TSTP Solution File: SYN039-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:53:16 EDT 2022
% Result : Unsatisfiable 0.21s 0.53s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 01:33:47 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.53 % SZS status Unsatisfiable
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 tff(s_type, type, (
% 0.21/0.53 s: ( $i * $i ) > $o)).
% 0.21/0.53 tff(f1_type, type, (
% 0.21/0.53 f1: ( $i * $i ) > $i)).
% 0.21/0.53 tff(elem_0_type, type, (
% 0.21/0.53 elem_0: $i)).
% 0.21/0.53 tff(q_type, type, (
% 0.21/0.53 q: ( $i * $i ) > $o)).
% 0.21/0.53 tff(p_type, type, (
% 0.21/0.53 p: ( $i * $i ) > $o)).
% 0.21/0.53 tff(1,assumption,(~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.21/0.53 tff(2,assumption,(~s(f1(elem!0, elem!0), f1(elem!0, elem!0))), introduced(assumption)).
% 0.21/0.53 tff(3,assumption,(s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.21/0.53 tff(4,assumption,(~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.21/0.53 tff(5,assumption,(q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.21/0.53 tff(6,plain,
% 0.21/0.53 (^[Z: $i, Z1: $i, X: $i, X1: $i] : refl(((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X)) <=> ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X)))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(7,plain,
% 0.21/0.53 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.53 tff(8,plain,
% 0.21/0.53 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(9,plain,
% 0.21/0.53 (^[Z: $i, Z1: $i, X: $i, X1: $i] : trans(monotonicity(rewrite((s(Z, X) | (~q(Z1, Z1))) <=> ((~q(Z1, Z1)) | s(Z, X))), (((s(Z, X) | (~q(Z1, Z1))) | (~s(X1, X1))) <=> (((~q(Z1, Z1)) | s(Z, X)) | (~s(X1, X1))))), rewrite((((~q(Z1, Z1)) | s(Z, X)) | (~s(X1, X1))) <=> ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))), (((s(Z, X) | (~q(Z1, Z1))) | (~s(X1, X1))) <=> ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(10,plain,
% 0.21/0.53 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((s(Z, X) | (~q(Z1, Z1))) | (~s(X1, X1))) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.53 tff(11,axiom,(![Z: $i, Z1: $i, X: $i, X1: $i] : ((s(Z, X) | (~q(Z1, Z1))) | (~s(X1, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_27')).
% 0.21/0.53 tff(12,plain,
% 0.21/0.53 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.53 tff(13,plain,
% 0.21/0.53 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.53 tff(14,plain,(
% 0.21/0.53 ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(skolemize,[status(sab)],[13])).
% 0.21/0.53 tff(15,plain,
% 0.21/0.53 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.53 tff(16,plain,
% 0.21/0.53 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(17,plain,
% 0.21/0.53 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(18,plain,
% 0.21/0.54 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.54 tff(19,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[18, 15, 2, 3, 5])).
% 0.21/0.54 tff(20,plain,((~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(21,plain,
% 0.21/0.54 (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[20, 3, 2])).
% 0.21/0.54 tff(22,plain,
% 0.21/0.54 (^[Z: $i, Z1: $i, X: $i, X1: $i] : refl((p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z)) <=> (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(23,plain,
% 0.21/0.54 (![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.54 tff(24,plain,
% 0.21/0.54 (![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(25,plain,
% 0.21/0.54 (^[Z: $i, Z1: $i, X: $i, X1: $i] : rewrite(((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | q(f1(X, X1), Z1)) <=> (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(26,plain,
% 0.21/0.54 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | q(f1(X, X1), Z1)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.54 tff(27,axiom,(![Z: $i, Z1: $i, X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | q(f1(X, X1), Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_5')).
% 0.21/0.54 tff(28,plain,
% 0.21/0.54 (![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.54 tff(29,plain,
% 0.21/0.54 (![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.54 tff(30,plain,(
% 0.21/0.54 ![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(skolemize,[status(sab)],[29])).
% 0.21/0.54 tff(31,plain,
% 0.21/0.54 (![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.54 tff(32,plain,
% 0.21/0.54 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(33,plain,
% 0.21/0.54 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(34,plain,
% 0.21/0.54 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.54 tff(35,plain,
% 0.21/0.54 (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[34, 31, 1, 4])).
% 0.21/0.54 tff(36,plain,
% 0.21/0.54 (^[Z: $i, X: $i, X1: $i] : refl(((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X)) <=> ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(37,plain,
% 0.21/0.54 (![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X)) <=> ![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.54 tff(38,plain,
% 0.21/0.54 (![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X)) <=> ![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(39,plain,
% 0.21/0.54 (^[Z: $i, X: $i, X1: $i] : trans(monotonicity(rewrite((s(Z, X) | (~s(X, f1(X, X1)))) <=> ((~s(X, f1(X, X1))) | s(Z, X))), (((s(Z, X) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> (((~s(X, f1(X, X1))) | s(Z, X)) | (~s(X1, X1))))), rewrite((((~s(X, f1(X, X1))) | s(Z, X)) | (~s(X1, X1))) <=> ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))), (((s(Z, X) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(40,plain,
% 0.21/0.54 (![Z: $i, X: $i, X1: $i] : ((s(Z, X) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> ![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.54 tff(41,axiom,(![Z: $i, X: $i, X1: $i] : ((s(Z, X) | (~s(X, f1(X, X1)))) | (~s(X1, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_21')).
% 0.21/0.54 tff(42,plain,
% 0.21/0.54 (![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.54 tff(43,plain,
% 0.21/0.54 (![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.54 tff(44,plain,(
% 0.21/0.54 ![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(skolemize,[status(sab)],[43])).
% 0.21/0.54 tff(45,plain,
% 0.21/0.54 (![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.21/0.54 tff(46,plain,
% 0.21/0.54 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(47,plain,
% 0.21/0.54 (((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) <=> (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(48,plain,
% 0.21/0.54 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.54 tff(49,plain,
% 0.21/0.54 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.54 inference(transitivity,[status(thm)],[48, 46])).
