%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN219-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:31 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN219-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:29:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 tff(s1_type, type, (
% 0.18/0.48 s1: $i > $o)).
% 0.18/0.48 tff(b_type, type, (
% 0.18/0.48 b: $i)).
% 0.18/0.48 tff(p0_type, type, (
% 0.18/0.48 p0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(e_type, type, (
% 0.18/0.48 e: $i)).
% 0.18/0.48 tff(l2_type, type, (
% 0.18/0.48 l2: ( $i * $i ) > $o)).
% 0.18/0.48 tff(m1_type, type, (
% 0.18/0.48 m1: ( $i * $i * $i ) > $o)).
% 0.18/0.48 tff(m0_type, type, (
% 0.18/0.48 m0: ( $i * $i * $i ) > $o)).
% 0.18/0.48 tff(l0_type, type, (
% 0.18/0.48 l0: $i > $o)).
% 0.18/0.48 tff(a_type, type, (
% 0.18/0.48 a: $i)).
% 0.18/0.48 tff(n0_type, type, (
% 0.18/0.48 n0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(q0_type, type, (
% 0.18/0.48 q0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(d_type, type, (
% 0.18/0.48 d: $i)).
% 0.18/0.48 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.18/0.48 tff(2,plain,
% 0.18/0.48 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(3,plain,
% 0.18/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.18/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.48 tff(4,plain,
% 0.18/0.48 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.18/0.48 tff(6,plain,
% 0.18/0.48 (![X: $i] : p0(b, X)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.48 tff(7,plain,(
% 0.18/0.48 ![X: $i] : p0(b, X)),
% 0.18/0.48 inference(skolemize,[status(sab)],[6])).
% 0.18/0.48 tff(8,plain,
% 0.18/0.48 (![X: $i] : p0(b, X)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.48 tff(9,plain,
% 0.18/0.48 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(10,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.48 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(12,plain,
% 0.18/0.48 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(13,plain,
% 0.18/0.48 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.48 tff(14,plain,
% 0.18/0.48 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.18/0.48 tff(16,plain,
% 0.18/0.48 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.48 tff(17,plain,(
% 0.18/0.48 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[16])).
% 0.18/0.48 tff(18,plain,
% 0.18/0.48 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.48 tff(19,plain,
% 0.18/0.48 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(20,plain,
% 0.18/0.48 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(21,plain,
% 0.18/0.48 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.48 tff(22,plain,
% 0.18/0.48 (s1(b)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.18/0.48 tff(23,plain,
% 0.18/0.48 (^[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)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(24,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.48 tff(25,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(26,plain,
% 0.18/0.48 (^[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))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(27,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.48 tff(28,axiom,(![B: $i, D: $i, C: $i] : ((m1(B, C, C) | (~l0(D))) | (~m0(C, C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_015')).
% 0.18/0.48 tff(29,plain,
% 0.18/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.48 tff(30,plain,
% 0.18/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.18/0.48 tff(31,plain,(
% 0.18/0.48 ![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.18/0.48 inference(skolemize,[status(sab)],[30])).
% 0.18/0.48 tff(32,plain,
% 0.18/0.48 (![B: $i, D: $i, C: $i] : ((~l0(D)) | (~m0(C, C, B)) | m1(B, C, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.18/0.48 tff(33,plain,
% 0.18/0.48 (m0(b, b, e) <=> m0(b, b, e)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(34,axiom,(m0(b, b, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.18/0.48 tff(35,plain,
% 0.18/0.48 (m0(b, b, e)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.48 tff(36,plain,
% 0.18/0.48 (l0(a) <=> l0(a)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(37,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.18/0.48 tff(38,plain,
% 0.18/0.48 (l0(a)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.48 tff(39,plain,
% 0.18/0.48 (((~![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))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(40,plain,
% 0.18/0.48 ((~![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))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(41,plain,
% 0.18/0.48 ((~![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)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.48 tff(42,plain,
% 0.18/0.48 (m1(e, b, b)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[41, 38, 35, 32])).
% 0.18/0.48 tff(43,plain,
% 0.18/0.48 (^[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))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(44,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.48 tff(45,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(46,plain,
% 0.18/0.48 (^[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)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(47,plain,
% 0.18/0.48 (![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)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.48 tff(48,axiom,(![I: $i, H: $i, G: $i] : (((l2(G, G) | (~m0(H, G, I))) | (~m1(I, H, H))) | (~p0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_134')).
% 0.18/0.48 tff(49,plain,
% 0.18/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.48 tff(50,plain,
% 0.18/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.18/0.48 tff(51,plain,(
% 0.18/0.48 ![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[50])).
% 0.18/0.48 tff(52,plain,
% 0.18/0.48 (![I: $i, H: $i, G: $i] : ((~m0(H, G, I)) | (~p0(H, G)) | l2(G, G) | (~m1(I, H, H)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.18/0.48 tff(53,plain,
% 0.18/0.48 (((~![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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(54,plain,
% 0.18/0.48 (((~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)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(55,plain,
% 0.18/0.48 (((~![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))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[54])).
% 0.18/0.48 tff(56,plain,
% 0.18/0.48 (((~![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)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[55, 53])).
% 0.18/0.48 tff(57,plain,
% 0.18/0.48 ((~![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)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(58,plain,
% 0.18/0.48 ((~![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))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.48 tff(59,plain,
% 0.18/0.48 (l2(b, b) | (~p0(b, b)) | (~m1(e, b, b))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[58, 35, 52])).
