%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN137-1 : 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 05:38:19 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN137-1 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 12:28:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(l2_type, type, (
% 0.20/0.48 l2: ( $i * $i ) > $o)).
% 0.20/0.48 tff(b_type, type, (
% 0.20/0.48 b: $i)).
% 0.20/0.48 tff(c_type, type, (
% 0.20/0.48 c: $i)).
% 0.20/0.48 tff(q2_type, type, (
% 0.20/0.48 q2: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(s2_type, type, (
% 0.20/0.48 s2: $i > $o)).
% 0.20/0.48 tff(p0_type, type, (
% 0.20/0.48 p0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(m1_type, type, (
% 0.20/0.48 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(e_type, type, (
% 0.20/0.48 e: $i)).
% 0.20/0.48 tff(m0_type, type, (
% 0.20/0.48 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(l0_type, type, (
% 0.20/0.48 l0: $i > $o)).
% 0.20/0.48 tff(a_type, type, (
% 0.20/0.48 a: $i)).
% 0.20/0.48 tff(k1_type, type, (
% 0.20/0.48 k1: $i > $o)).
% 0.20/0.48 tff(n0_type, type, (
% 0.20/0.48 n0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(d_type, type, (
% 0.20/0.48 d: $i)).
% 0.20/0.48 tff(s1_type, type, (
% 0.20/0.48 s1: $i > $o)).
% 0.20/0.48 tff(m3_type, type, (
% 0.20/0.48 m3: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(q0_type, type, (
% 0.20/0.48 q0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (![X: $i] : p0(b, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,(
% 0.20/0.48 ![X: $i] : p0(b, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[6])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (![X: $i] : p0(b, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.48 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (^[B: $i, D: $i, C: $i] : refl(((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C)) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (^[B: $i, D: $i, C: $i] : trans(monotonicity(rewrite((m1(B, C, C) | (~l0(D))) <=> ((~l0(D)) | m1(B, C, C))), (((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> (((~l0(D)) | m1(B, C, C)) | (~m0(C, C, B))))), rewrite((((~l0(D)) | m1(B, C, C)) | (~m0(C, C, B))) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))), (((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B))) <=> ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.48 tff(17,axiom,(![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_015')).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.48 tff(20,plain,(
% 0.20/0.48 ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(skolemize,[status(sab)],[19])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (m0(b, b, e) <=> m0(b, b, e)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(23,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (m0(b, b, e)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (l0(a) <=> l0(a)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(26,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (l0(a)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | ((~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | (~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | ((~l0(a)) | (~m0(b, b, e)) | m1(e, b, b))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 ((~![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))) | (~l0(a)) | (~m0(b, b, e)) | m1(e, b, b)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (m1(e, b, b)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[30, 27, 24, 21])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (^[I: $i, H: $i, G: $i] : refl(((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (^[I: $i, H: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(G, G) | (~m0(H, G, I))) <=> ((~m0(H, G, I)) | l2(G, G))), (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) <=> (((~m0(H, G, I)) | l2(G, G)) | (~m1(I, H, H))))), rewrite((((~m0(H, G, I)) | l2(G, G)) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H)))), (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) <=> ((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))))), ((((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> (((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))) | (~p0(H, G))))), rewrite((((~m0(H, G, I)) | l2(G, G) | (~m1(I, H, H))) | (~p0(H, G))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))), ((((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G))) <=> ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.48 tff(37,axiom,(![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_134')).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.48 tff(40,plain,(
% 0.20/0.48 ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[39])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b))) <=> (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | (l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | ((~m0(b, b, e)) | (~p0(b, b)) | l2(b, b) | (~m1(e, b, b)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))) | l2(b, b) | (~m0(b, b, e)) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (l2(b, b) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[47, 24, 41])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (l2(b, b) | (~p0(b, b))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[48, 31])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (l2(b, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[49, 11])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (^[D: $i, E: $i] : refl(((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(D, c, E) | (~k1(E))) <=> ((~k1(E)) | q2(D, c, E))), (((q2(D, c, E) | (~k1(E))) | (~l0(c))) <=> (((~k1(E)) | q2(D, c, E)) | (~l0(c))))), rewrite((((~k1(E)) | q2(D, c, E)) | (~l0(c))) <=> ((~k1(E)) | (~l0(c)) | q2(D, c, E))), (((q2(D, c, E) | (~k1(E))) | (~l0(c))) <=> ((~k1(E)) | (~l0(c)) | q2(D, c, E)))), ((((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> (((~k1(E)) | (~l0(c)) | q2(D, c, E)) | (~l2(E, D))))), rewrite((((~k1(E)) | (~l0(c)) | q2(D, c, E)) | (~l2(E, D))) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))), ((((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (![D: $i, E: $i] : (((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.49 tff(56,axiom,(![D: $i, E: $i] : (((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_183')).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.49 tff(59,plain,(