% 0.21/0.54 tff(50,plain,
% 0.21/0.54 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(51,plain,
% 0.21/0.54 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.55 tff(52,plain,
% 0.21/0.55 (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[51, 45])).
% 0.21/0.55 tff(53,plain,
% 0.21/0.55 (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[52, 1, 3])).
% 0.21/0.55 tff(54,plain,
% 0.21/0.55 (^[Z: $i, X: $i, X1: $i] : refl(((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X))) <=> ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(55,plain,
% 0.21/0.55 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X))) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.55 tff(56,plain,
% 0.21/0.55 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X))) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(57,plain,
% 0.21/0.55 (^[Z: $i, X: $i, X1: $i] : rewrite((((~p(X, X)) | s(f1(X, X1), Z)) | (~q(X1, f1(X, X1)))) <=> ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(58,plain,
% 0.21/0.55 (![Z: $i, X: $i, X1: $i] : (((~p(X, X)) | s(f1(X, X1), Z)) | (~q(X1, f1(X, X1)))) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.55 tff(59,axiom,(![Z: $i, X: $i, X1: $i] : (((~p(X, X)) | s(f1(X, X1), Z)) | (~q(X1, f1(X, X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_13')).
% 0.21/0.55 tff(60,plain,
% 0.21/0.55 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.55 tff(61,plain,
% 0.21/0.55 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.55 tff(62,plain,(
% 0.21/0.55 ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[61])).
% 0.21/0.55 tff(63,plain,
% 0.21/0.55 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.21/0.55 tff(64,plain,
% 0.21/0.55 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(65,plain,
% 0.21/0.55 (((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(66,plain,
% 0.21/0.56 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.56 tff(67,plain,
% 0.21/0.56 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[66, 64])).
% 0.21/0.56 tff(68,plain,
% 0.21/0.56 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(69,plain,
% 0.21/0.56 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.56 tff(70,plain,
% 0.21/0.56 ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[69, 63, 53])).
% 0.21/0.56 tff(71,plain,
% 0.21/0.56 (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[70, 35])).
% 0.21/0.56 tff(72,plain,
% 0.21/0.56 (^[Z: $i, Z1: $i, X: $i, X1: $i] : refl((q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X))) <=> (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(73,plain,
% 0.48/0.56 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X))) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[72])).
% 0.48/0.56 tff(74,plain,
% 0.48/0.56 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X))) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(75,plain,
% 0.48/0.56 (^[Z: $i, Z1: $i, X: $i, X1: $i] : rewrite((((~p(X, X)) | s(f1(X, X1), Z)) | q(f1(X, X1), Z1)) <=> (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X))))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(76,plain,
% 0.48/0.56 (![Z: $i, Z1: $i, X: $i, X1: $i] : (((~p(X, X)) | s(f1(X, X1), Z)) | q(f1(X, X1), Z1)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[75])).
% 0.48/0.56 tff(77,axiom,(![Z: $i, Z1: $i, X: $i, X1: $i] : (((~p(X, X)) | s(f1(X, X1), Z)) | q(f1(X, X1), Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_14')).
% 0.48/0.56 tff(78,plain,
% 0.48/0.56 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.48/0.56 tff(79,plain,
% 0.48/0.56 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.48/0.56 tff(80,plain,(
% 0.48/0.56 ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(skolemize,[status(sab)],[79])).
% 0.48/0.56 tff(81,plain,
% 0.48/0.56 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.48/0.56 tff(82,plain,
% 0.48/0.56 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.48/0.56 inference(rewrite,[status(thm)],[])).
% 0.48/0.56 tff(83,plain,
% 0.48/0.56 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.48/0.56 inference(quant_inst,[status(thm)],[])).
% 0.48/0.56 tff(84,plain,
% 0.48/0.56 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.48/0.56 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.48/0.56 tff(85,plain,
% 0.48/0.56 (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))),
% 0.48/0.56 inference(unit_resolution,[status(thm)],[84, 81, 1, 4])).
% 0.48/0.56 tff(86,plain,
% 0.48/0.56 (^[Z: $i, X: $i, X1: $i] : refl((p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z)) <=> (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z)))),
% 0.48/0.56 inference(bind,[status(th)],[])).
% 0.48/0.56 tff(87,plain,
% 0.48/0.56 (![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z)) <=> ![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.56 inference(quant_intro,[status(thm)],[86])).
% 0.48/0.56 tff(88,plain,
% 0.48/0.56 (![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z)) <=> ![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(89,plain,
% 0.48/0.57 (^[Z: $i, X: $i, X1: $i] : rewrite(((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | (~s(X1, X1))) <=> (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z)))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(90,plain,
% 0.48/0.57 (![Z: $i, X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | (~s(X1, X1))) <=> ![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[89])).
% 0.48/0.57 tff(91,axiom,(![Z: $i, X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | (~s(X1, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_6')).
% 0.48/0.57 tff(92,plain,
% 0.48/0.57 (![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.48/0.57 tff(93,plain,
% 0.48/0.57 (![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.48/0.57 tff(94,plain,(
% 0.48/0.57 ![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.57 inference(skolemize,[status(sab)],[93])).
% 0.48/0.57 tff(95,plain,
% 0.48/0.57 (![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.48/0.57 tff(96,plain,
% 0.48/0.57 (((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | (p(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(elem!0, elem!0)) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | p(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(elem!0, elem!0)) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(97,plain,
% 0.48/0.57 ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | (p(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(elem!0, elem!0)) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(98,plain,
% 0.48/0.57 ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | p(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(elem!0, elem!0)) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.48/0.57 tff(99,plain,
% 0.48/0.57 (p(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(elem!0, elem!0))),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[98, 95, 2])).
% 0.48/0.57 tff(100,plain,
% 0.48/0.57 (~s(elem!0, elem!0)),
% 0.48/0.57 inference(unit_resolution,[status(thm)],[99, 85])).
% 0.48/0.57 tff(101,plain,
% 0.48/0.57 (^[Z: $i, Z1: $i, X: $i, X1: $i] : refl((q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X)) <=> (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X)))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(102,plain,
% 0.48/0.57 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[101])).
