%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN349-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:38:51 AM UTC 2025
% Result : Unsatisfiable 4.90s 5.07s
% Output : Proof 4.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN349-1 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:31:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.90/5.07 % SZS status Unsatisfiable
% 4.90/5.07 % SZS output start Proof
% 4.90/5.07 tff(f_type, type, (
% 4.90/5.07 f: ( $i * $i ) > $o)).
% 4.90/5.07 tff(w_type, type, (
% 4.90/5.07 w: $i > $i)).
% 4.90/5.07 tff(g_type, type, (
% 4.90/5.07 g: ( $i * $i ) > $i)).
% 4.90/5.07 tff(elem_0_type, type, (
% 4.90/5.07 elem_0: $i)).
% 4.90/5.07 tff(1,assumption,(~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))), introduced(assumption)).
% 4.90/5.07 tff(2,plain,
% 4.90/5.07 (^[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))))),
% 4.90/5.07 inference(bind,[status(th)],[])).
% 4.90/5.07 tff(3,plain,
% 4.90/5.07 (![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)))),
% 4.90/5.07 inference(quant_intro,[status(thm)],[2])).
% 4.90/5.07 tff(4,plain,
% 4.90/5.07 (![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)))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(5,plain,
% 4.90/5.07 (^[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))))),
% 4.90/5.07 inference(bind,[status(th)],[])).
% 4.90/5.07 tff(6,plain,
% 4.90/5.07 (![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)))),
% 4.90/5.07 inference(quant_intro,[status(thm)],[5])).
% 4.90/5.07 tff(7,axiom,(![Y: $i, X: $i] : (f(X, g(X, Y)) | (~f(w(X), g(X, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 4.90/5.07 tff(8,plain,
% 4.90/5.07 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[7, 6])).
% 4.90/5.07 tff(9,plain,
% 4.90/5.07 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[8, 4])).
% 4.90/5.07 tff(10,plain,(
% 4.90/5.07 ![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 4.90/5.07 inference(skolemize,[status(sab)],[9])).
% 4.90/5.07 tff(11,plain,
% 4.90/5.07 (![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[10, 3])).
% 4.90/5.07 tff(12,plain,
% 4.90/5.07 (((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | ((~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(13,plain,
% 4.90/5.07 ((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | ((~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.07 inference(quant_inst,[status(thm)],[])).
% 4.90/5.07 tff(14,plain,
% 4.90/5.07 ((~![Y: $i, X: $i] : ((~f(w(X), g(X, Y))) | f(X, g(X, Y)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[13, 12])).
% 4.90/5.07 tff(15,plain,
% 4.90/5.07 (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.07 inference(unit_resolution,[status(thm)],[14, 11, 1])).
% 4.90/5.07 tff(16,plain,
% 4.90/5.07 (^[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)))))),
% 4.90/5.07 inference(bind,[status(th)],[])).
% 4.90/5.07 tff(17,plain,
% 4.90/5.07 (![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))))),
% 4.90/5.07 inference(quant_intro,[status(thm)],[16])).
% 4.90/5.07 tff(18,plain,
% 4.90/5.07 (![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))))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(19,plain,
% 4.90/5.07 (^[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))))))),
% 4.90/5.07 inference(bind,[status(th)],[])).
% 4.90/5.07 tff(20,plain,
% 4.90/5.07 (![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))))),
% 4.90/5.07 inference(quant_intro,[status(thm)],[19])).
% 4.90/5.07 tff(21,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/sandbox/benchmark/theBenchmark.p','clause8')).
% 4.90/5.07 tff(22,plain,
% 4.90/5.07 (![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))))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[21, 20])).
% 4.90/5.07 tff(23,plain,
% 4.90/5.07 (![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))))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[22, 18])).
% 4.90/5.07 tff(24,plain,(
% 4.90/5.07 ![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))))),
% 4.90/5.07 inference(skolemize,[status(sab)],[23])).
% 4.90/5.07 tff(25,plain,
% 4.90/5.07 (![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))))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[24, 17])).
% 4.90/5.07 tff(26,plain,
% 4.90/5.07 (((~![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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(27,plain,
% 4.90/5.07 ((f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) <=> (f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(28,plain,
% 4.90/5.07 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))))),
% 4.90/5.07 inference(monotonicity,[status(thm)],[27])).
% 4.90/5.07 tff(29,plain,
% 4.90/5.07 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.07 inference(transitivity,[status(thm)],[28, 26])).
% 4.90/5.07 tff(30,plain,
% 4.90/5.07 ((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.07 inference(quant_inst,[status(thm)],[])).
% 4.90/5.07 tff(31,plain,
% 4.90/5.07 ((~![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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[30, 29])).
% 4.90/5.07 tff(32,plain,
% 4.90/5.07 (f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.07 inference(unit_resolution,[status(thm)],[31, 25, 1])).
% 4.90/5.07 tff(33,plain,
% 4.90/5.07 (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))),
% 4.90/5.07 inference(unit_resolution,[status(thm)],[32, 15])).
