, 16])).
% 0.46/0.57 tff(912,plain,
% 0.46/0.57 ((~ssPv4(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv1(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[911, 674])).
% 0.46/0.57 tff(913,plain,
% 0.46/0.57 (ssPv1(elem!0)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[912, 904, 848])).
% 0.46/0.57 tff(914,plain,
% 0.46/0.57 (^[V: $i, U: $i] : refl(((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))))),
% 0.46/0.57 inference(bind,[status(th)],[])).
% 0.46/0.57 tff(915,plain,
% 0.46/0.57 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.57 inference(quant_intro,[status(thm)],[914])).
% 0.46/0.57 tff(916,plain,
% 0.46/0.57 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U))) <=> ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(917,plain,
% 0.46/0.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv1(V))) <=> ((~ssPv1(V)) | (~ssRr(U, V)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)))), ((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | (~ssPv3(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U)))), (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U))))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U))) <=> (((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U))) | (~ssPv4(U))))), rewrite((((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))), ((((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U))) <=> ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))))),
% 0.46/0.57 inference(bind,[status(th)],[])).
% 0.46/0.57 tff(918,plain,
% 0.46/0.57 (![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U))) <=> ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.57 inference(quant_intro,[status(thm)],[917])).
% 0.46/0.57 tff(919,axiom,(![V: $i, U: $i] : (((((~ssRr(U, V)) | (~ssPv1(V))) | (~ssPv2(U))) | (~ssPv3(U))) | (~ssPv4(U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 0.46/0.57 tff(920,plain,
% 0.46/0.57 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.46/0.58 tff(921,plain,
% 0.46/0.58 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[920, 916])).
% 0.46/0.58 tff(922,plain,(
% 0.46/0.58 ![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.58 inference(skolemize,[status(sab)],[921])).
% 0.46/0.58 tff(923,plain,
% 0.46/0.58 (![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[922, 915])).
% 0.46/0.58 tff(924,plain,
% 0.46/0.58 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(925,plain,
% 0.46/0.58 (((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(926,plain,
% 0.46/0.58 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[925])).
% 0.46/0.58 tff(927,plain,
% 0.46/0.58 (((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))) <=> ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[926, 924])).
% 0.46/0.58 tff(928,plain,
% 0.46/0.58 ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | ((~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv4(elem!0)) | (~ssPv3(elem!0)))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(929,plain,
% 0.46/0.58 ((~![V: $i, U: $i] : ((~ssPv1(V)) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv4(U)) | (~ssPv3(U)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.46/0.58 tff(930,plain,
% 0.46/0.58 ((~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | (~ssPv4(elem!0)) | (~ssPv2(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[929, 923, 16])).
% 0.46/0.58 tff(931,plain,
% 0.46/0.58 (~ssPv2(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[930, 904, 867, 886])).
% 0.46/0.58 tff(932,plain,
% 0.46/0.58 (ssPv2(skf1(elem!0)) | (~ssPv1(elem!0)) | ssPv2(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[331, 674])).
% 0.46/0.58 tff(933,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[932, 931, 913, 2])).
% 0.46/0.58 tff(934,plain,(ssPv2(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(935,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(936,plain,
% 0.46/0.58 (((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0)))) <=> ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(937,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[936])).
% 0.46/0.58 tff(938,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[937, 935])).
% 0.46/0.58 tff(939,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | ((~ssPv1(elem!0)) | ssPv4(skf1(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(skf1(elem!0))))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(940,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~ssPv1(U)) | ssPv4(X) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv2(W)))) | (~ssPv2(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.46/0.58 tff(941,plain,
% 0.46/0.58 ((~ssPv2(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[940, 833, 16])).
% 0.46/0.58 tff(942,plain,
% 0.46/0.58 ((~ssPv2(skf1(elem!0))) | ssPv4(skf1(elem!0)) | (~ssPv1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[941, 674])).
% 0.46/0.58 tff(943,plain,
% 0.46/0.58 (~ssPv1(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[942, 1, 934])).
% 0.46/0.58 tff(944,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(945,plain,
% 0.46/0.58 ((ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0))))) <=> ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(946,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[945])).
% 0.46/0.58 tff(947,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0))))),
% 0.46/0.58 inference(transitivity,[status(thm)],[946, 944])).
