%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN208-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:29 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.82s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN208-1 : TPTP v9.0.0. Released v1.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:30:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.61/0.82 % SZS status Unsatisfiable
% 0.61/0.82 % SZS output start Proof
% 0.61/0.82 tff(m0_type, type, (
% 0.61/0.82 m0: ( $i * $i * $i ) > $o)).
% 0.61/0.82 tff(b_type, type, (
% 0.61/0.82 b: $i)).
% 0.61/0.82 tff(d_type, type, (
% 0.61/0.82 d: $i)).
% 0.61/0.82 tff(q2_type, type, (
% 0.61/0.82 q2: ( $i * $i * $i ) > $o)).
% 0.61/0.82 tff(n1_type, type, (
% 0.61/0.82 n1: ( $i * $i * $i ) > $o)).
% 0.61/0.82 tff(q0_type, type, (
% 0.61/0.82 q0: ( $i * $i ) > $o)).
% 0.61/0.82 tff(s3_type, type, (
% 0.61/0.82 s3: ( $i * $i ) > $o)).
% 0.61/0.82 tff(s2_type, type, (
% 0.61/0.82 s2: $i > $o)).
% 0.61/0.82 tff(s1_type, type, (
% 0.61/0.82 s1: $i > $o)).
% 0.61/0.82 tff(p0_type, type, (
% 0.61/0.82 p0: ( $i * $i ) > $o)).
% 0.61/0.82 tff(r1_type, type, (
% 0.61/0.82 r1: $i > $o)).
% 0.61/0.82 tff(q1_type, type, (
% 0.61/0.82 q1: ( $i * $i * $i ) > $o)).
% 0.61/0.82 tff(s0_type, type, (
% 0.61/0.82 s0: $i > $o)).
% 0.61/0.82 tff(k0_type, type, (
% 0.61/0.82 k0: $i > $o)).
% 0.61/0.82 tff(e_type, type, (
% 0.61/0.82 e: $i)).
% 0.61/0.82 tff(1,plain,
% 0.61/0.82 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(2,plain,
% 0.61/0.82 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.61/0.82 inference(quant_intro,[status(thm)],[1])).
% 0.61/0.82 tff(3,plain,
% 0.61/0.82 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(4,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.61/0.82 tff(5,plain,
% 0.61/0.82 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.61/0.82 tff(6,plain,(
% 0.61/0.82 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.61/0.82 inference(skolemize,[status(sab)],[5])).
% 0.61/0.82 tff(7,plain,
% 0.61/0.82 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.61/0.82 tff(8,plain,
% 0.61/0.82 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, b)),
% 0.61/0.82 inference(quant_inst,[status(thm)],[])).
% 0.61/0.82 tff(9,plain,
% 0.61/0.82 (m0(d, d, b)),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.61/0.82 tff(10,plain,
% 0.61/0.82 (^[B: $i, D: $i, C: $i] : refl(((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)) <=> ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(11,plain,
% 0.61/0.82 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)) <=> ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[10])).
% 0.61/0.82 tff(12,plain,
% 0.61/0.82 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B)) <=> ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(13,plain,
% 0.61/0.82 (^[B: $i, D: $i, C: $i] : trans(monotonicity(rewrite((q2(B, B, B) | (~q0(C, B))) <=> ((~q0(C, B)) | q2(B, B, B))), (((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D))) <=> (((~q0(C, B)) | q2(B, B, B)) | (~n1(C, B, D))))), rewrite((((~q0(C, B)) | q2(B, B, B)) | (~n1(C, B, D))) <=> ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))), (((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D))) <=> ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(14,plain,
% 0.61/0.82 (![B: $i, D: $i, C: $i] : ((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D))) <=> ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[13])).
% 0.61/0.82 tff(15,axiom,(![B: $i, D: $i, C: $i] : ((q2(B, B, B) | (~q0(C, B))) | (~n1(C, B, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_178')).
% 0.61/0.83 tff(16,plain,
% 0.61/0.83 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.61/0.83 tff(17,plain,
% 0.61/0.83 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.61/0.83 tff(18,plain,(
% 0.61/0.83 ![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.83 inference(skolemize,[status(sab)],[17])).