% 4.90/5.07 tff(34,plain,
% 4.90/5.07 (^[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)))),
% 4.90/5.07 inference(bind,[status(th)],[])).
% 4.90/5.07 tff(35,plain,
% 4.90/5.07 (![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))),
% 4.90/5.07 inference(quant_intro,[status(thm)],[34])).
% 4.90/5.07 tff(36,plain,
% 4.90/5.07 (![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))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(37,plain,
% 4.90/5.07 (^[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))))),
% 4.90/5.07 inference(bind,[status(th)],[])).
% 4.90/5.07 tff(38,plain,
% 4.90/5.07 (![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))),
% 4.90/5.07 inference(quant_intro,[status(thm)],[37])).
% 4.90/5.07 tff(39,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/sandbox/benchmark/theBenchmark.p','clause5')).
% 4.90/5.07 tff(40,plain,
% 4.90/5.07 (![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))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[39, 38])).
% 4.90/5.07 tff(41,plain,
% 4.90/5.07 (![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))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[40, 36])).
% 4.90/5.07 tff(42,plain,(
% 4.90/5.07 ![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))),
% 4.90/5.07 inference(skolemize,[status(sab)],[41])).
% 4.90/5.07 tff(43,plain,
% 4.90/5.07 (![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))),
% 4.90/5.07 inference(modus_ponens,[status(thm)],[42, 35])).
% 4.90/5.07 tff(44,plain,
% 4.90/5.07 (((~![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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(45,plain,
% 4.90/5.07 ((f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) <=> (f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.07 inference(rewrite,[status(thm)],[])).
% 4.90/5.07 tff(46,plain,
% 4.90/5.07 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(monotonicity,[status(thm)],[45])).
% 4.90/5.08 tff(47,plain,
% 4.90/5.08 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.08 inference(transitivity,[status(thm)],[46, 44])).
% 4.90/5.08 tff(48,plain,
% 4.90/5.08 ((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.08 inference(quant_inst,[status(thm)],[])).
% 4.90/5.08 tff(49,plain,
% 4.90/5.08 ((~![Y: $i, X: $i] : (f(X, g(X, Y)) | f(g(X, Y), w(X)) | f(Y, g(X, Y)) | f(g(X, Y), Y))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[48, 47])).
% 4.90/5.08 tff(50,plain,
% 4.90/5.08 (f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))),
% 4.90/5.08 inference(unit_resolution,[status(thm)],[49, 43, 1])).
% 4.90/5.08 tff(51,plain,
% 4.90/5.08 ($false),
% 4.90/5.08 inference(unit_resolution,[status(thm)],[50, 33, 15])).
% 4.90/5.08 tff(52,plain,(f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 4.90/5.08 tff(53,plain,
% 4.90/5.08 (^[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))))),
% 4.90/5.08 inference(bind,[status(th)],[])).
% 4.90/5.08 tff(54,plain,
% 4.90/5.08 (![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)))),
% 4.90/5.08 inference(quant_intro,[status(thm)],[53])).
% 4.90/5.08 tff(55,plain,
% 4.90/5.08 (![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)))),
% 4.90/5.08 inference(rewrite,[status(thm)],[])).
% 4.90/5.08 tff(56,axiom,(![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 4.90/5.08 tff(57,plain,
% 4.90/5.08 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[56, 55])).
% 4.90/5.08 tff(58,plain,(
% 4.90/5.08 ![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 4.90/5.08 inference(skolemize,[status(sab)],[57])).
% 4.90/5.08 tff(59,plain,
% 4.90/5.08 (![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[58, 54])).
% 4.90/5.08 tff(60,plain,
% 4.90/5.08 (((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | ((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | (~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(rewrite,[status(thm)],[])).
% 4.90/5.08 tff(61,plain,
% 4.90/5.08 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | ((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(quant_inst,[status(thm)],[])).
% 4.90/5.08 tff(62,plain,
% 4.90/5.08 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(w(X), g(X, Y)))) | (~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[61, 60])).
% 4.90/5.08 tff(63,plain,
% 4.90/5.08 ((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.08 inference(unit_resolution,[status(thm)],[62, 59])).
% 4.90/5.08 tff(64,plain,
% 4.90/5.08 (f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.08 inference(unit_resolution,[status(thm)],[63, 52])).
% 4.90/5.08 tff(65,plain,
% 4.90/5.08 (^[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)))))),
% 4.90/5.08 inference(bind,[status(th)],[])).
% 4.90/5.08 tff(66,plain,
% 4.90/5.08 (![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))))),
% 4.90/5.08 inference(quant_intro,[status(thm)],[65])).
% 4.90/5.08 tff(67,plain,
% 4.90/5.08 (![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))))),
% 4.90/5.08 inference(rewrite,[status(thm)],[])).
% 4.90/5.08 tff(68,plain,
% 4.90/5.08 (^[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))))))),
% 4.90/5.08 inference(bind,[status(th)],[])).