% 0.46/0.58 tff(948,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (ssPv4(skf1(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | (~ssPv1(skf1(skf1(elem!0)))))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(949,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (ssPv4(X) | (~ssPv3(U)) | (~ssPv3(V)) | (~ssRr(U, X)) | (~ssRr(U, W)) | (~ssRr(U, V)) | (~ssPv1(W)))) | (~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | (~ssRr(skf1(elem!0), skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.46/0.58 tff(950,plain,
% 0.46/0.58 ((~ssPv3(skf1(elem!0))) | (~ssPv1(skf1(skf1(elem!0)))) | (~ssPv3(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[949, 733, 36])).
% 0.46/0.58 tff(951,plain,
% 0.46/0.58 ((~ssPv1(skf1(skf1(elem!0)))) | ssPv4(skf1(skf1(elem!0)))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[950, 674, 804])).
% 0.46/0.58 tff(952,plain,
% 0.46/0.58 (~ssPv1(skf1(skf1(elem!0)))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[951, 3])).
% 0.46/0.58 tff(953,plain,
% 0.46/0.58 (ssPv4(skf1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[128, 952, 823, 3])).
% 0.46/0.58 tff(954,plain,
% 0.46/0.58 (~ssPv3(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[499, 953, 934, 823])).
% 0.46/0.58 tff(955,plain,
% 0.46/0.58 (ssPv4(skf1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[336, 280, 279])).
% 0.46/0.58 tff(956,plain,
% 0.46/0.58 (ssPv3(skf1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[481, 955, 280])).
% 0.46/0.58 tff(957,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(958,plain,
% 0.46/0.58 ((ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(959,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0)))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[958])).
% 0.46/0.58 tff(960,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0))),
% 0.46/0.58 inference(transitivity,[status(thm)],[959, 957])).
% 0.46/0.58 tff(961,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv2(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(962,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv2(U) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv4(V)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.46/0.58 tff(963,plain,
% 0.46/0.58 ((~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(elem!0) | ssPv2(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[962, 250, 16])).
% 0.46/0.58 tff(964,plain,
% 0.46/0.58 (ssPv4(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[963, 956, 955, 279])).
% 0.46/0.58 tff(965,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(966,plain,
% 0.46/0.58 ((ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0)))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(967,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[966])).
% 0.46/0.58 tff(968,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[967, 965])).
% 0.46/0.58 tff(969,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0)) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(970,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : (ssPv3(U) | (~ssRr(U, V)) | (~ssPv4(V)) | (~ssPv4(U)) | (~ssRr(U, W)) | (~ssPv3(W)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[969, 968])).
% 0.46/0.58 tff(971,plain,
% 0.46/0.58 (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[970, 139, 16])).
% 0.46/0.58 tff(972,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[971, 964, 956, 280, 955])).
% 0.46/0.58 tff(973,plain,(ssPv3(elem!0) | ssPv2(elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(974,plain,
% 0.46/0.58 (ssPv2(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[973, 954])).
% 0.46/0.58 tff(975,plain,
% 0.46/0.58 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(976,plain,
% 0.46/0.58 ((ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))) <=> (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(977,plain,
% 0.46/0.58 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[976])).
% 0.46/0.58 tff(978,plain,
% 0.46/0.58 (((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))) <=> ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(transitivity,[status(thm)],[977, 975])).
% 0.46/0.58 tff(979,plain,
% 0.46/0.58 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0)))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(980,plain,
% 0.46/0.58 ((~![V: $i, U: $i] : (ssPv3(U) | (~ssPv1(V)) | (~ssRr(U, V)) | ssPv4(U) | (~ssPv2(U)))) | ssPv3(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.46/0.58 tff(981,plain,
% 0.46/0.58 (ssPv3(elem!0) | (~ssPv1(skf1(elem!0))) | ssPv4(elem!0) | (~ssPv2(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[980, 383, 16])).
% 0.46/0.58 tff(982,plain,
% 0.46/0.58 (ssPv4(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[981, 954, 823, 974])).
% 0.46/0.58 tff(983,plain,
% 0.46/0.58 (ssPv3(elem!0) | (~ssPv4(skf1(elem!0))) | (~ssPv4(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[971, 674])).
% 0.46/0.58 tff(984,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[983, 982, 954, 953])).
% 0.46/0.58 tff(985,plain,(ssPv4(skf1(skf1(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(986,plain,
% 0.46/0.58 (ssPv1(skf1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[866, 985])).
% 0.46/0.58 tff(987,plain,
% 0.46/0.58 ((~ssPv1(skf1(elem!0))) | (~ssPv3(elem!0)) | ssPv4(skf1(elem!0))),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[740, 674])).