% 0.48/0.57 tff(103,plain,
% 0.48/0.57 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(104,plain,
% 0.48/0.57 (^[Z: $i, Z1: $i, X: $i, X1: $i] : trans(monotonicity(rewrite((s(Z, X) | (~q(Z1, Z1))) <=> ((~q(Z1, Z1)) | s(Z, X))), (((s(Z, X) | (~q(Z1, Z1))) | q(f1(X, X1), Z1)) <=> (((~q(Z1, Z1)) | s(Z, X)) | q(f1(X, X1), Z1)))), rewrite((((~q(Z1, Z1)) | s(Z, X)) | q(f1(X, X1), Z1)) <=> (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))), (((s(Z, X) | (~q(Z1, Z1))) | q(f1(X, X1), Z1)) <=> (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))))),
% 0.48/0.57 inference(bind,[status(th)],[])).
% 0.48/0.57 tff(105,plain,
% 0.48/0.57 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((s(Z, X) | (~q(Z1, Z1))) | q(f1(X, X1), Z1)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(quant_intro,[status(thm)],[104])).
% 0.48/0.57 tff(106,axiom,(![Z: $i, Z1: $i, X: $i, X1: $i] : ((s(Z, X) | (~q(Z1, Z1))) | q(f1(X, X1), Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_26')).
% 0.48/0.57 tff(107,plain,
% 0.48/0.57 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.48/0.57 tff(108,plain,
% 0.48/0.57 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.48/0.57 tff(109,plain,(
% 0.48/0.57 ![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(skolemize,[status(sab)],[108])).
% 0.48/0.57 tff(110,plain,
% 0.48/0.57 (![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))),
% 0.48/0.57 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.48/0.57 tff(111,plain,
% 0.48/0.57 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (s(elem!0, elem!0) | q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | s(elem!0, elem!0) | q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(112,plain,
% 0.48/0.57 ((q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(elem!0, elem!0)) <=> (s(elem!0, elem!0) | q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.48/0.57 inference(rewrite,[status(thm)],[])).
% 0.48/0.57 tff(113,plain,
% 0.48/0.57 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(elem!0, elem!0))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (s(elem!0, elem!0) | q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))))),
% 0.48/0.57 inference(monotonicity,[status(thm)],[112])).
% 0.48/0.57 tff(114,plain,
% 0.48/0.57 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(elem!0, elem!0))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | s(elem!0, elem!0) | q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.48/0.57 inference(transitivity,[status(thm)],[113, 111])).
% 0.48/0.57 tff(115,plain,
% 0.48/0.57 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(elem!0, elem!0))),
% 0.48/0.57 inference(quant_inst,[status(thm)],[])).
% 0.48/0.57 tff(116,plain,
% 0.48/0.57 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | s(elem!0, elem!0) | q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.48/0.58 tff(117,plain,
% 0.48/0.58 (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[116, 110, 100, 71])).
% 0.48/0.58 tff(118,plain,
% 0.48/0.58 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(119,plain,
% 0.48/0.58 ((q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(120,plain,
% 0.48/0.58 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.48/0.58 inference(monotonicity,[status(thm)],[119])).
% 0.48/0.58 tff(121,plain,
% 0.48/0.58 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.48/0.58 inference(transitivity,[status(thm)],[120, 118])).
% 0.48/0.58 tff(122,plain,
% 0.48/0.58 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.48/0.58 inference(quant_inst,[status(thm)],[])).
% 0.48/0.58 tff(123,plain,
% 0.48/0.58 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.48/0.58 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.48/0.58 tff(124,plain,
% 0.48/0.58 ($false),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[123, 81, 35, 53, 117])).
% 0.48/0.58 tff(125,plain,(s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.58 tff(126,plain,
% 0.48/0.58 (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.48/0.58 inference(unit_resolution,[status(thm)],[125, 4, 2, 3])).
% 0.48/0.58 tff(127,assumption,(~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.48/0.58 tff(128,assumption,(s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.48/0.58 tff(129,assumption,(~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.48/0.58 tff(130,plain,
% 0.48/0.58 (^[Z: $i, Z1: $i, X: $i, X1: $i] : refl(((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X)) <=> ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X)))),
% 0.48/0.58 inference(bind,[status(th)],[])).
% 0.48/0.58 tff(131,plain,
% 0.48/0.58 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.58 inference(quant_intro,[status(thm)],[130])).
% 0.48/0.58 tff(132,plain,
% 0.48/0.58 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.58 inference(rewrite,[status(thm)],[])).
% 0.48/0.58 tff(133,plain,
% 0.48/0.58 (^[Z: $i, Z1: $i, X: $i, X1: $i] : trans(monotonicity(rewrite((s(Z, X) | (~s(X, f1(X, X1)))) <=> ((~s(X, f1(X, X1))) | s(Z, X))), (((s(Z, X) | (~s(X, f1(X, X1)))) | q(f1(X, X1), Z1)) <=> (((~s(X, f1(X, X1))) | s(Z, X)) | q(f1(X, X1), Z1)))), rewrite((((~s(X, f1(X, X1))) | s(Z, X)) | q(f1(X, X1), Z1)) <=> ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))), (((s(Z, X) | (~s(X, f1(X, X1)))) | q(f1(X, X1), Z1)) <=> ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))))),
% 0.48/0.58 inference(bind,[status(th)],[])).
% 0.48/0.59 tff(134,plain,
% 0.48/0.59 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((s(Z, X) | (~s(X, f1(X, X1)))) | q(f1(X, X1), Z1)) <=> ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.59 inference(quant_intro,[status(thm)],[133])).
% 0.48/0.59 tff(135,axiom,(![Z: $i, Z1: $i, X: $i, X1: $i] : ((s(Z, X) | (~s(X, f1(X, X1)))) | q(f1(X, X1), Z1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_20')).
% 0.48/0.59 tff(136,plain,
% 0.48/0.59 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.59 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.48/0.59 tff(137,plain,
% 0.48/0.59 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.59 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.48/0.59 tff(138,plain,(
% 0.48/0.59 ![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.59 inference(skolemize,[status(sab)],[137])).
