%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN196-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:38:28 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN196-1 : TPTP v9.0.0. Released v1.1.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 : Fri Jun 20 12:30:46 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(s1_type, type, (
% 0.20/0.48 s1: $i > $o)).
% 0.20/0.48 tff(b_type, type, (
% 0.20/0.48 b: $i)).
% 0.20/0.48 tff(p0_type, type, (
% 0.20/0.48 p0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(a_type, type, (
% 0.20/0.48 a: $i)).
% 0.20/0.48 tff(q0_type, type, (
% 0.20/0.48 q0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![X: $i] : p0(b, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,(
% 0.20/0.48 ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[6])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![X: $i] : p0(b, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.48 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.48 tff(17,plain,(
% 0.20/0.48 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (s1(b)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 ((~s1(a)) <=> (~s1(a))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(24,axiom,(~s1(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (~s1(a)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.48 tff(31,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.49 tff(34,plain,(
% 0.20/0.49 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(skolemize,[status(sab)],[33])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (q0(a, b) <=> q0(a, b)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(37,axiom,(q0(a, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (q0(a, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (s1(a) | (~s1(b)) | (~q0(a, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (((~q0(a, b)) | (~s1(b)) | s1(a)) <=> (s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (s1(a) | (~s1(b)) | (~q0(a, b))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[44, 38, 35, 25, 22])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------