%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN264-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN264-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.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 12:30:11 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(p1_type, type, (
% 0.19/0.47 p1: ( $i * $i * $i ) > $o)).
% 0.19/0.47 tff(e_type, type, (
% 0.19/0.47 e: $i)).
% 0.19/0.47 tff(c_type, type, (
% 0.19/0.47 c: $i)).
% 0.19/0.47 tff(n0_type, type, (
% 0.19/0.47 n0: ( $i * $i ) > $o)).
% 0.19/0.47 tff(d_type, type, (
% 0.19/0.47 d: $i)).
% 0.19/0.47 tff(k0_type, type, (
% 0.19/0.47 k0: $i > $o)).
% 0.19/0.47 tff(s0_type, type, (
% 0.19/0.47 s0: $i > $o)).
% 0.19/0.47 tff(b_type, type, (
% 0.19/0.47 b: $i)).
% 0.19/0.47 tff(l0_type, type, (
% 0.19/0.47 l0: $i > $o)).
% 0.19/0.47 tff(a_type, type, (
% 0.19/0.47 a: $i)).
% 0.19/0.47 tff(1,assumption,(~p1(c, c, e)), introduced(assumption)).
% 0.19/0.47 tff(2,plain,
% 0.19/0.47 (^[D: $i, E: $i] : refl(((~k0(E)) | (~n0(d, D)) | p1(D, D, E)) <=> ((~k0(E)) | (~n0(d, D)) | p1(D, D, E)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(3,plain,
% 0.19/0.47 (![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E)) <=> ![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.47 tff(4,plain,
% 0.19/0.47 (![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E)) <=> ![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(5,plain,
% 0.19/0.47 (^[D: $i, E: $i] : trans(monotonicity(rewrite((p1(D, D, E) | (~n0(d, D))) <=> ((~n0(d, D)) | p1(D, D, E))), (((p1(D, D, E) | (~n0(d, D))) | (~k0(E))) <=> (((~n0(d, D)) | p1(D, D, E)) | (~k0(E))))), rewrite((((~n0(d, D)) | p1(D, D, E)) | (~k0(E))) <=> ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))), (((p1(D, D, E) | (~n0(d, D))) | (~k0(E))) <=> ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (![D: $i, E: $i] : ((p1(D, D, E) | (~n0(d, D))) | (~k0(E))) <=> ![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.47 tff(7,axiom,(![D: $i, E: $i] : ((p1(D, D, E) | (~n0(d, D))) | (~k0(E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_063')).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 (![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.47 tff(10,plain,(
% 0.19/0.47 ![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(skolemize,[status(sab)],[9])).
% 0.19/0.47 tff(11,plain,
% 0.19/0.47 (![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 (k0(e) <=> k0(e)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(13,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.19/0.47 tff(14,plain,
% 0.19/0.47 (k0(e)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.47 tff(15,plain,
% 0.19/0.47 (n0(d, c) <=> n0(d, c)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(16,axiom,(n0(d, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 (n0(d, c)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (((~![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))) | ((~k0(e)) | (~n0(d, c)) | p1(c, c, e))) <=> ((~![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))) | (~k0(e)) | (~n0(d, c)) | p1(c, c, e))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 ((~![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))) | ((~k0(e)) | (~n0(d, c)) | p1(c, c, e))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 ((~![D: $i, E: $i] : ((~k0(E)) | (~n0(d, D)) | p1(D, D, E))) | (~k0(e)) | (~n0(d, c)) | p1(c, c, e)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[20, 17, 14, 11, 1])).
% 0.19/0.47 tff(22,plain,(p1(c, c, e)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 ((~p1(e, c, e)) <=> (~p1(e, c, e))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(24,axiom,(~p1(e, c, e)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (~p1(e, c, e)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H)) <=> ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((p1(H, I, H) | (~l0(J))) <=> ((~l0(J)) | p1(H, I, H))), (((p1(H, I, H) | (~l0(J))) | (~p1(I, A, H))) <=> (((~l0(J)) | p1(H, I, H)) | (~p1(I, A, H))))), rewrite((((~l0(J)) | p1(H, I, H)) | (~p1(I, A, H))) <=> ((~l0(J)) | (~p1(I, A, H)) | p1(H, I, H))), (((p1(H, I, H) | (~l0(J))) | (~p1(I, A, H))) <=> ((~l0(J)) | (~p1(I, A, H)) | p1(H, I, H)))), ((((p1(H, I, H) | (~l0(J))) | (~p1(I, A, H))) | (~s0(b))) <=> (((~l0(J)) | (~p1(I, A, H)) | p1(H, I, H)) | (~s0(b))))), rewrite((((~l0(J)) | (~p1(I, A, H)) | p1(H, I, H)) | (~s0(b))) <=> ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))), ((((p1(H, I, H) | (~l0(J))) | (~p1(I, A, H))) | (~s0(b))) <=> ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 (![I: $i, A: $i, J: $i, H: $i] : (((p1(H, I, H) | (~l0(J))) | (~p1(I, A, H))) | (~s0(b))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.49 tff(31,axiom,(![I: $i, A: $i, J: $i, H: $i] : (((p1(H, I, H) | (~l0(J))) | (~p1(I, A, H))) | (~s0(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_071')).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.49 tff(34,plain,(
% 0.19/0.49 ![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(skolemize,[status(sab)],[33])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (l0(a) <=> l0(a)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(37,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (l0(a)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (s0(b) <=> s0(b)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(40,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (s0(b)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (((~![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))) | ((~l0(a)) | (~s0(b)) | (~p1(c, c, e)) | p1(e, c, e))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))) | (~l0(a)) | (~s0(b)) | (~p1(c, c, e)) | p1(e, c, e))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 ((~![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))) | ((~l0(a)) | (~s0(b)) | (~p1(c, c, e)) | p1(e, c, e))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 ((~![I: $i, A: $i, J: $i, H: $i] : ((~l0(J)) | (~s0(b)) | (~p1(I, A, H)) | p1(H, I, H))) | (~l0(a)) | (~s0(b)) | (~p1(c, c, e)) | p1(e, c, e)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[44, 41, 38, 35, 25, 22])).
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------