% 0.48/0.59 tff(139,plain,
% 0.48/0.59 (![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))),
% 0.48/0.59 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.48/0.59 tff(140,plain,
% 0.48/0.59 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.48/0.59 inference(rewrite,[status(thm)],[])).
% 0.48/0.59 tff(141,plain,
% 0.48/0.59 (((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.48/0.59 inference(rewrite,[status(thm)],[])).
% 0.48/0.59 tff(142,plain,
% 0.48/0.59 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.48/0.59 inference(monotonicity,[status(thm)],[141])).
% 0.48/0.59 tff(143,plain,
% 0.48/0.59 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.51/0.59 inference(transitivity,[status(thm)],[142, 140])).
% 0.51/0.59 tff(144,plain,
% 0.51/0.59 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(145,plain,
% 0.51/0.59 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.51/0.59 tff(146,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[145, 139, 129, 128, 127])).
% 0.51/0.59 tff(147,plain,(q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(148,plain,
% 0.51/0.59 (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[147, 126, 21])).
% 0.51/0.59 tff(149,plain,
% 0.51/0.59 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(150,plain,
% 0.51/0.59 (((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))) <=> (s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(151,plain,
% 0.51/0.59 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.51/0.59 inference(monotonicity,[status(thm)],[150])).
% 0.51/0.59 tff(152,plain,
% 0.51/0.59 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.60 inference(transitivity,[status(thm)],[151, 149])).
% 0.51/0.60 tff(153,plain,
% 0.51/0.60 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(154,plain,
% 0.51/0.60 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.51/0.60 tff(155,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[154, 139, 2, 148, 4])).
% 0.51/0.60 tff(156,plain,(q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(157,plain,
% 0.51/0.60 (q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[156, 3, 2])).
% 0.51/0.60 tff(158,plain,
% 0.51/0.60 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(159,plain,
% 0.51/0.60 (((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))) <=> (s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(160,plain,
% 0.51/0.60 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[159])).
% 0.51/0.60 tff(161,plain,
% 0.51/0.60 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.51/0.60 inference(transitivity,[status(thm)],[160, 158])).
% 0.51/0.60 tff(162,plain,
% 0.51/0.60 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(163,plain,
% 0.51/0.60 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X1, X1)) | (~q(Z1, Z1)) | s(Z, X))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.51/0.60 tff(164,plain,
% 0.51/0.60 ($false),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[163, 15, 2, 3, 157])).
% 0.51/0.60 tff(165,plain,((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.60 tff(166,plain,
% 0.51/0.60 (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[165, 2])).
% 0.51/0.60 tff(167,assumption,(p(f1(elem!0, elem!0), f1(elem!0, elem!0))), introduced(assumption)).
% 0.51/0.60 tff(168,assumption,(q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))), introduced(assumption)).
% 0.51/0.60 tff(169,assumption,(~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))), introduced(assumption)).
% 0.51/0.60 tff(170,plain,
% 0.51/0.60 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(171,plain,
% 0.51/0.60 (((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(172,plain,
% 0.51/0.60 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[171])).
% 0.51/0.61 tff(173,plain,
% 0.51/0.61 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.51/0.61 inference(transitivity,[status(thm)],[172, 170])).
% 0.51/0.61 tff(174,plain,
% 0.51/0.61 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(175,plain,
% 0.51/0.61 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.51/0.61 tff(176,plain,
% 0.51/0.61 ($false),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[175, 63, 167, 168, 169])).
% 0.51/0.61 tff(177,plain,(s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.61 tff(178,plain,
% 0.51/0.61 (s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[177, 168, 167])).
% 0.51/0.61 tff(179,plain,
% 0.51/0.61 (^[Z: $i, X: $i, X1: $i] : refl(((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X)) <=> ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X)))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(180,plain,
% 0.51/0.61 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X)) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[179])).
% 0.51/0.61 tff(181,plain,
% 0.51/0.61 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X)) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(182,plain,
% 0.51/0.62 (^[Z: $i, X: $i, X1: $i] : trans(monotonicity(rewrite((s(Z, X) | (~s(X, f1(X, X1)))) <=> ((~s(X, f1(X, X1))) | s(Z, X))), (((s(Z, X) | (~s(X, f1(X, X1)))) | (~q(X1, f1(X, X1)))) <=> (((~s(X, f1(X, X1))) | s(Z, X)) | (~q(X1, f1(X, X1)))))), rewrite((((~s(X, f1(X, X1))) | s(Z, X)) | (~q(X1, f1(X, X1)))) <=> ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))), (((s(Z, X) | (~s(X, f1(X, X1)))) | (~q(X1, f1(X, X1)))) <=> ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(183,plain,
% 0.51/0.62 (![Z: $i, X: $i, X1: $i] : ((s(Z, X) | (~s(X, f1(X, X1)))) | (~q(X1, f1(X, X1)))) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[182])).
% 0.51/0.62 tff(184,axiom,(![Z: $i, X: $i, X1: $i] : ((s(Z, X) | (~s(X, f1(X, X1)))) | (~q(X1, f1(X, X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_19')).
% 0.51/0.62 tff(185,plain,
% 0.51/0.62 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.51/0.62 tff(186,plain,
% 0.51/0.62 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.51/0.62 tff(187,plain,(
% 0.51/0.62 ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.62 inference(skolemize,[status(sab)],[186])).
% 0.51/0.62 tff(188,plain,
% 0.51/0.62 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.51/0.62 tff(189,plain,
% 0.51/0.62 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(190,plain,
% 0.51/0.62 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(191,plain,
% 0.51/0.62 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.51/0.62 tff(192,plain,
% 0.51/0.62 (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[191, 188, 2, 168])).
% 0.51/0.62 tff(193,plain,
% 0.51/0.62 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.51/0.63 inference(rewrite,[status(thm)],[])).
% 0.51/0.63 tff(194,plain,
% 0.51/0.63 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.51/0.63 inference(quant_inst,[status(thm)],[])).
% 0.51/0.63 tff(195,plain,
% 0.51/0.63 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.51/0.63 tff(196,plain,
% 0.51/0.63 (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[195, 188, 192, 178])).
