%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN178-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:25 AM UTC 2025
% Result : Unsatisfiable 0.71s 0.89s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN178-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:29:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.71/0.89 % SZS status Unsatisfiable
% 0.71/0.89 % SZS output start Proof
% 0.71/0.89 tff(q2_type, type, (
% 0.71/0.89 q2: ( $i * $i * $i ) > $o)).
% 0.71/0.89 tff(d_type, type, (
% 0.71/0.89 d: $i)).
% 0.71/0.89 tff(b_type, type, (
% 0.71/0.89 b: $i)).
% 0.71/0.89 tff(q3_type, type, (
% 0.71/0.89 q3: ( $i * $i ) > $o)).
% 0.71/0.89 tff(n0_type, type, (
% 0.71/0.89 n0: ( $i * $i ) > $o)).
% 0.71/0.89 tff(q1_type, type, (
% 0.71/0.89 q1: ( $i * $i * $i ) > $o)).
% 0.71/0.89 tff(c_type, type, (
% 0.71/0.89 c: $i)).
% 0.71/0.89 tff(p0_type, type, (
% 0.71/0.89 p0: ( $i * $i ) > $o)).
% 0.71/0.89 tff(r1_type, type, (
% 0.71/0.89 r1: $i > $o)).
% 0.71/0.89 tff(s0_type, type, (
% 0.71/0.89 s0: $i > $o)).
% 0.71/0.89 tff(q0_type, type, (
% 0.71/0.89 q0: ( $i * $i ) > $o)).
% 0.71/0.89 tff(m0_type, type, (
% 0.71/0.89 m0: ( $i * $i * $i ) > $o)).
% 0.71/0.89 tff(k0_type, type, (
% 0.71/0.89 k0: $i > $o)).
% 0.71/0.89 tff(1,plain,
% 0.71/0.89 ((~q3(b, d)) <=> (~q3(b, d))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(2,axiom,(~q3(b, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.71/0.89 tff(3,plain,
% 0.71/0.89 (~q3(b, d)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.71/0.89 tff(4,plain,
% 0.71/0.89 (^[I: $i, H: $i, G: $i] : refl(((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(5,plain,
% 0.71/0.89 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[4])).
% 0.71/0.89 tff(6,plain,
% 0.71/0.89 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(7,plain,
% 0.71/0.89 (^[I: $i, H: $i, G: $i] : trans(monotonicity(rewrite((q3(G, H) | (~q2(I, G, H))) <=> ((~q2(I, G, H)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> (((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))))), rewrite((((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(8,plain,
% 0.71/0.89 (![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[7])).
% 0.71/0.89 tff(9,axiom,(![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_255')).
% 0.71/0.89 tff(10,plain,
% 0.71/0.89 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.71/0.89 tff(11,plain,
% 0.71/0.89 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.71/0.89 tff(12,plain,(
% 0.71/0.89 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(skolemize,[status(sab)],[11])).
% 0.71/0.89 tff(13,plain,
% 0.71/0.89 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.71/0.89 tff(14,plain,
% 0.71/0.89 (n0(d, b) <=> n0(d, b)),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(15,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.71/0.89 tff(16,plain,
% 0.71/0.89 (n0(d, b)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.71/0.89 tff(17,plain,
% 0.71/0.89 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(18,plain,
% 0.71/0.89 (((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d)) <=> (q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(19,plain,
% 0.71/0.89 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(b, d) | (~n0(d, b)) | (~q2(d, b, d))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[18])).
% 0.71/0.89 tff(20,plain,
% 0.71/0.89 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[19, 17])).
% 0.71/0.89 tff(21,plain,
% 0.71/0.89 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(22,plain,
% 0.71/0.89 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(b, d) | (~n0(d, b)) | (~q2(d, b, d))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.71/0.89 tff(23,plain,
% 0.71/0.89 (~q2(d, b, d)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[22, 16, 13, 3])).
% 0.71/0.89 tff(24,plain,
% 0.71/0.89 (^[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)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(25,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[24])).
% 0.71/0.89 tff(26,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(27,plain,
% 0.71/0.89 (^[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))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(28,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[27])).
% 0.71/0.89 tff(29,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.71/0.89 tff(30,plain,
% 0.71/0.89 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.71/0.89 tff(31,plain,
% 0.71/0.89 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.71/0.89 tff(32,plain,(
% 0.71/0.89 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.71/0.89 inference(skolemize,[status(sab)],[31])).
% 0.71/0.89 tff(33,plain,
% 0.71/0.89 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.71/0.89 tff(34,plain,
% 0.71/0.89 (n0(d, c) <=> n0(d, c)),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(35,axiom,(n0(d, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.71/0.89 tff(36,plain,
% 0.71/0.89 (n0(d, c)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.71/0.89 tff(37,plain,
% 0.71/0.89 (p0(c, b) <=> p0(c, b)),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(38,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.71/0.89 tff(39,plain,
% 0.71/0.89 (p0(c, b)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.71/0.89 tff(40,plain,
% 0.71/0.89 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(41,plain,
% 0.71/0.89 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(42,plain,
% 0.71/0.89 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.71/0.89 tff(43,plain,
% 0.71/0.89 (q1(b, c, b)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[42, 39, 36, 33])).
% 0.71/0.89 tff(44,plain,
% 0.71/0.89 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(45,plain,
% 0.71/0.89 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[44])).
% 0.71/0.89 tff(46,plain,
% 0.71/0.89 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(47,plain,
% 0.71/0.89 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(48,plain,
% 0.71/0.89 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[47])).
