%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN142-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:20 AM UTC 2025
% Result : Unsatisfiable 0.60s 0.80s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN142-1 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:28:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.60/0.80 % SZS status Unsatisfiable
% 0.60/0.80 % SZS output start Proof
% 0.60/0.80 tff(q2_type, type, (
% 0.60/0.80 q2: ( $i * $i * $i ) > $o)).
% 0.60/0.80 tff(b_type, type, (
% 0.60/0.80 b: $i)).
% 0.60/0.80 tff(a_type, type, (
% 0.60/0.80 a: $i)).
% 0.60/0.80 tff(n1_type, type, (
% 0.60/0.80 n1: ( $i * $i * $i ) > $o)).
% 0.60/0.80 tff(p0_type, type, (
% 0.60/0.80 p0: ( $i * $i ) > $o)).
% 0.60/0.80 tff(s0_type, type, (
% 0.60/0.80 s0: $i > $o)).
% 0.60/0.80 tff(l0_type, type, (
% 0.60/0.80 l0: $i > $o)).
% 0.60/0.80 tff(l1_type, type, (
% 0.60/0.80 l1: ( $i * $i ) > $o)).
% 0.60/0.80 tff(n0_type, type, (
% 0.60/0.80 n0: ( $i * $i ) > $o)).
% 0.60/0.80 tff(s1_type, type, (
% 0.60/0.80 s1: $i > $o)).
% 0.60/0.80 tff(s2_type, type, (
% 0.60/0.80 s2: $i > $o)).
% 0.60/0.80 tff(s3_type, type, (
% 0.60/0.80 s3: ( $i * $i ) > $o)).
% 0.60/0.80 tff(e_type, type, (
% 0.60/0.80 e: $i)).
% 0.60/0.80 tff(m4_type, type, (
% 0.60/0.80 m4: ( $i * $i ) > $o)).
% 0.60/0.80 tff(m5_type, type, (
% 0.60/0.80 m5: ( $i * $i ) > $o)).
% 0.60/0.80 tff(d_type, type, (
% 0.60/0.80 d: $i)).
% 0.60/0.80 tff(s4_type, type, (
% 0.60/0.80 s4: $i > $o)).
% 0.60/0.80 tff(p3_type, type, (
% 0.60/0.80 p3: ( $i * $i * $i ) > $o)).
% 0.60/0.80 tff(n2_type, type, (
% 0.60/0.80 n2: $i > $o)).
% 0.60/0.80 tff(p1_type, type, (
% 0.60/0.80 p1: ( $i * $i * $i ) > $o)).
% 0.60/0.80 tff(k1_type, type, (
% 0.60/0.80 k1: $i > $o)).
% 0.60/0.80 tff(c_type, type, (
% 0.60/0.80 c: $i)).
% 0.60/0.80 tff(l2_type, type, (
% 0.60/0.80 l2: ( $i * $i ) > $o)).
% 0.60/0.80 tff(m0_type, type, (
% 0.60/0.80 m0: ( $i * $i * $i ) > $o)).
% 0.60/0.80 tff(k0_type, type, (
% 0.60/0.80 k0: $i > $o)).
% 0.60/0.80 tff(r0_type, type, (
% 0.60/0.80 r0: $i > $o)).
% 0.60/0.80 tff(1,assumption,(~n1(a, b, a)), introduced(assumption)).
% 0.60/0.80 tff(2,assumption,(~p0(b, b)), introduced(assumption)).
% 0.60/0.80 tff(3,plain,
% 0.60/0.80 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(4,plain,
% 0.60/0.80 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.60/0.80 inference(quant_intro,[status(thm)],[3])).
% 0.60/0.80 tff(5,plain,
% 0.60/0.80 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(6,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.60/0.80 tff(7,plain,
% 0.60/0.80 (![X: $i] : p0(b, X)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.60/0.80 tff(8,plain,(
% 0.60/0.80 ![X: $i] : p0(b, X)),
% 0.60/0.80 inference(skolemize,[status(sab)],[7])).
% 0.60/0.80 tff(9,plain,
% 0.60/0.80 (![X: $i] : p0(b, X)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.60/0.80 tff(10,plain,
% 0.60/0.80 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(11,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.60/0.80 tff(12,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(13,plain,
% 0.60/0.80 (^[D: $i, E: $i] : refl(((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(14,plain,
% 0.60/0.80 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[13])).
