%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN284-1 : 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 05:38:40 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN284-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n002.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:31:47 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(q1_type, type, (
% 0.20/0.46 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(a_type, type, (
% 0.20/0.46 a: $i)).
% 0.20/0.46 tff(c_type, type, (
% 0.20/0.46 c: $i)).
% 0.20/0.46 tff(n0_type, type, (
% 0.20/0.46 n0: ( $i * $i ) > $o)).
% 0.20/0.46 tff(p0_type, type, (
% 0.20/0.46 p0: ( $i * $i ) > $o)).
% 0.20/0.46 tff(b_type, type, (
% 0.20/0.46 b: $i)).
% 0.20/0.46 tff(d_type, type, (
% 0.20/0.46 d: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 ((~q1(a, c, a)) <=> (~q1(a, c, a))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(2,axiom,(~q1(a, c, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (~q1(a, c, a)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.46 tff(9,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.46 tff(12,plain,(
% 0.20/0.46 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(skolemize,[status(sab)],[11])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.46 tff(14,assumption,(~p0(b, a)), introduced(assumption)).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(18,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![X: $i] : p0(b, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.46 tff(20,plain,(
% 0.20/0.46 ![X: $i] : p0(b, X)),
% 0.20/0.46 inference(skolemize,[status(sab)],[19])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (![X: $i] : p0(b, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ((~![X: $i] : p0(b, X)) | p0(b, a)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.20/0.46 tff(24,plain,(p0(b, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (n0(d, c) <=> n0(d, c)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(26,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (n0(d, c)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, a)) | q1(a, c, a) | (~n0(d, c)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, a)) | q1(a, c, a) | (~n0(d, c)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (((~p0(b, a)) | (~n0(d, c)) | q1(a, c, a)) <=> ((~p0(b, a)) | q1(a, c, a) | (~n0(d, c)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, a)) | (~n0(d, c)) | q1(a, c, a))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, a)) | q1(a, c, a) | (~n0(d, c))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, a)) | (~n0(d, c)) | q1(a, c, a))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, a)) | q1(a, c, a) | (~n0(d, c)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, a)) | (~n0(d, c)) | q1(a, c, a))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, a)) | q1(a, c, a) | (~n0(d, c))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[33, 27, 24, 13, 3])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------