% 0.18/0.48 tff(60,plain,
% 0.18/0.48 (l2(b, b) | (~p0(b, b))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[59, 42])).
% 0.18/0.48 tff(61,plain,
% 0.18/0.48 (l2(b, b)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[60, 11])).
% 0.18/0.48 tff(62,plain,
% 0.18/0.48 ((~l2(e, b)) <=> (~l2(e, b))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(63,axiom,(~l2(e, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.18/0.48 tff(64,plain,
% 0.18/0.48 (~l2(e, b)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.48 tff(65,plain,
% 0.18/0.48 (^[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)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(66,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.48 tff(67,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(68,plain,
% 0.18/0.48 (^[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))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(69,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.48 tff(70,axiom,(![D: $i, E: $i] : (((l2(D, E) | (~s1(D))) | (~n0(e, E))) | (~l2(E, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_131')).
% 0.18/0.48 tff(71,plain,
% 0.18/0.48 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.48 tff(72,plain,
% 0.18/0.48 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.48 tff(73,plain,(
% 0.18/0.48 ![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.18/0.48 inference(skolemize,[status(sab)],[72])).
% 0.18/0.48 tff(74,plain,
% 0.18/0.48 (![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.48 tff(75,plain,
% 0.18/0.48 (n0(e, b) <=> n0(e, b)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(76,axiom,(n0(e, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_11')).
% 0.18/0.48 tff(77,plain,
% 0.18/0.48 (n0(e, b)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.48 tff(78,plain,
% 0.18/0.48 (((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~n0(e, b)) | l2(e, b) | (~l2(b, b)) | (~s1(e)))) <=> ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | (~n0(e, b)) | l2(e, b) | (~l2(b, b)) | (~s1(e)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(79,plain,
% 0.18/0.48 (((~l2(b, b)) | (~n0(e, b)) | (~s1(e)) | l2(e, b)) <=> ((~n0(e, b)) | l2(e, b) | (~l2(b, b)) | (~s1(e)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(80,plain,
% 0.18/0.48 (((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~l2(b, b)) | (~n0(e, b)) | (~s1(e)) | l2(e, b))) <=> ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~n0(e, b)) | l2(e, b) | (~l2(b, b)) | (~s1(e))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[79])).
% 0.18/0.48 tff(81,plain,
% 0.18/0.48 (((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~l2(b, b)) | (~n0(e, b)) | (~s1(e)) | l2(e, b))) <=> ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | (~n0(e, b)) | l2(e, b) | (~l2(b, b)) | (~s1(e)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[80, 78])).
% 0.18/0.48 tff(82,plain,
% 0.18/0.48 ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | ((~l2(b, b)) | (~n0(e, b)) | (~s1(e)) | l2(e, b))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(83,plain,
% 0.18/0.48 ((~![D: $i, E: $i] : ((~l2(E, E)) | (~n0(e, E)) | (~s1(D)) | l2(D, E))) | (~n0(e, b)) | l2(e, b) | (~l2(b, b)) | (~s1(e))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.48 tff(84,plain,
% 0.18/0.48 ((~l2(b, b)) | (~s1(e))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[83, 77, 74, 64])).
% 0.18/0.48 tff(85,plain,
% 0.18/0.48 (~s1(e)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[84, 61])).
% 0.18/0.48 tff(86,plain,
% 0.18/0.48 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(87,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.48 tff(88,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(89,plain,
% 0.18/0.48 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(90,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.48 tff(91,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')).
% 0.18/0.49 tff(92,plain,
% 0.18/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.49 tff(93,plain,
% 0.18/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.18/0.49 tff(94,plain,(
% 0.18/0.49 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.18/0.49 inference(skolemize,[status(sab)],[93])).
% 0.18/0.49 tff(95,plain,
% 0.18/0.49 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.18/0.49 tff(96,plain,
% 0.18/0.49 (q0(e, d) <=> q0(e, d)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(97,axiom,(q0(e, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.18/0.49 tff(98,plain,
% 0.18/0.49 (q0(e, d)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.18/0.49 tff(99,plain,
% 0.18/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~s1(b)) | (~q0(e, d)) | s1(e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~s1(b)) | (~q0(e, d)) | s1(e))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(100,plain,
% 0.18/0.49 (((~q0(e, d)) | (~s1(b)) | s1(e)) <=> ((~s1(b)) | (~q0(e, d)) | s1(e))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(101,plain,
% 0.18/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(e, d)) | (~s1(b)) | s1(e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~s1(b)) | (~q0(e, d)) | s1(e)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[100])).
% 0.18/0.49 tff(102,plain,
% 0.18/0.49 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(e, d)) | (~s1(b)) | s1(e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~s1(b)) | (~q0(e, d)) | s1(e))),
% 0.18/0.49 inference(transitivity,[status(thm)],[101, 99])).
% 0.18/0.49 tff(103,plain,
% 0.18/0.49 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(e, d)) | (~s1(b)) | s1(e))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(104,plain,
% 0.18/0.49 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~s1(b)) | (~q0(e, d)) | s1(e)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.49 tff(105,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[104, 98, 95, 85, 22])).
% 0.18/0.49 % SZS output end Proof
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------