%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN218-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:38:31 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN218-1 : TPTP v9.0.0. Released v1.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 12:33:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 tff(l2_type, type, (
% 0.19/0.47 l2: ( $i * $i ) > $o)).
% 0.19/0.47 tff(c_type, type, (
% 0.19/0.47 c: $i)).
% 0.19/0.47 tff(s1_type, type, (
% 0.19/0.47 s1: $i > $o)).
% 0.19/0.47 tff(b_type, type, (
% 0.19/0.47 b: $i)).
% 0.19/0.47 tff(p0_type, type, (
% 0.19/0.47 p0: ( $i * $i ) > $o)).
% 0.19/0.47 tff(m0_type, type, (
% 0.19/0.47 m0: ( $i * $i * $i ) > $o)).
% 0.19/0.47 tff(e_type, type, (
% 0.19/0.47 e: $i)).
% 0.19/0.47 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.19/0.47 tff(2,plain,
% 0.19/0.47 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(3,plain,
% 0.19/0.47 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.19/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.47 tff(4,plain,
% 0.19/0.47 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (![X: $i] : p0(b, X)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.47 tff(7,plain,(
% 0.19/0.47 ![X: $i] : p0(b, X)),
% 0.19/0.47 inference(skolemize,[status(sab)],[6])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (![X: $i] : p0(b, X)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.47 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(13,plain,
% 0.19/0.47 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.47 tff(14,plain,
% 0.19/0.47 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.47 tff(17,plain,(
% 0.19/0.47 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[16])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (s1(b)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.47 tff(28,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.47 tff(31,plain,(
% 0.19/0.47 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(skolemize,[status(sab)],[30])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 (m0(e, b, c) <=> m0(e, b, c)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(34,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (m0(e, b, c)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (l2(c, c) | (~s1(b)) | (~m0(e, b, c)) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | l2(c, c) | (~s1(b)) | (~m0(e, b, c)) | (~p0(b, b)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (((~p0(b, b)) | (~m0(e, b, c)) | (~s1(b)) | l2(c, c)) <=> (l2(c, c) | (~s1(b)) | (~m0(e, b, c)) | (~p0(b, b)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(e, b, c)) | (~s1(b)) | l2(c, c))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (l2(c, c) | (~s1(b)) | (~m0(e, b, c)) | (~p0(b, b))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(e, b, c)) | (~s1(b)) | l2(c, c))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | l2(c, c) | (~s1(b)) | (~m0(e, b, c)) | (~p0(b, b)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(e, b, c)) | (~s1(b)) | l2(c, c))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | l2(c, c) | (~s1(b)) | (~m0(e, b, c)) | (~p0(b, b))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (l2(c, c) | (~s1(b))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[41, 35, 32, 11])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (l2(c, c)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[42, 22])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (^[X: $i] : refl((~l2(c, X)) <=> (~l2(c, X)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (![X: $i] : (~l2(c, X)) <=> ![X: $i] : (~l2(c, X))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 (![X: $i] : (~l2(c, X)) <=> ![X: $i] : (~l2(c, X))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(47,axiom,(![X: $i] : (~l2(c, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (![X: $i] : (~l2(c, X))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.47 tff(49,plain,(
% 0.19/0.47 ![X: $i] : (~l2(c, X))),
% 0.19/0.47 inference(skolemize,[status(sab)],[48])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![X: $i] : (~l2(c, X))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 ((~![X: $i] : (~l2(c, X))) | (~l2(c, c))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[51, 50, 43])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------