% 0.46/0.58 tff(988,plain,
% 0.46/0.58 (~ssPv3(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[987, 1, 986])).
% 0.46/0.58 tff(989,plain,
% 0.46/0.58 (ssPv2(elem!0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[336, 1, 988])).
% 0.46/0.58 tff(990,plain,
% 0.46/0.58 (^[W: $i, V: $i, U: $i] : refl((ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(991,plain,
% 0.46/0.58 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[990])).
% 0.46/0.58 tff(992,plain,
% 0.46/0.58 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(993,plain,
% 0.46/0.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ssRr(U, V)) | (~ssPv3(V))) <=> ((~ssRr(U, V)) | (~ssPv3(V)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> (((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W)))), ((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) <=> ((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> (((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(U))))), rewrite((((~ssRr(U, V)) | (~ssPv3(V)) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)))), (((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W))))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) <=> ((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U)) <=> (((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)))), rewrite((((~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))), (((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U)) <=> (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(994,plain,
% 0.46/0.58 (![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U)) <=> ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[993])).
% 0.46/0.58 tff(995,axiom,(![W: $i, V: $i, U: $i] : ((((((~ssRr(U, V)) | (~ssPv3(V))) | (~ssRr(U, W))) | (~ssPv2(U))) | ssPv4(W)) | ssPv1(U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause28')).
% 0.46/0.58 tff(996,plain,
% 0.46/0.58 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.46/0.58 tff(997,plain,
% 0.46/0.58 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[996, 992])).
% 0.46/0.58 tff(998,plain,(
% 0.46/0.58 ![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(skolemize,[status(sab)],[997])).
% 0.46/0.58 tff(999,plain,
% 0.46/0.58 (![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[998, 991])).
% 0.46/0.58 tff(1000,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)))),
% 0.48/0.59 inference(rewrite,[status(thm)],[])).
% 0.48/0.59 tff(1001,plain,
% 0.48/0.59 ((ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0))) <=> ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)))),
% 0.48/0.59 inference(rewrite,[status(thm)],[])).
% 0.48/0.59 tff(1002,plain,
% 0.48/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | ((~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0))))),
% 0.48/0.59 inference(monotonicity,[status(thm)],[1001])).
% 0.48/0.59 tff(1003,plain,
% 0.48/0.59 (((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0)))),
% 0.48/0.59 inference(transitivity,[status(thm)],[1002, 1000])).
% 0.48/0.59 tff(1004,plain,
% 0.48/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (ssPv1(elem!0) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv2(elem!0)) | (~ssPv3(skf1(elem!0))) | (~ssRr(elem!0, skf1(elem!0))) | ssPv4(skf1(elem!0)))),
% 0.48/0.59 inference(quant_inst,[status(thm)],[])).
% 0.48/0.59 tff(1005,plain,
% 0.48/0.59 ((~![W: $i, V: $i, U: $i] : (ssPv1(U) | (~ssRr(U, V)) | (~ssPv2(U)) | (~ssPv3(V)) | (~ssRr(U, W)) | ssPv4(W))) | (~ssRr(elem!0, skf1(elem!0))) | (~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0))),
% 0.48/0.59 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 0.48/0.59 tff(1006,plain,
% 0.48/0.59 ((~ssPv3(skf1(elem!0))) | ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0))),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[1005, 999, 16])).
% 0.48/0.59 tff(1007,plain,
% 0.48/0.59 (ssPv4(skf1(elem!0)) | ssPv1(elem!0) | (~ssPv2(elem!0))),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[1006, 674])).
% 0.48/0.59 tff(1008,plain,
% 0.48/0.59 ($false),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[1007, 989, 943, 1])).
% 0.48/0.59 tff(1009,plain,(ssPv4(skf1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.59 tff(1010,plain,
% 0.48/0.59 (~ssPv3(elem!0)),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[499, 1009, 934, 986])).
% 0.48/0.59 tff(1011,plain,
% 0.48/0.59 (ssPv2(elem!0)),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[973, 1010])).
% 0.48/0.59 tff(1012,plain,
% 0.48/0.59 (ssPv4(elem!0)),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[981, 1010, 986, 1011])).
% 0.48/0.59 tff(1013,plain,
% 0.48/0.59 ($false),
% 0.48/0.59 inference(unit_resolution,[status(thm)],[983, 1012, 1010, 1009])).
% 0.48/0.59 % SZS output end Proof
%------------------------------------------------------------------------------