% 0.20/0.49 ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(skolemize,[status(sab)],[58])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(64,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.49 tff(66,plain,(
% 0.20/0.49 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[65])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (n0(d, b) <=> n0(d, b)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(69,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (n0(d, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (k1(b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[73, 70, 67])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (l0(c) <=> l0(c)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(76,axiom,(l0(c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (l0(c)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(b)) | (~l0(c)) | (~l2(b, b)) | q2(b, c, b))) <=> ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(b)) | (~l0(c)) | (~l2(b, b)) | q2(b, c, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(b)) | (~l0(c)) | (~l2(b, b)) | q2(b, c, b))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(b)) | (~l0(c)) | (~l2(b, b)) | q2(b, c, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (q2(b, c, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[80, 77, 74, 60, 50])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(85,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.49 tff(87,plain,(
% 0.20/0.49 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[86])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 (s1(b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[91, 88, 11])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.49 tff(98,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.20/0.49 tff(101,plain,(
% 0.20/0.49 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[100])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(c) | (~q2(b, c, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(c) | (~q2(b, c, b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(c) | (~q2(b, c, b)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(c) | (~q2(b, c, b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (s2(c)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[105, 102, 92, 81])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 ((~m3(b, c, b)) <=> (~m3(b, c, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(108,axiom,(~m3(b, c, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 (~m3(b, c, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (^[J: $i] : refl(((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J)) <=> ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J)) <=> ![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J)) <=> ![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (^[J: $i] : trans(monotonicity(rewrite((m3(J, c, J) | (~s2(c))) <=> ((~s2(c)) | m3(J, c, J))), (((m3(J, c, J) | (~s2(c))) | (~q2(J, c, c))) <=> (((~s2(c)) | m3(J, c, J)) | (~q2(J, c, c))))), rewrite((((~s2(c)) | m3(J, c, J)) | (~q2(J, c, c))) <=> ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))), (((m3(J, c, J) | (~s2(c))) | (~q2(J, c, c))) <=> ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (![J: $i] : ((m3(J, c, J) | (~s2(c))) | (~q2(J, c, c))) <=> ![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.49 tff(115,axiom,(![J: $i] : ((m3(J, c, J) | (~s2(c))) | (~q2(J, c, c)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_237')).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.49 tff(118,plain,(
% 0.20/0.49 ![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(skolemize,[status(sab)],[117])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (((~![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))) | ((~s2(c)) | (~q2(b, c, c)) | m3(b, c, b))) <=> ((~![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))) | (~s2(c)) | (~q2(b, c, c)) | m3(b, c, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 ((~![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))) | ((~s2(c)) | (~q2(b, c, c)) | m3(b, c, b))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 ((~![J: $i] : ((~s2(c)) | (~q2(J, c, c)) | m3(J, c, J))) | (~s2(c)) | (~q2(b, c, c)) | m3(b, c, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 ((~s2(c)) | (~q2(b, c, c))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[122, 119, 109])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (~q2(b, c, c)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[123, 106])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (n0(d, c) <=> n0(d, c)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(126,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (n0(d, c)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(c) | (~n0(d, c)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(c) | (~n0(d, c)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(c) | (~n0(d, c)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(c) | (~n0(d, c))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (k1(c)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[130, 127, 67])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(c)) | (~l0(c)) | (~l2(c, b)) | q2(b, c, c))) <=> ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(c)) | (~l0(c)) | (~l2(c, b)) | q2(b, c, c))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(c)) | (~l0(c)) | (~l2(c, b)) | q2(b, c, c))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(c)) | (~l0(c)) | (~l2(c, b)) | q2(b, c, c)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (~l2(c, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[134, 77, 131, 60, 124])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.49 tff(141,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.20/0.49 tff(144,plain,(
% 0.20/0.49 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(skolemize,[status(sab)],[143])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.20/0.49 tff(146,assumption,(~q0(c, d)), introduced(assumption)).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(150,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (![X: $i] : q0(X, d)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.49 tff(152,plain,(
% 0.20/0.49 ![X: $i] : q0(X, d)),
% 0.20/0.49 inference(skolemize,[status(sab)],[151])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (![X: $i] : q0(X, d)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 ((~![X: $i] : q0(X, d)) | q0(c, d)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[154, 153, 146])).