% 0.51/0.63 tff(197,plain,
% 0.51/0.63 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.51/0.63 inference(rewrite,[status(thm)],[])).
% 0.51/0.63 tff(198,plain,
% 0.51/0.63 ((q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.51/0.64 inference(rewrite,[status(thm)],[])).
% 0.51/0.64 tff(199,plain,
% 0.51/0.64 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))))),
% 0.51/0.64 inference(monotonicity,[status(thm)],[198])).
% 0.51/0.64 tff(200,plain,
% 0.51/0.64 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.51/0.64 inference(transitivity,[status(thm)],[199, 197])).
% 0.51/0.64 tff(201,plain,
% 0.51/0.64 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.51/0.64 inference(quant_inst,[status(thm)],[])).
% 0.51/0.64 tff(202,plain,
% 0.51/0.64 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.56/0.65 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.56/0.65 tff(203,plain,
% 0.56/0.65 (~q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.56/0.65 inference(unit_resolution,[status(thm)],[202, 110, 166, 196])).
% 0.56/0.65 tff(204,plain,
% 0.56/0.65 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(205,plain,
% 0.56/0.65 (((~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(206,plain,
% 0.56/0.65 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[205])).
% 0.57/0.65 tff(207,plain,
% 0.57/0.65 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.57/0.65 inference(transitivity,[status(thm)],[206, 204])).
% 0.57/0.65 tff(208,plain,
% 0.57/0.65 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.65 inference(quant_inst,[status(thm)],[])).
% 0.57/0.65 tff(209,plain,
% 0.57/0.65 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)), f1(f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.65 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.57/0.65 tff(210,plain,
% 0.57/0.65 ($false),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[209, 139, 192, 178, 203])).
% 0.57/0.65 tff(211,plain,((~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.65 tff(212,plain,
% 0.57/0.65 (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[211, 167, 2])).
% 0.57/0.65 tff(213,plain,
% 0.57/0.65 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(214,plain,
% 0.57/0.66 ((q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(215,plain,
% 0.57/0.66 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.57/0.66 inference(monotonicity,[status(thm)],[214])).
% 0.57/0.66 tff(216,plain,
% 0.57/0.66 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.66 inference(transitivity,[status(thm)],[215, 213])).
% 0.57/0.66 tff(217,plain,
% 0.57/0.66 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(218,plain,
% 0.57/0.66 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.57/0.66 tff(219,plain,
% 0.57/0.66 ($false),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[218, 81, 167, 166, 212])).
% 0.57/0.66 tff(220,plain,((~p(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.66 tff(221,plain,
% 0.57/0.66 (~p(f1(elem!0, elem!0), f1(elem!0, elem!0))),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[220, 2])).
% 0.57/0.66 tff(222,plain,
% 0.57/0.66 (~s(elem!0, elem!0)),
% 0.57/0.66 inference(unit_resolution,[status(thm)],[99, 221])).
% 0.57/0.66 tff(223,assumption,(~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.57/0.66 tff(224,assumption,(~s(elem!0, elem!0)), introduced(assumption)).
% 0.57/0.66 tff(225,assumption,(~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.57/0.66 tff(226,plain,
% 0.57/0.66 (^[Z: $i, X: $i, X1: $i] : refl(((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) <=> ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(227,plain,
% 0.57/0.66 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[226])).
% 0.57/0.66 tff(228,plain,
% 0.57/0.66 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(229,plain,
% 0.57/0.66 (^[Z: $i, X: $i, X1: $i] : rewrite(((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | (~q(X1, f1(X, X1)))) <=> ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)))),
% 0.57/0.66 inference(bind,[status(th)],[])).
% 0.57/0.66 tff(230,plain,
% 0.57/0.66 (![Z: $i, X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | (~q(X1, f1(X, X1)))) <=> ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(quant_intro,[status(thm)],[229])).
% 0.57/0.66 tff(231,axiom,(![Z: $i, X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z)) | (~q(X1, f1(X, X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_4')).
% 0.57/0.66 tff(232,plain,
% 0.57/0.66 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.57/0.66 tff(233,plain,
% 0.57/0.66 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.57/0.66 tff(234,plain,(
% 0.57/0.66 ![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(skolemize,[status(sab)],[233])).
% 0.57/0.66 tff(235,plain,
% 0.57/0.66 (![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.57/0.66 tff(236,plain,
% 0.57/0.66 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))) | ((~q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))) | (~q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.66 inference(rewrite,[status(thm)],[])).
% 0.57/0.66 tff(237,plain,
% 0.57/0.66 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))) | ((~q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.66 inference(quant_inst,[status(thm)],[])).
% 0.57/0.66 tff(238,plain,
% 0.57/0.66 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | s(f1(X, X1), Z))) | (~q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.57/0.66 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.57/0.66 tff(239,plain,
% 0.57/0.66 ((~q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[238, 235, 223])).
% 0.57/0.67 tff(240,plain,
% 0.57/0.67 (~q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[239, 225])).
% 0.57/0.67 tff(241,plain,
% 0.57/0.67 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(242,plain,
% 0.57/0.67 ((q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(elem!0, elem!0)) <=> (q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.67 inference(rewrite,[status(thm)],[])).
% 0.57/0.67 tff(243,plain,
% 0.57/0.67 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(elem!0, elem!0))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.57/0.67 inference(monotonicity,[status(thm)],[242])).
% 0.57/0.67 tff(244,plain,
% 0.57/0.67 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(elem!0, elem!0))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.67 inference(transitivity,[status(thm)],[243, 241])).
% 0.57/0.67 tff(245,plain,
% 0.57/0.67 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | (q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(elem!0, elem!0))),
% 0.57/0.67 inference(quant_inst,[status(thm)],[])).
% 0.57/0.67 tff(246,plain,
% 0.57/0.67 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | (~q(Z1, Z1)) | s(Z, X))) | q(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0) | (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.67 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.57/0.67 tff(247,plain,
% 0.57/0.67 (~q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.57/0.67 inference(unit_resolution,[status(thm)],[246, 110, 224, 240])).