% 0.61/0.83 tff(19,plain,
% 0.61/0.83 (![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.61/0.83 tff(20,plain,
% 0.61/0.83 (q0(d, d) <=> q0(d, d)),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(21,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.61/0.83 tff(22,plain,
% 0.61/0.83 (q0(d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.61/0.83 tff(23,plain,
% 0.61/0.83 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(24,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 0.61/0.83 tff(25,plain,
% 0.61/0.83 (n1(d, d, d) | (~q0(d, d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.61/0.83 tff(26,plain,
% 0.61/0.83 (n1(d, d, d) | (~q0(d, d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.61/0.83 tff(27,plain,
% 0.61/0.83 (n1(d, d, d) | (~q0(d, d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.61/0.83 tff(28,plain,
% 0.61/0.83 (n1(d, d, d) | (~q0(d, d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.61/0.83 tff(29,plain,
% 0.61/0.83 (n1(d, d, d) | (~q0(d, d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.61/0.83 tff(30,plain,
% 0.61/0.83 (n1(d, d, d)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[29, 22])).
% 0.61/0.83 tff(31,plain,
% 0.61/0.83 (((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | ((~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d))) <=> ((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | (~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(32,plain,
% 0.61/0.83 ((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | ((~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(33,plain,
% 0.61/0.83 ((~![B: $i, D: $i, C: $i] : ((~q0(C, B)) | (~n1(C, B, D)) | q2(B, B, B))) | (~q0(d, d)) | (~n1(d, d, d)) | q2(d, d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.61/0.83 tff(34,plain,
% 0.61/0.83 (q2(d, d, d)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[33, 22, 30, 19])).
% 0.61/0.83 tff(35,plain,
% 0.61/0.83 ((~s3(d, b)) <=> (~s3(d, b))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(36,axiom,(~s3(d, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.61/0.83 tff(37,plain,
% 0.61/0.83 (~s3(d, b)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.61/0.83 tff(38,plain,
% 0.61/0.83 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(39,plain,
% 0.61/0.83 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[38])).
% 0.61/0.83 tff(40,plain,
% 0.61/0.83 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(41,plain,
% 0.61/0.83 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(42,plain,
% 0.61/0.83 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[41])).
% 0.61/0.83 tff(43,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 0.61/0.83 tff(44,plain,
% 0.61/0.83 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.61/0.83 tff(45,plain,
% 0.61/0.83 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.61/0.83 tff(46,plain,(
% 0.61/0.83 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(skolemize,[status(sab)],[45])).
% 0.61/0.83 tff(47,plain,
% 0.61/0.83 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.61/0.83 tff(48,assumption,(~p0(b, b)), introduced(assumption)).
% 0.61/0.83 tff(49,plain,
% 0.61/0.83 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(50,plain,
% 0.61/0.83 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.61/0.83 inference(quant_intro,[status(thm)],[49])).
% 0.61/0.83 tff(51,plain,
% 0.61/0.83 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(52,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.61/0.83 tff(53,plain,
% 0.61/0.83 (![X: $i] : p0(b, X)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.61/0.83 tff(54,plain,(
% 0.61/0.83 ![X: $i] : p0(b, X)),
% 0.61/0.83 inference(skolemize,[status(sab)],[53])).
% 0.61/0.83 tff(55,plain,
% 0.61/0.83 (![X: $i] : p0(b, X)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.61/0.83 tff(56,plain,
% 0.61/0.83 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(57,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 0.61/0.83 tff(58,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(59,plain,
% 0.61/0.83 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(60,plain,
% 0.61/0.83 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[59])).
% 0.61/0.83 tff(61,plain,
% 0.61/0.83 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(62,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.61/0.83 tff(63,plain,
% 0.61/0.83 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.61/0.83 tff(64,plain,(
% 0.61/0.83 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.83 inference(skolemize,[status(sab)],[63])).
% 0.61/0.83 tff(65,plain,
% 0.61/0.83 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.61/0.83 tff(66,plain,
% 0.61/0.83 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(67,plain,
% 0.61/0.83 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(68,plain,
% 0.61/0.83 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.61/0.83 tff(69,plain,
% 0.61/0.83 (s1(b)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[68, 65, 58])).
% 0.61/0.83 tff(70,plain,
% 0.61/0.83 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(71,plain,
% 0.61/0.83 (![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))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[70])).
% 0.61/0.83 tff(72,plain,
% 0.61/0.83 (![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))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(73,plain,
% 0.61/0.83 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(74,plain,
% 0.61/0.83 (![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))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[73])).
% 0.61/0.83 tff(75,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.61/0.83 tff(76,plain,
% 0.61/0.83 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.61/0.83 tff(77,plain,
% 0.61/0.83 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.61/0.83 tff(78,plain,(
% 0.61/0.83 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.61/0.83 inference(skolemize,[status(sab)],[77])).