% 0.60/0.80 tff(15,plain,
% 0.60/0.80 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D)) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(16,plain,
% 0.60/0.80 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(D, E, D) | (~s0(b))) <=> ((~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> (((~s0(b)) | n1(D, E, D)) | (~l0(D))))), rewrite((((~s0(b)) | n1(D, E, D)) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D))), (((n1(D, E, D) | (~s0(b))) | (~l0(D))) <=> ((~l0(D)) | (~s0(b)) | n1(D, E, D)))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> (((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))))), rewrite((((~l0(D)) | (~s0(b)) | n1(D, E, D)) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))), ((((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(17,plain,
% 0.60/0.80 (![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E))) <=> ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[16])).
% 0.60/0.80 tff(18,axiom,(![D: $i, E: $i] : (((n1(D, E, D) | (~s0(b))) | (~l0(D))) | (~p0(b, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_050')).
% 0.60/0.80 tff(19,plain,
% 0.60/0.80 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.60/0.80 tff(20,plain,
% 0.60/0.80 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.60/0.80 tff(21,plain,(
% 0.60/0.80 ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(skolemize,[status(sab)],[20])).
% 0.60/0.80 tff(22,plain,
% 0.60/0.80 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.60/0.80 tff(23,plain,
% 0.60/0.80 (l0(a) <=> l0(a)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(24,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.60/0.80 tff(25,plain,
% 0.60/0.80 (l0(a)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.60/0.80 tff(26,plain,
% 0.60/0.80 (s0(b) <=> s0(b)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(27,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.60/0.80 tff(28,plain,
% 0.60/0.80 (s0(b)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.60/0.80 tff(29,plain,
% 0.60/0.80 (((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a))) <=> ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(30,plain,
% 0.60/0.80 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | ((~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(31,plain,
% 0.60/0.80 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.60/0.80 tff(32,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[31, 28, 25, 22, 12, 1])).
% 0.60/0.80 tff(33,plain,(n1(a, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(34,plain,
% 0.60/0.80 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(35,plain,
% 0.60/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[34])).
% 0.60/0.80 tff(36,plain,
% 0.60/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(37,plain,
% 0.60/0.80 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(38,plain,
% 0.60/0.80 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[37])).
% 0.60/0.80 tff(39,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.60/0.80 tff(40,plain,
% 0.60/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.60/0.80 tff(41,plain,
% 0.60/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.60/0.80 tff(42,plain,(
% 0.60/0.80 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(skolemize,[status(sab)],[41])).
% 0.60/0.80 tff(43,plain,
% 0.60/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.60/0.80 tff(44,plain,
% 0.60/0.80 (n0(b, a) <=> n0(b, a)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(45,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.60/0.80 tff(46,plain,
% 0.60/0.80 (n0(b, a)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.60/0.80 tff(47,plain,
% 0.60/0.80 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(48,plain,
% 0.60/0.80 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(49,plain,
% 0.60/0.80 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.60/0.80 tff(50,plain,
% 0.60/0.80 (l1(a, a)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[49, 46, 43])).
% 0.60/0.80 tff(51,plain,
% 0.60/0.80 (^[E: $i, F: $i, G: $i] : refl(((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(52,plain,
% 0.60/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[51])).
% 0.60/0.80 tff(53,plain,
% 0.60/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(54,plain,
% 0.60/0.80 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(E, F, F) | (~l0(G))) <=> ((~l0(G)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> (((~l0(G)) | n1(E, F, F)) | (~l1(G, E))))), rewrite((((~l0(G)) | n1(E, F, F)) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F)))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> (((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))))), rewrite((((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(55,plain,
% 0.60/0.80 (![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[54])).
% 0.60/0.80 tff(56,axiom,(![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_054')).
% 0.60/0.80 tff(57,plain,
% 0.60/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.60/0.80 tff(58,plain,
% 0.60/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.60/0.80 tff(59,plain,(
% 0.60/0.80 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(skolemize,[status(sab)],[58])).
% 0.60/0.80 tff(60,plain,
% 0.60/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.60/0.80 tff(61,plain,
% 0.60/0.80 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(62,plain,
% 0.60/0.80 (((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b)) <=> ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(63,plain,
% 0.60/0.80 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[62])).
% 0.60/0.80 tff(64,plain,
% 0.60/0.80 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[63, 61])).
% 0.60/0.80 tff(65,plain,
% 0.60/0.80 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(66,plain,
% 0.60/0.80 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.60/0.80 tff(67,plain,
% 0.60/0.80 (n1(a, b, b) | (~n1(a, b, a))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[66, 25, 60, 50])).
% 0.60/0.80 tff(68,plain,
% 0.60/0.80 (n1(a, b, b)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[67, 33])).
% 0.60/0.80 tff(69,plain,
% 0.60/0.80 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(70,plain,
% 0.60/0.80 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[69])).
% 0.60/0.80 tff(71,plain,
% 0.60/0.80 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(72,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.60/0.80 tff(73,plain,
% 0.60/0.80 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.60/0.80 tff(74,plain,(
% 0.60/0.80 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[73])).
