%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN396+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:59 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN396+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:33:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(f_type, type, (
% 0.20/0.37 f: $i > $o)).
% 0.20/0.37 tff(tptp_fun_X_0_type, type, (
% 0.20/0.37 tptp_fun_X_0: $i)).
% 0.20/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.37 tptp_fun_Y_1: $i)).
% 0.20/0.37 tff(1,assumption,(![X: $i] : f(X)), introduced(assumption)).
% 0.20/0.37 tff(2,assumption,(~f(Y!1)), introduced(assumption)).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 ((~![X: $i] : f(X)) | f(Y!1)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[3, 2, 1])).
% 0.20/0.37 tff(5,plain,(f(Y!1) | (~![X: $i] : f(X))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (f(Y!1)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[5, 1])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 ((![X: $i] : f(X) | ![Y: $i] : f(Y)) <=> (![X: $i] : f(X) | ![Y: $i] : f(Y))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 ((((~f(X!0)) | (~f(Y!1))) & (![X: $i] : f(X) | ![Y: $i] : f(Y))) <=> (((~f(X!0)) | (~f(Y!1))) & (![X: $i] : f(X) | ![Y: $i] : f(Y)))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))) <=> (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ((~(~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))))) <=> (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 ((~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y)))) <=> (~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y))) <=> (~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 ((~![X: $i] : f(X)) <=> (~![X: $i] : f(X))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y))) <=> ((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y)))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y))) <=> (~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[14, 12])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y))) <=> (~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[15, 11])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 ((~((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y)))) <=> (~(~(![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y)))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 ((~((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y)))) <=> (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y)))),
% 0.20/0.37 inference(transitivity,[status(thm)],[17, 10])).
% 0.20/0.37 tff(19,axiom,(~((~![X: $i] : f(X)) <=> ?[Y: $i] : (~f(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish203')).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 9])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[21, 9])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![X: $i] : f(X) <=> ?[Y: $i] : (~f(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.20/0.37 tff(24,plain,(
% 0.20/0.37 ((~f(X!0)) | (~f(Y!1))) & (![X: $i] : f(X) | ![Y: $i] : f(Y))),
% 0.20/0.37 inference(skolemize,[status(sab)],[23])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (((~f(X!0)) | (~f(Y!1))) & (![X: $i] : f(X) | ![Y: $i] : f(Y))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[24, 8])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ((~f(X!0)) | (~f(Y!1))),
% 0.20/0.37 inference(and_elim,[status(thm)],[25])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (~f(X!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[26, 6])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 ((~![X: $i] : f(X)) | f(X!0)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[28, 27, 1])).
% 0.20/0.37 tff(30,plain,(~![X: $i] : f(X)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 ((![X: $i] : f(X) | ![Y: $i] : f(Y)) <=> (![X: $i] : f(X) | ![Y: $i] : f(Y))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (![X: $i] : f(X) | ![Y: $i] : f(Y)),
% 0.20/0.37 inference(and_elim,[status(thm)],[25])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (![X: $i] : f(X) | ![Y: $i] : f(Y)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (![Y: $i] : f(Y)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((~![Y: $i] : f(Y)) | f(Y!1)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[35, 2, 34])).
% 0.20/0.37 tff(37,plain,(f(Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (~f(X!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[26, 37])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 ((~![Y: $i] : f(Y)) | f(X!0)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[39, 38, 34])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------