%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN343-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:50 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN343-1 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 12:36:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(f_type, type, (
% 0.19/0.38 f: ( $i * $i ) > $o)).
% 0.19/0.38 tff(a_type, type, (
% 0.19/0.38 a: $i)).
% 0.19/0.38 tff(1,assumption,(~f(a, a)), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[Y1: $i] : refl((f(a, a) | f(a, Y1)) <=> (f(a, a) | f(a, Y1)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![Y1: $i] : (f(a, a) | f(a, Y1)) <=> ![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![Y1: $i] : (f(a, a) | f(a, Y1)) <=> ![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (^[Y1: $i] : rewrite((f(a, Y1) | f(a, a)) <=> (f(a, a) | f(a, Y1)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![Y1: $i] : (f(a, Y1) | f(a, a)) <=> ![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.38 tff(7,axiom,(![Y1: $i] : (f(a, Y1) | f(a, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.38 tff(10,plain,(
% 0.19/0.38 ![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(skolemize,[status(sab)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![Y1: $i] : (f(a, a) | f(a, Y1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (((~![Y1: $i] : (f(a, a) | f(a, Y1))) | f(a, a)) <=> ((~![Y1: $i] : (f(a, a) | f(a, Y1))) | f(a, a))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((f(a, a) | f(a, a)) <=> f(a, a)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (((~![Y1: $i] : (f(a, a) | f(a, Y1))) | (f(a, a) | f(a, a))) <=> ((~![Y1: $i] : (f(a, a) | f(a, Y1))) | f(a, a))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (((~![Y1: $i] : (f(a, a) | f(a, Y1))) | (f(a, a) | f(a, a))) <=> ((~![Y1: $i] : (f(a, a) | f(a, Y1))) | f(a, a))),
% 0.19/0.38 inference(transitivity,[status(thm)],[14, 12])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~![Y1: $i] : (f(a, a) | f(a, Y1))) | (f(a, a) | f(a, a))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~![Y1: $i] : (f(a, a) | f(a, Y1))) | f(a, a)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[17, 11, 1])).
% 0.19/0.38 tff(19,plain,(f(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (^[Y2: $i, Y1: $i] : refl(((~f(a, a)) | (~f(Y1, Y2))) <=> ((~f(a, a)) | (~f(Y1, Y2))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2))) <=> ![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(23,axiom,(![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.38 tff(25,plain,(
% 0.19/0.38 ![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[24])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | (~f(a, a))) <=> ((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | (~f(a, a)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (((~f(a, a)) | (~f(a, a))) <=> (~f(a, a))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | ((~f(a, a)) | (~f(a, a)))) <=> ((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | (~f(a, a)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | ((~f(a, a)) | (~f(a, a)))) <=> ((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | (~f(a, a)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | ((~f(a, a)) | (~f(a, a)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![Y2: $i, Y1: $i] : ((~f(a, a)) | (~f(Y1, Y2)))) | (~f(a, a))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[32, 26, 19])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------