% 0.20/0.49 tff(156,plain,(q0(c, d)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(c, d)) | s1(c) | (~s1(b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(c, d)) | s1(c) | (~s1(b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (((~q0(c, d)) | (~s1(b)) | s1(c)) <=> ((~q0(c, d)) | s1(c) | (~s1(b)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(c, d)) | (~s1(b)) | s1(c))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(c, d)) | s1(c) | (~s1(b))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(c, d)) | (~s1(b)) | s1(c))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(c, d)) | s1(c) | (~s1(b)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(c, d)) | (~s1(b)) | s1(c))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(c, d)) | s1(c) | (~s1(b))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 (s1(c)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[162, 156, 145, 92])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (^[D: $i, E: $i] : refl(((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E)) <=> ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E)) <=> ![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E)) <=> ![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(D, E) | (~s1(D))) <=> ((~s1(D)) | l2(D, E))), (((l2(D, E) | (~s1(D))) | (~n0(e, E))) <=> (((~s1(D)) | l2(D, E)) | (~n0(e, E))))), rewrite((((~s1(D)) | l2(D, E)) | (~n0(e, E))) <=> ((~n0(e, E)) | (~s1(D)) | l2(D, E))), (((l2(D, E) | (~s1(D))) | (~n0(e, E))) <=> ((~n0(e, E)) | (~s1(D)) | l2(D, E)))), ((((l2(D, E) | (~s1(D))) | (~n0(e, E))) | (~l2(E, E))) <=> (((~n0(e, E)) | (~s1(D)) | l2(D, E)) | (~l2(E, E))))), rewrite((((~n0(e, E)) | (~s1(D)) | l2(D, E)) | (~l2(E, E))) <=> ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))), ((((l2(D, E) | (~s1(D))) | (~n0(e, E))) | (~l2(E, E))) <=> ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (![D: $i, E: $i] : (((l2(D, E) | (~s1(D))) | (~n0(e, E))) | (~l2(E, E))) <=> ![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.49 tff(169,axiom,(![D: $i, E: $i] : (((l2(D, E) | (~s1(D))) | (~n0(e, E))) | (~l2(E, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_131')).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.50 tff(172,plain,(
% 0.20/0.50 ![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.50 inference(skolemize,[status(sab)],[171])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (n0(e, b) <=> n0(e, b)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(175,axiom,(n0(e, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_11')).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 (n0(e, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~n0(e, b)) | (~s1(c)) | (~l2(b, b)) | l2(c, b))) <=> ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | (~n0(e, b)) | (~s1(c)) | (~l2(b, b)) | l2(c, b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 (((~l2(b, b)) | (~n0(e, b)) | (~s1(c)) | l2(c, b)) <=> ((~n0(e, b)) | (~s1(c)) | (~l2(b, b)) | l2(c, b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~l2(b, b)) | (~n0(e, b)) | (~s1(c)) | l2(c, b))) <=> ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~n0(e, b)) | (~s1(c)) | (~l2(b, b)) | l2(c, b)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[178])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~l2(b, b)) | (~n0(e, b)) | (~s1(c)) | l2(c, b))) <=> ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | (~n0(e, b)) | (~s1(c)) | (~l2(b, b)) | l2(c, b))),
% 0.20/0.50 inference(transitivity,[status(thm)],[179, 177])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~l2(b, b)) | (~n0(e, b)) | (~s1(c)) | l2(c, b))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | (~n0(e, b)) | (~s1(c)) | (~l2(b, b)) | l2(c, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[182, 176, 173, 163, 50, 135])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------