TSTP Solution File: SYN349-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN349-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:54:54 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN349-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:51:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(f_type, type, (
% 0.20/0.45 f: ( $i * $i ) > $o)).
% 0.20/0.45 tff(g_type, type, (
% 0.20/0.45 g: ( $i * $i ) > $i)).
% 0.20/0.45 tff(w_type, type, (
% 0.20/0.45 w: $i > $i)).
% 0.20/0.45 tff(elem_0_type, type, (
% 0.20/0.45 elem_0: $i)).
% 0.20/0.45 tff(1,assumption,(~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))), introduced(assumption)).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : refl(((~f(X, g(X, Y))) | f(w(X), g(X, Y))) <=> ((~f(X, g(X, Y))) | f(w(X), g(X, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y))) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(5,axiom,(![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.45 tff(7,plain,(
% 0.20/0.45 ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[6])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : refl((f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))) <=> ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))) <=> ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((f(X, g(X, Y)) | (~f(g(X, Y), Y))) <=> (f(X, g(X, Y)) | (~f(g(X, Y), Y)))), (((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) <=> ((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))))), rewrite(((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)))), (((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y))))), ((((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) | (~f(g(X, Y), w(X)))) <=> ((f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y))) | (~f(g(X, Y), w(X)))))), rewrite(((f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y))) | (~f(g(X, Y), w(X)))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))), ((((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) | (~f(g(X, Y), w(X)))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) | (~f(g(X, Y), w(X)))) <=> ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.46 tff(19,axiom,(![Y: $i, X: $i] : (((f(X, g(X, Y)) | (~f(g(X, Y), Y))) | f(Y, g(X, Y))) | (~f(g(X, Y), w(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.46 tff(22,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[21])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 ((f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(Y, g(X, Y)) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[29, 23, 13, 1])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl((f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y)) <=> (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y)) <=> ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y)) <=> ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((f(X, g(X, Y)) | f(g(X, Y), Y)) <=> (f(X, g(X, Y)) | f(g(X, Y), Y))), (((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))) <=> ((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))))), rewrite(((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | f(g(X, Y), Y))), (((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))) <=> (f(X, g(X, Y)) | f(Y, g(X, Y)) | f(g(X, Y), Y)))), ((((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))) | f(g(X, Y), w(X))) <=> ((f(X, g(X, Y)) | f(Y, g(X, Y)) | f(g(X, Y), Y)) | f(g(X, Y), w(X))))), rewrite(((f(X, g(X, Y)) | f(Y, g(X, Y)) | f(g(X, Y), Y)) | f(g(X, Y), w(X))) <=> (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))), ((((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))) | f(g(X, Y), w(X))) <=> (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(35,plain,
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% 0.20/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.46 tff(36,axiom,(![Y: $i, X: $i] : (((f(X, g(X, Y)) | f(g(X, Y), Y)) | f(Y, g(X, Y))) | f(g(X, Y), w(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.46 tff(39,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))),
% 0.20/0.46 inference(skolemize,[status(sab)],[38])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 ((f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) <=> (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[46, 40, 13, 1, 30])).
% 0.20/0.46 tff(48,plain,(f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl(((~f(w(X), g(X, Y))) | f(X, g(X, Y))) <=> ((~f(w(X), g(X, Y))) | f(X, g(X, Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y))) <=> ![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y))) <=> ![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : rewrite((f(X, g(X, Y)) | (~f(w(X), g(X, Y)))) <=> ((~f(w(X), g(X, Y))) | f(X, g(X, Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (![Y: $i, X: $i] : (f(X, g(X, Y)) | (~f(w(X), g(X, Y)))) <=> ![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.46 tff(54,axiom,(![Y: $i, X: $i] : (f(X, g(X, Y)) | (~f(w(X), g(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.46 tff(57,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[56])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | ((~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | ((~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 (f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl(((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))) <=> ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X)))) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) <=> ((~f(X, g(X, Y))) | (~f(g(X, Y), Y)))), ((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) <=> (((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))))), rewrite((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) <=> ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)))), ((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) <=> ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y))))), (((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) | (~f(g(X, Y), w(X)))) <=> (((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(g(X, Y), w(X)))))), rewrite((((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(g(X, Y), w(X)))) <=> ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))), (((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) | (~f(g(X, Y), w(X)))) <=> ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) | (~f(g(X, Y), w(X)))) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.47 tff(68,axiom,(![Y: $i, X: $i] : ((((~f(X, g(X, Y))) | (~f(g(X, Y), Y))) | (~f(Y, g(X, Y)))) | (~f(g(X, Y), w(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.47 tff(71,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[70])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | (~f(g(X, Y), Y)) | (~f(g(X, Y), w(X))))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[78, 72, 48])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (~f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[79, 62])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : refl(((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y)) <=> ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y)) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y)) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : trans(monotonicity(rewrite((((~f(X, g(X, Y))) | f(g(X, Y), Y)) | (~f(Y, g(X, Y)))) <=> ((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))), (((((~f(X, g(X, Y))) | f(g(X, Y), Y)) | (~f(Y, g(X, Y)))) | f(g(X, Y), w(X))) <=> (((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | f(g(X, Y), Y)) | f(g(X, Y), w(X))))), rewrite((((~f(X, g(X, Y))) | (~f(Y, g(X, Y))) | f(g(X, Y), Y)) | f(g(X, Y), w(X))) <=> ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))), (((((~f(X, g(X, Y))) | f(g(X, Y), Y)) | (~f(Y, g(X, Y)))) | f(g(X, Y), w(X))) <=> ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((((~f(X, g(X, Y))) | f(g(X, Y), Y)) | (~f(Y, g(X, Y)))) | f(g(X, Y), w(X))) <=> ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.47 tff(86,axiom,(![Y: $i, X: $i] : ((((~f(X, g(X, Y))) | f(g(X, Y), Y)) | (~f(Y, g(X, Y)))) | f(g(X, Y), w(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.47 tff(89,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(skolemize,[status(sab)],[88])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))) <=> ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | (~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | (~f(w(g(elem!0, elem!0)), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 ((~f(g(elem!0, elem!0), g(g(elem!0, elem!0), w(g(elem!0, elem!0))))) | f(g(g(elem!0, elem!0), w(g(elem!0, elem!0))), w(g(elem!0, elem!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[96, 90, 48])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[97, 80, 62])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------