% 0.57/0.67 tff(248,plain,
% 0.57/0.67 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(249,plain,
% 0.57/0.68 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(250,plain,
% 0.57/0.68 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | q(f1(X, X1), Z1) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | q(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.57/0.68 tff(251,plain,
% 0.57/0.68 ($false),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[250, 31, 225, 223, 247])).
% 0.57/0.68 tff(252,plain,(p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(elem!0, elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.68 tff(253,plain,
% 0.57/0.68 (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[252, 224, 223])).
% 0.57/0.68 tff(254,assumption,(s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))), introduced(assumption)).
% 0.57/0.68 tff(255,plain,
% 0.57/0.68 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(256,plain,
% 0.57/0.68 (((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) <=> (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.57/0.68 inference(rewrite,[status(thm)],[])).
% 0.57/0.68 tff(257,plain,
% 0.57/0.68 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))))),
% 0.57/0.68 inference(monotonicity,[status(thm)],[256])).
% 0.57/0.68 tff(258,plain,
% 0.57/0.68 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.57/0.68 inference(transitivity,[status(thm)],[257, 255])).
% 0.57/0.68 tff(259,plain,
% 0.57/0.68 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.57/0.68 inference(quant_inst,[status(thm)],[])).
% 0.57/0.68 tff(260,plain,
% 0.57/0.68 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.68 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.57/0.68 tff(261,plain,
% 0.57/0.68 (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))),
% 0.57/0.68 inference(unit_resolution,[status(thm)],[260, 45, 254, 1])).
% 0.57/0.68 tff(262,plain,
% 0.57/0.68 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(263,plain,
% 0.57/0.69 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(264,plain,
% 0.57/0.69 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.57/0.69 tff(265,plain,
% 0.57/0.69 (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[264, 188, 254, 1])).
% 0.57/0.69 tff(266,assumption,(p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), introduced(assumption)).
% 0.57/0.69 tff(267,plain,
% 0.57/0.69 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(268,plain,
% 0.57/0.69 ((q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(269,plain,
% 0.57/0.70 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))))),
% 0.57/0.70 inference(monotonicity,[status(thm)],[268])).
% 0.57/0.70 tff(270,plain,
% 0.57/0.70 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.70 inference(transitivity,[status(thm)],[269, 267])).
% 0.57/0.70 tff(271,plain,
% 0.57/0.70 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(272,plain,
% 0.57/0.70 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.57/0.70 tff(273,plain,
% 0.57/0.70 ($false),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[272, 81, 266, 265, 261])).
% 0.57/0.70 tff(274,plain,((~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.57/0.70 tff(275,plain,
% 0.57/0.70 (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[274, 253, 1])).
% 0.62/0.70 tff(276,assumption,(~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))), introduced(assumption)).
% 0.62/0.70 tff(277,plain,
% 0.62/0.70 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(278,plain,
% 0.62/0.70 ((q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> (s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(279,plain,
% 0.62/0.70 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[278])).
% 0.62/0.70 tff(280,plain,
% 0.62/0.70 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.71 inference(transitivity,[status(thm)],[279, 277])).
% 0.62/0.71 tff(281,plain,
% 0.62/0.71 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.71 inference(quant_inst,[status(thm)],[])).
% 0.62/0.71 tff(282,plain,
% 0.62/0.71 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : (q(f1(X, X1), Z1) | s(f1(X, X1), Z) | (~p(X, X)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.62/0.71 tff(283,plain,
% 0.62/0.71 ($false),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[282, 81, 266, 276, 127])).
% 0.62/0.71 tff(284,plain,(s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.71 tff(285,plain,
% 0.62/0.71 (q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[284, 275, 253])).
% 0.62/0.71 tff(286,plain,
% 0.62/0.71 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.71 inference(rewrite,[status(thm)],[])).
% 0.62/0.71 tff(287,plain,
% 0.62/0.71 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.71 inference(quant_inst,[status(thm)],[])).
% 0.62/0.71 tff(288,plain,
% 0.62/0.71 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | s(f1(X, X1), Z) | (~p(X, X)))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.62/0.72 tff(289,plain,
% 0.62/0.72 (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[288, 63, 253, 275])).
% 0.62/0.72 tff(290,plain,
% 0.62/0.72 ($false),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[116, 110, 224, 289, 285])).
% 0.62/0.72 tff(291,plain,(s(elem!0, elem!0) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.72 tff(292,plain,
% 0.62/0.72 (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[291, 222, 166])).
% 0.62/0.72 tff(293,plain,
% 0.62/0.72 (((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(294,plain,
% 0.62/0.72 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | ((~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(quant_inst,[status(thm)],[])).
% 0.62/0.72 tff(295,plain,
% 0.62/0.72 ((~![Z: $i, X: $i, X1: $i] : ((~q(X1, f1(X, X1))) | (~s(X, f1(X, X1))) | s(Z, X))) | (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.62/0.72 tff(296,plain,
% 0.62/0.72 (~q(f1(elem!0, elem!0), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[295, 188, 166, 292])).
% 0.62/0.72 tff(297,plain,
% 0.62/0.72 (~q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[116, 110, 222, 296])).
% 0.62/0.72 tff(298,plain,
% 0.62/0.72 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(299,plain,
% 0.62/0.72 (((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(rewrite,[status(thm)],[])).
% 0.62/0.72 tff(300,plain,
% 0.62/0.72 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | (s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.62/0.72 inference(monotonicity,[status(thm)],[299])).
% 0.62/0.72 tff(301,plain,
% 0.62/0.72 (((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(transitivity,[status(thm)],[300, 298])).
% 0.62/0.72 tff(302,plain,
% 0.62/0.72 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.72 inference(quant_inst,[status(thm)],[])).
% 0.62/0.72 tff(303,plain,
% 0.62/0.72 ((~![Z: $i, Z1: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | q(f1(X, X1), Z1) | s(Z, X))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | q(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.72 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.62/0.72 tff(304,plain,
% 0.62/0.72 ($false),
% 0.62/0.72 inference(unit_resolution,[status(thm)],[303, 139, 166, 292, 297])).