% 0.61/0.83 tff(79,plain,
% 0.61/0.83 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.61/0.83 tff(80,plain,
% 0.61/0.83 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(81,plain,
% 0.61/0.83 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(82,plain,
% 0.61/0.83 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.61/0.83 tff(83,plain,
% 0.61/0.83 (s1(d)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[82, 22, 79, 69])).
% 0.61/0.83 tff(84,plain,
% 0.61/0.83 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(85,plain,
% 0.61/0.83 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[84])).
% 0.61/0.83 tff(86,plain,
% 0.61/0.83 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(87,plain,
% 0.61/0.83 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(88,plain,
% 0.61/0.83 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[87])).
% 0.61/0.83 tff(89,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.61/0.83 tff(90,plain,
% 0.61/0.83 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.61/0.83 tff(91,plain,
% 0.61/0.83 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.61/0.83 tff(92,plain,(
% 0.61/0.83 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(skolemize,[status(sab)],[91])).
% 0.61/0.83 tff(93,plain,
% 0.61/0.83 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.61/0.83 tff(94,plain,
% 0.61/0.83 (k0(e) <=> k0(e)),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(95,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.61/0.83 tff(96,plain,
% 0.61/0.83 (k0(e)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.61/0.83 tff(97,plain,
% 0.61/0.83 (s0(d) <=> s0(d)),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(98,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.61/0.83 tff(99,plain,
% 0.61/0.83 (s0(d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.61/0.83 tff(100,plain,
% 0.61/0.83 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(101,plain,
% 0.61/0.83 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(102,plain,
% 0.61/0.83 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(103,plain,
% 0.61/0.83 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[102])).
% 0.61/0.83 tff(104,plain,
% 0.61/0.83 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.61/0.83 inference(transitivity,[status(thm)],[103, 101])).
% 0.61/0.83 tff(105,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.61/0.83 tff(106,plain,
% 0.61/0.83 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.61/0.83 tff(107,plain,
% 0.61/0.83 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[106, 100])).
% 0.61/0.83 tff(108,plain,
% 0.61/0.83 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.61/0.83 tff(109,plain,
% 0.61/0.83 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[108, 100])).
% 0.61/0.83 tff(110,plain,
% 0.61/0.83 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[109, 100])).
% 0.61/0.83 tff(111,plain,
% 0.61/0.83 (q1(d, d, d)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[110, 99, 96])).
% 0.61/0.83 tff(112,plain,
% 0.61/0.83 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(113,plain,
% 0.61/0.83 (((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d)) <=> ((~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(114,plain,
% 0.61/0.83 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d))))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[113])).
% 0.61/0.83 tff(115,plain,
% 0.61/0.83 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 0.61/0.83 inference(transitivity,[status(thm)],[114, 112])).
% 0.61/0.83 tff(116,plain,
% 0.61/0.83 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(117,plain,
% 0.61/0.83 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.61/0.83 tff(118,plain,
% 0.61/0.83 (r1(d)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[117, 99, 22, 111, 93])).
% 0.61/0.83 tff(119,plain,
% 0.61/0.83 (((~r1(d)) | s2(d) | (~s1(d))) <=> ((~r1(d)) | s2(d) | (~s1(d)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(120,plain,
% 0.61/0.83 (((s2(d) | (~r1(d))) | (~s1(d))) <=> ((~r1(d)) | s2(d) | (~s1(d)))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(121,axiom,((s2(d) | (~r1(d))) | (~s1(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_191')).
% 0.61/0.83 tff(122,plain,
% 0.61/0.83 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.61/0.83 tff(123,plain,
% 0.61/0.83 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[122, 119])).
% 0.61/0.83 tff(124,plain,
% 0.61/0.83 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.61/0.83 tff(125,plain,
% 0.61/0.83 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[124, 119])).
% 0.61/0.83 tff(126,plain,
% 0.61/0.83 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[125, 119])).
% 0.61/0.83 tff(127,plain,
% 0.61/0.83 (s2(d) | (~s1(d))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[126, 118])).
% 0.61/0.83 tff(128,plain,
% 0.61/0.83 (s2(d)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[127, 83])).
% 0.61/0.83 tff(129,plain,
% 0.61/0.83 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(130,plain,
% 0.61/0.83 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.84 tff(131,plain,
% 0.61/0.84 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(d)) | (~m0(d, d, b)) | (~q2(d, d, d)) | s3(d, b)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.61/0.84 tff(132,plain,
% 0.61/0.84 ($false),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[131, 128, 47, 37, 34, 9])).
% 0.61/0.84 % SZS output end Proof
% 0.61/0.84 % E exiting
%------------------------------------------------------------------------------