% 4.90/5.08 tff(69,plain,
% 4.90/5.08 (![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))))),
% 4.90/5.08 inference(quant_intro,[status(thm)],[68])).
% 4.90/5.08 tff(70,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/sandbox/benchmark/theBenchmark.p','clause10')).
% 4.90/5.08 tff(71,plain,
% 4.90/5.08 (![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))))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[70, 69])).
% 4.90/5.08 tff(72,plain,
% 4.90/5.08 (![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))))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[71, 67])).
% 4.90/5.08 tff(73,plain,(
% 4.90/5.08 ![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))))),
% 4.90/5.08 inference(skolemize,[status(sab)],[72])).
% 4.90/5.08 tff(74,plain,
% 4.90/5.08 (![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))))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[73, 66])).
% 4.90/5.08 tff(75,plain,
% 4.90/5.08 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(rewrite,[status(thm)],[])).
% 4.90/5.08 tff(76,plain,
% 4.90/5.08 (((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) <=> ((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(rewrite,[status(thm)],[])).
% 4.90/5.08 tff(77,plain,
% 4.90/5.08 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))))),
% 4.90/5.08 inference(monotonicity,[status(thm)],[76])).
% 4.90/5.08 tff(78,plain,
% 4.90/5.08 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(transitivity,[status(thm)],[77, 75])).
% 4.90/5.08 tff(79,plain,
% 4.90/5.08 ((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.08 inference(quant_inst,[status(thm)],[])).
% 4.90/5.08 tff(80,plain,
% 4.90/5.08 ((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[79, 78])).
% 4.90/5.08 tff(81,plain,
% 4.90/5.08 (~f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))),
% 4.90/5.08 inference(unit_resolution,[status(thm)],[80, 74, 52, 64])).
% 4.90/5.08 tff(82,plain,
% 4.90/5.08 (^[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)))),
% 4.90/5.08 inference(bind,[status(th)],[])).
% 4.90/5.08 tff(83,plain,
% 4.90/5.08 (![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))),
% 4.90/5.08 inference(quant_intro,[status(thm)],[82])).
% 4.90/5.08 tff(84,plain,
% 4.90/5.08 (![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))),
% 4.90/5.08 inference(rewrite,[status(thm)],[])).
% 4.90/5.08 tff(85,plain,
% 4.90/5.08 (^[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))))),
% 4.90/5.08 inference(bind,[status(th)],[])).
% 4.90/5.08 tff(86,plain,
% 4.90/5.08 (![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))),
% 4.90/5.08 inference(quant_intro,[status(thm)],[85])).
% 4.90/5.08 tff(87,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/sandbox/benchmark/theBenchmark.p','clause3')).
% 4.90/5.08 tff(88,plain,
% 4.90/5.08 (![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))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[87, 86])).
% 4.90/5.08 tff(89,plain,
% 4.90/5.08 (![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))),
% 4.90/5.08 inference(modus_ponens,[status(thm)],[88, 84])).
% 4.90/5.08 tff(90,plain,(
% 4.90/5.08 ![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))),
% 4.90/5.08 inference(skolemize,[status(sab)],[89])).
% 4.90/5.09 tff(91,plain,
% 4.90/5.09 (![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))),
% 4.90/5.09 inference(modus_ponens,[status(thm)],[90, 83])).
% 4.90/5.09 tff(92,plain,
% 4.90/5.09 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), 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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))))),
% 4.90/5.09 inference(rewrite,[status(thm)],[])).
% 4.90/5.09 tff(93,plain,
% 4.90/5.09 (((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))) <=> ((~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))))),
% 4.90/5.09 inference(rewrite,[status(thm)],[])).
% 4.90/5.09 tff(94,plain,
% 4.90/5.09 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))))),
% 4.90/5.09 inference(monotonicity,[status(thm)],[93])).
% 4.90/5.09 tff(95,plain,
% 4.90/5.09 (((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), 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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))))),
% 4.90/5.09 inference(transitivity,[status(thm)],[94, 92])).
% 4.90/5.09 tff(96,plain,
% 4.90/5.09 ((~![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(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))),
% 4.90/5.09 inference(quant_inst,[status(thm)],[])).
% 4.90/5.09 tff(97,plain,
% 4.90/5.09 ((~![Y: $i, X: $i] : ((~f(X, g(X, Y))) | f(g(X, Y), w(X)) | (~f(Y, g(X, Y))) | f(g(X, Y), Y))) | (~f(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))))) | f(g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)))) | (~f(w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))), g(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0)), w(g(g(elem!0, g(elem!0, elem!0)), g(elem!0, elem!0))))))),
% 4.90/5.09 inference(modus_ponens,[status(thm)],[96, 95])).
% 4.90/5.09 tff(98,plain,
% 4.90/5.09 ($false),
% 4.90/5.09 inference(unit_resolution,[status(thm)],[97, 91, 52, 64, 81])).
% 4.90/5.09 % SZS output end Proof
% 4.90/5.09 % E exiting
%------------------------------------------------------------------------------