% 0.62/0.73 tff(305,plain,(s(f1(elem!0, elem!0), f1(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.73 tff(306,plain,
% 0.62/0.73 (((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.73 inference(rewrite,[status(thm)],[])).
% 0.62/0.73 tff(307,plain,
% 0.62/0.73 ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.73 inference(quant_inst,[status(thm)],[])).
% 0.62/0.73 tff(308,plain,
% 0.62/0.73 ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.62/0.73 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.62/0.73 tff(309,plain,
% 0.62/0.73 (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.62/0.73 inference(unit_resolution,[status(thm)],[308, 95, 305, 223])).
% 0.62/0.73 tff(310,plain,
% 0.62/0.73 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.62/0.73 inference(rewrite,[status(thm)],[])).
% 0.62/0.73 tff(311,plain,
% 0.62/0.73 (((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.62/0.73 inference(rewrite,[status(thm)],[])).
% 0.62/0.73 tff(312,plain,
% 0.62/0.73 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))))),
% 0.62/0.73 inference(monotonicity,[status(thm)],[311])).
% 0.62/0.73 tff(313,plain,
% 0.62/0.73 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.62/0.73 inference(transitivity,[status(thm)],[312, 310])).
% 0.62/0.73 tff(314,plain,
% 0.62/0.73 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.73 inference(quant_inst,[status(thm)],[])).
% 0.62/0.73 tff(315,plain,
% 0.62/0.73 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.73 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.62/0.73 tff(316,plain,
% 0.62/0.73 (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.73 inference(unit_resolution,[status(thm)],[315, 45, 305, 223])).
% 0.62/0.73 tff(317,plain,
% 0.62/0.73 (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0)))),
% 0.62/0.73 inference(unit_resolution,[status(thm)],[274, 316, 309])).
% 0.62/0.73 tff(318,plain,
% 0.62/0.73 (^[Z: $i, X: $i, X1: $i] : refl(((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X))) <=> ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X))))),
% 0.62/0.73 inference(bind,[status(th)],[])).
% 0.62/0.73 tff(319,plain,
% 0.62/0.73 (![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X))) <=> ![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(quant_intro,[status(thm)],[318])).
% 0.62/0.73 tff(320,plain,
% 0.62/0.73 (![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X))) <=> ![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(rewrite,[status(thm)],[])).
% 0.62/0.73 tff(321,plain,
% 0.62/0.73 (^[Z: $i, X: $i, X1: $i] : rewrite((((~p(X, X)) | s(f1(X, X1), Z)) | (~s(X1, X1))) <=> ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X))))),
% 0.62/0.73 inference(bind,[status(th)],[])).
% 0.62/0.73 tff(322,plain,
% 0.62/0.73 (![Z: $i, X: $i, X1: $i] : (((~p(X, X)) | s(f1(X, X1), Z)) | (~s(X1, X1))) <=> ![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(quant_intro,[status(thm)],[321])).
% 0.62/0.73 tff(323,axiom,(![Z: $i, X: $i, X1: $i] : (((~p(X, X)) | s(f1(X, X1), Z)) | (~s(X1, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_15')).
% 0.62/0.73 tff(324,plain,
% 0.62/0.73 (![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.62/0.73 tff(325,plain,
% 0.62/0.73 (![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.62/0.73 tff(326,plain,(
% 0.62/0.73 ![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(skolemize,[status(sab)],[325])).
% 0.62/0.73 tff(327,plain,
% 0.62/0.73 (![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))),
% 0.62/0.73 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.62/0.73 tff(328,plain,
% 0.62/0.73 (((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.74 inference(rewrite,[status(thm)],[])).
% 0.62/0.74 tff(329,plain,
% 0.62/0.74 ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.74 inference(quant_inst,[status(thm)],[])).
% 0.62/0.74 tff(330,plain,
% 0.62/0.74 ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.74 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.62/0.74 tff(331,plain,
% 0.62/0.74 ($false),
% 0.62/0.74 inference(unit_resolution,[status(thm)],[330, 327, 309, 305, 317])).
% 0.62/0.74 tff(332,plain,(s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.74 tff(333,plain,
% 0.62/0.74 (~s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.74 inference(unit_resolution,[status(thm)],[52, 1, 332])).
% 0.62/0.74 tff(334,plain,
% 0.62/0.74 (((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.74 inference(rewrite,[status(thm)],[])).
% 0.62/0.74 tff(335,plain,
% 0.62/0.74 (((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.74 inference(rewrite,[status(thm)],[])).
% 0.62/0.74 tff(336,plain,
% 0.62/0.74 (((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.62/0.74 inference(monotonicity,[status(thm)],[335])).
% 0.62/0.74 tff(337,plain,
% 0.62/0.74 (((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.74 inference(transitivity,[status(thm)],[336, 334])).
% 0.62/0.74 tff(338,plain,
% 0.62/0.74 ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.74 inference(quant_inst,[status(thm)],[])).
% 0.62/0.74 tff(339,plain,
% 0.62/0.74 ((~![Z: $i, X: $i, X1: $i] : ((~s(X1, X1)) | s(f1(X, X1), Z) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | s(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.62/0.74 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.62/0.74 tff(340,plain,
% 0.62/0.74 (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.62/0.74 inference(unit_resolution,[status(thm)],[339, 327, 305, 333])).
% 0.62/0.74 tff(341,plain,
% 0.62/0.74 (((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.74 inference(rewrite,[status(thm)],[])).
% 0.62/0.74 tff(342,plain,
% 0.62/0.74 ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.62/0.74 inference(quant_inst,[status(thm)],[])).
% 0.62/0.74 tff(343,plain,
% 0.62/0.74 ((~![Z: $i, X: $i, X1: $i] : (p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)) | s(f1(X, X1), Z))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))),
% 0.62/0.74 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.62/0.74 tff(344,plain,
% 0.62/0.74 ($false),
% 0.62/0.74 inference(unit_resolution,[status(thm)],[343, 95, 340, 305, 1])).
% 0.62/0.74 tff(345,plain,(s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.75 tff(346,plain,
% 0.62/0.75 (^[X: $i, X1: $i] : refl(((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X))) <=> ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X))))),
% 0.62/0.75 inference(bind,[status(th)],[])).
