%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN263-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:37 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN263-1 : TPTP v9.0.0. Released v1.1.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:29:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(p1_type, type, (
% 0.19/0.51 p1: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(a_type, type, (
% 0.19/0.51 a: $i)).
% 0.19/0.51 tff(d_type, type, (
% 0.19/0.51 d: $i)).
% 0.19/0.51 tff(m0_type, type, (
% 0.19/0.51 m0: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(l0_type, type, (
% 0.19/0.51 l0: $i > $o)).
% 0.19/0.51 tff(1,assumption,(~m0(a, d, a)), introduced(assumption)).
% 0.19/0.51 tff(2,plain,
% 0.19/0.51 (^[X: $i] : refl(m0(a, X, a) <=> m0(a, X, a))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(3,plain,
% 0.19/0.51 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 0.19/0.51 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.51 tff(4,plain,
% 0.19/0.51 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(5,axiom,(![X: $i] : m0(a, X, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_12')).
% 0.19/0.51 tff(6,plain,
% 0.19/0.51 (![X: $i] : m0(a, X, a)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.51 tff(7,plain,(
% 0.19/0.51 ![X: $i] : m0(a, X, a)),
% 0.19/0.51 inference(skolemize,[status(sab)],[6])).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 (![X: $i] : m0(a, X, a)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.51 tff(9,plain,
% 0.19/0.51 ((~![X: $i] : m0(a, X, a)) | m0(a, d, a)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.51 tff(11,plain,(m0(a, d, a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 ((~p1(d, d, a)) <=> (~p1(d, d, a))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(13,axiom,(~p1(d, d, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.51 tff(14,plain,
% 0.19/0.51 (~p1(d, d, a)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.51 tff(15,plain,
% 0.19/0.51 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(16,plain,
% 0.19/0.51 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(18,plain,
% 0.19/0.51 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(rewrite((p1(H, I, J) | (~m0(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J))), (((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A))) <=> (((~m0(J, H, A)) | p1(H, I, J)) | (~p1(J, H, A))))), rewrite((((~m0(J, H, A)) | p1(H, I, J)) | (~p1(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))), (((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A))) <=> ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(19,plain,
% 0.19/0.51 (![I: $i, A: $i, J: $i, H: $i] : ((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.51 tff(20,axiom,(![I: $i, A: $i, J: $i, H: $i] : ((p1(H, I, J) | (~m0(J, H, A))) | (~p1(J, H, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_082')).
% 0.19/0.51 tff(21,plain,
% 0.19/0.51 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.51 tff(22,plain,
% 0.19/0.51 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.51 tff(23,plain,(
% 0.19/0.51 ![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[22])).
% 0.19/0.51 tff(24,plain,
% 0.19/0.51 (![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.51 tff(25,plain,
% 0.19/0.51 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (p1(d, d, a) | (~m0(a, d, a)) | (~p1(a, d, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | p1(d, d, a) | (~m0(a, d, a)) | (~p1(a, d, a)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(26,plain,
% 0.19/0.51 (((~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a))) <=> (p1(d, d, a) | (~m0(a, d, a)) | (~p1(a, d, a)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(27,plain,
% 0.19/0.51 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (p1(d, d, a) | (~m0(a, d, a)) | (~p1(a, d, a))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.51 tff(28,plain,
% 0.19/0.51 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | p1(d, d, a) | (~m0(a, d, a)) | (~p1(a, d, a)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.51 tff(29,plain,
% 0.19/0.51 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, d, a)) | p1(d, d, a) | (~p1(a, d, a)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(30,plain,
% 0.19/0.51 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | p1(d, d, a) | (~m0(a, d, a)) | (~p1(a, d, a))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.51 tff(31,plain,
% 0.19/0.51 (~p1(a, d, a)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[30, 24, 14, 11])).
% 0.19/0.51 tff(32,assumption,(~m0(a, a, a)), introduced(assumption)).
% 0.19/0.51 tff(33,plain,
% 0.19/0.51 ((~![X: $i] : m0(a, X, a)) | m0(a, a, a)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(34,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[33, 8, 32])).
% 0.19/0.51 tff(35,plain,(m0(a, a, a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(36,plain,
% 0.19/0.51 (l0(a) <=> l0(a)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(37,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.19/0.51 tff(38,plain,
% 0.19/0.51 (l0(a)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.51 tff(39,plain,
% 0.19/0.51 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(40,plain,
% 0.19/0.52 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(41,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.19/0.52 tff(42,plain,
% 0.19/0.52 ((~l0(a)) | p1(a, a, a)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.52 tff(43,plain,
% 0.19/0.52 ((~l0(a)) | p1(a, a, a)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.19/0.52 tff(44,plain,
% 0.19/0.52 (p1(a, a, a)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.19/0.52 tff(45,plain,
% 0.19/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(46,plain,
% 0.19/0.52 (((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(47,plain,
% 0.19/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a)))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.52 tff(48,plain,
% 0.19/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a)))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a))),
% 0.19/0.52 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.52 tff(49,plain,
% 0.19/0.52 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | ((~m0(a, a, a)) | p1(a, d, a) | (~p1(a, a, a)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(50,plain,
% 0.19/0.52 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m0(J, H, A)) | p1(H, I, J) | (~p1(J, H, A)))) | (~p1(a, a, a)) | (~m0(a, a, a)) | p1(a, d, a)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.53 tff(51,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[50, 44, 24, 35, 31])).
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53 % E exiting
%------------------------------------------------------------------------------