% 0.71/0.89 tff(49,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 0.71/0.89 tff(50,plain,
% 0.71/0.89 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.71/0.89 tff(51,plain,
% 0.71/0.89 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.71/0.89 tff(52,plain,(
% 0.71/0.89 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(skolemize,[status(sab)],[51])).
% 0.71/0.89 tff(53,plain,
% 0.71/0.89 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.71/0.89 tff(54,plain,
% 0.71/0.89 (((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))) <=> ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(55,plain,
% 0.71/0.89 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(56,plain,
% 0.71/0.89 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.71/0.89 tff(57,plain,
% 0.71/0.89 (q2(b, b, b)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.71/0.89 tff(58,plain,
% 0.71/0.89 (p0(b, d) <=> p0(b, d)),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(59,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.71/0.89 tff(60,plain,
% 0.71/0.89 (p0(b, d)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.71/0.89 tff(61,plain,
% 0.71/0.89 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(62,plain,
% 0.71/0.89 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(63,plain,
% 0.71/0.89 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.71/0.89 tff(64,plain,
% 0.71/0.89 (q1(d, b, d)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[63, 16, 60, 33])).
% 0.71/0.89 tff(65,plain,
% 0.71/0.89 (^[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)))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(66,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[65])).
% 0.71/0.89 tff(67,plain,
% 0.71/0.89 (![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))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(68,plain,
% 0.71/0.89 (^[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))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(69,plain,
% 0.71/0.90 (![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))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[68])).
% 0.71/0.90 tff(70,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')).
% 0.71/0.90 tff(71,plain,
% 0.71/0.90 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.71/0.90 tff(72,plain,
% 0.71/0.90 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.71/0.90 tff(73,plain,(
% 0.71/0.90 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.71/0.90 inference(skolemize,[status(sab)],[72])).
% 0.71/0.90 tff(74,plain,
% 0.71/0.90 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.71/0.90 tff(75,plain,
% 0.71/0.90 (q0(b, b) <=> q0(b, b)),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(76,axiom,(q0(b, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_6')).
% 0.71/0.90 tff(77,plain,
% 0.71/0.90 (q0(b, b)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.71/0.90 tff(78,plain,
% 0.71/0.90 (s0(d) <=> s0(d)),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(79,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.71/0.90 tff(80,plain,
% 0.71/0.90 (s0(d)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.71/0.90 tff(81,plain,
% 0.71/0.90 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(82,plain,
% 0.71/0.90 (((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b)) <=> ((~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(83,plain,
% 0.71/0.90 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[82])).
% 0.71/0.90 tff(84,plain,
% 0.71/0.90 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[83, 81])).
% 0.71/0.90 tff(85,plain,
% 0.71/0.90 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(86,plain,
% 0.71/0.90 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.71/0.90 tff(87,plain,
% 0.71/0.90 (r1(b)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[86, 80, 77, 74, 64])).
% 0.71/0.90 tff(88,assumption,(~m0(d, d, d)), introduced(assumption)).
% 0.71/0.90 tff(89,plain,
% 0.71/0.90 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(90,plain,
% 0.71/0.90 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.71/0.90 inference(quant_intro,[status(thm)],[89])).
% 0.71/0.90 tff(91,plain,
% 0.71/0.90 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(92,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.71/0.90 tff(93,plain,
% 0.71/0.90 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.71/0.90 tff(94,plain,(
% 0.71/0.90 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.71/0.90 inference(skolemize,[status(sab)],[93])).
% 0.71/0.90 tff(95,plain,
% 0.71/0.90 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.71/0.90 tff(96,plain,
% 0.71/0.90 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, d)),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(97,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[96, 95, 88])).
% 0.71/0.90 tff(98,plain,(m0(d, d, d)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(99,plain,
% 0.71/0.90 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(100,plain,
% 0.71/0.90 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[99])).
% 0.71/0.90 tff(101,plain,
% 0.71/0.90 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(102,plain,
% 0.71/0.90 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((q2(C, D, C) | (~r1(D))) <=> ((~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> (((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))))), rewrite((((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> (((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))))), rewrite((((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> (((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))))), rewrite((((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(103,plain,
% 0.71/0.90 (![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[102])).
% 0.71/0.90 tff(104,axiom,(![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 0.71/0.90 tff(105,plain,
% 0.71/0.90 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.71/0.90 tff(106,plain,
% 0.71/0.90 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.71/0.90 tff(107,plain,(
% 0.71/0.90 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(skolemize,[status(sab)],[106])).
% 0.71/0.90 tff(108,plain,
% 0.71/0.90 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.71/0.90 tff(109,plain,
% 0.71/0.90 (k0(b) <=> k0(b)),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(110,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.71/0.90 tff(111,plain,
% 0.71/0.90 (k0(b)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.71/0.90 tff(112,plain,
% 0.71/0.90 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(113,plain,
% 0.75/0.90 (((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d)) <=> ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(114,plain,
% 0.75/0.90 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[113])).
% 0.75/0.90 tff(115,plain,
% 0.75/0.90 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 0.75/0.90 inference(transitivity,[status(thm)],[114, 112])).
% 0.75/0.90 tff(116,plain,
% 0.75/0.90 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(117,plain,
% 0.75/0.90 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.75/0.90 tff(118,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[117, 111, 108, 98, 87, 57, 23])).
% 0.75/0.90 % SZS output end Proof
% 0.75/0.91 % E exiting
%------------------------------------------------------------------------------