% 0.62/0.75 tff(347,plain,
% 0.62/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X))) <=> ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(quant_intro,[status(thm)],[346])).
% 0.62/0.75 tff(348,plain,
% 0.62/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X))) <=> ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(349,plain,
% 0.62/0.75 (^[X: $i, X1: $i] : rewrite((((~p(X, X)) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X))))),
% 0.62/0.75 inference(bind,[status(th)],[])).
% 0.62/0.75 tff(350,plain,
% 0.62/0.75 (![X: $i, X1: $i] : (((~p(X, X)) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(quant_intro,[status(thm)],[349])).
% 0.62/0.75 tff(351,axiom,(![X: $i, X1: $i] : (((~p(X, X)) | (~s(X, f1(X, X1)))) | (~s(X1, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_12')).
% 0.62/0.75 tff(352,plain,
% 0.62/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.62/0.75 tff(353,plain,
% 0.62/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[352, 348])).
% 0.62/0.75 tff(354,plain,(
% 0.62/0.75 ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(skolemize,[status(sab)],[353])).
% 0.62/0.75 tff(355,plain,
% 0.62/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))),
% 0.62/0.75 inference(modus_ponens,[status(thm)],[354, 347])).
% 0.62/0.75 tff(356,plain,
% 0.62/0.75 (((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(357,plain,
% 0.62/0.75 (((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.62/0.75 inference(rewrite,[status(thm)],[])).
% 0.62/0.75 tff(358,plain,
% 0.62/0.75 (((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))))),
% 0.62/0.75 inference(monotonicity,[status(thm)],[357])).
% 0.62/0.75 tff(359,plain,
% 0.62/0.75 (((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))) <=> ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.67/0.75 inference(transitivity,[status(thm)],[358, 356])).
% 0.67/0.75 tff(360,plain,
% 0.67/0.75 ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(361,plain,
% 0.67/0.75 ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | (~p(X, X)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.67/0.75 tff(362,plain,
% 0.67/0.75 (~p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[361, 355, 305, 345])).
% 0.67/0.75 tff(363,plain,
% 0.67/0.75 (^[X: $i, X1: $i] : refl(((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1))) <=> ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1))))),
% 0.67/0.75 inference(bind,[status(th)],[])).
% 0.67/0.75 tff(364,plain,
% 0.67/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1))) <=> ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(quant_intro,[status(thm)],[363])).
% 0.67/0.75 tff(365,plain,
% 0.67/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1))) <=> ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(rewrite,[status(thm)],[])).
% 0.67/0.75 tff(366,plain,
% 0.67/0.75 (^[X: $i, X1: $i] : trans(monotonicity(rewrite((p(f1(X, X1), f1(X, X1)) | (~s(X, f1(X, X1)))) <=> ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)))), (((p(f1(X, X1), f1(X, X1)) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> (((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1))) | (~s(X1, X1))))), rewrite((((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1))) | (~s(X1, X1))) <=> ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))), (((p(f1(X, X1), f1(X, X1)) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))))),
% 0.67/0.75 inference(bind,[status(th)],[])).
% 0.67/0.75 tff(367,plain,
% 0.67/0.75 (![X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | (~s(X, f1(X, X1)))) | (~s(X1, X1))) <=> ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(quant_intro,[status(thm)],[366])).
% 0.67/0.75 tff(368,axiom,(![X: $i, X1: $i] : ((p(f1(X, X1), f1(X, X1)) | (~s(X, f1(X, X1)))) | (~s(X1, X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_3')).
% 0.67/0.75 tff(369,plain,
% 0.67/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.67/0.75 tff(370,plain,
% 0.67/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[369, 365])).
% 0.67/0.75 tff(371,plain,(
% 0.67/0.75 ![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(skolemize,[status(sab)],[370])).
% 0.67/0.75 tff(372,plain,
% 0.67/0.75 (![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[371, 364])).
% 0.67/0.75 tff(373,plain,
% 0.67/0.75 (((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(374,plain,
% 0.67/0.76 (((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(375,plain,
% 0.67/0.76 (((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | ((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0)))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[374])).
% 0.67/0.76 tff(376,plain,
% 0.67/0.76 (((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | ((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(transitivity,[status(thm)],[375, 373])).
% 0.67/0.76 tff(377,plain,
% 0.67/0.76 ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | ((~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(378,plain,
% 0.67/0.76 ((~![X: $i, X1: $i] : ((~s(X, f1(X, X1))) | p(f1(X, X1), f1(X, X1)) | (~s(X1, X1)))) | p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.67/0.76 tff(379,plain,
% 0.67/0.76 (p(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[378, 372, 305])).
% 0.67/0.76 tff(380,plain,
% 0.67/0.76 (~s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[379, 362])).
% 0.67/0.76 tff(381,plain,
% 0.67/0.76 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(382,plain,
% 0.67/0.76 (((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0)))) <=> ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(383,plain,
% 0.67/0.76 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))))),
% 0.67/0.76 inference(monotonicity,[status(thm)],[382])).
% 0.67/0.76 tff(384,plain,
% 0.67/0.76 (((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))) <=> ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))))),
% 0.67/0.76 inference(transitivity,[status(thm)],[383, 381])).
% 0.67/0.76 tff(385,plain,
% 0.67/0.76 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | ((~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0)))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(quant_inst,[status(thm)],[])).
% 0.67/0.76 tff(386,plain,
% 0.67/0.76 ((~![Z: $i, X: $i, X1: $i] : ((~s(X, f1(X, X1))) | (~s(X1, X1)) | s(Z, X))) | (~s(f1(elem!0, elem!0), f1(elem!0, elem!0))) | s(f1(elem!0, elem!0), f1(f1(elem!0, elem!0), f1(elem!0, elem!0))) | (~s(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(f1(f1(elem!0, elem!0), f1(elem!0, elem!0)), f1(elem!0, elem!0))))),
% 0.67/0.76 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.67/0.76 tff(387,plain,
% 0.67/0.76 ($false),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[386, 45, 305, 380, 345])).
% 0.67/0.76 % SZS output end Proof
%------------------------------------------------------------------------------