% 0.60/0.80 tff(75,plain,
% 0.60/0.80 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.60/0.80 tff(76,plain,
% 0.60/0.80 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(77,plain,
% 0.60/0.80 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(78,plain,
% 0.60/0.80 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.60/0.80 tff(79,plain,
% 0.60/0.80 (s1(b)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[78, 75, 12])).
% 0.60/0.80 tff(80,plain,
% 0.60/0.80 (^[X: $i] : refl((~m5(d, X)) <=> (~m5(d, X)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(81,plain,
% 0.60/0.80 (![X: $i] : (~m5(d, X)) <=> ![X: $i] : (~m5(d, X))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[80])).
% 0.60/0.80 tff(82,plain,
% 0.60/0.80 (![X: $i] : (~m5(d, X)) <=> ![X: $i] : (~m5(d, X))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(83,axiom,(![X: $i] : (~m5(d, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.60/0.80 tff(84,plain,
% 0.60/0.80 (![X: $i] : (~m5(d, X))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.60/0.80 tff(85,plain,(
% 0.60/0.80 ![X: $i] : (~m5(d, X))),
% 0.60/0.80 inference(skolemize,[status(sab)],[84])).
% 0.60/0.80 tff(86,plain,
% 0.60/0.80 (![X: $i] : (~m5(d, X))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.60/0.80 tff(87,plain,
% 0.60/0.80 ((~![X: $i] : (~m5(d, X))) | (~m5(d, d))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(88,plain,
% 0.60/0.80 (~m5(d, d)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.60/0.80 tff(89,plain,
% 0.60/0.80 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(90,plain,
% 0.60/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[89])).
% 0.60/0.80 tff(91,plain,
% 0.60/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(92,plain,
% 0.60/0.80 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(93,plain,
% 0.60/0.80 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[92])).
% 0.60/0.80 tff(94,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.60/0.80 tff(95,plain,
% 0.60/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.60/0.80 tff(96,plain,
% 0.60/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.60/0.80 tff(97,plain,(
% 0.60/0.80 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(skolemize,[status(sab)],[96])).
% 0.60/0.80 tff(98,plain,
% 0.60/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.60/0.80 tff(99,plain,
% 0.60/0.80 (p0(b, d) <=> p0(b, d)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(100,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.60/0.80 tff(101,plain,
% 0.60/0.80 (p0(b, d)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.60/0.80 tff(102,plain,
% 0.60/0.80 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(b, d)) | p1(d, d, d))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(b, d)) | p1(d, d, d))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(103,plain,
% 0.60/0.80 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(b, d)) | p1(d, d, d))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(104,plain,
% 0.60/0.80 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(b, d)) | p1(d, d, d)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.60/0.80 tff(105,plain,
% 0.60/0.80 (p1(d, d, d)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[104, 101, 98])).
% 0.60/0.80 tff(106,plain,
% 0.60/0.80 (^[B: $i, A: $i, C: $i] : refl((n2(A) | (~p1(B, C, A))) <=> (n2(A) | (~p1(B, C, A))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(107,plain,
% 0.60/0.80 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[106])).
% 0.60/0.80 tff(108,plain,
% 0.60/0.80 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(109,axiom,(![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_137')).
% 0.60/0.80 tff(110,plain,
% 0.60/0.80 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.60/0.80 tff(111,plain,(
% 0.60/0.80 ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[110])).
% 0.60/0.80 tff(112,plain,
% 0.60/0.80 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.60/0.80 tff(113,plain,
% 0.60/0.80 (((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(d) | (~p1(d, d, d)))) <=> ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(d) | (~p1(d, d, d)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(114,plain,
% 0.60/0.80 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(d) | (~p1(d, d, d)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(115,plain,
% 0.60/0.80 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(d) | (~p1(d, d, d))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.60/0.80 tff(116,plain,
% 0.60/0.80 (n2(d)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[115, 112, 105])).
% 0.60/0.80 tff(117,plain,
% 0.60/0.80 (^[H: $i] : refl(((~k1(H)) | (~n2(H)) | p3(H, H, H)) <=> ((~k1(H)) | (~n2(H)) | p3(H, H, H)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(118,plain,
% 0.60/0.80 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H)) <=> ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[117])).
% 0.60/0.80 tff(119,plain,
% 0.60/0.80 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H)) <=> ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(120,plain,
% 0.60/0.80 (^[H: $i] : trans(monotonicity(rewrite((p3(H, H, H) | (~k1(H))) <=> ((~k1(H)) | p3(H, H, H))), (((p3(H, H, H) | (~k1(H))) | (~n2(H))) <=> (((~k1(H)) | p3(H, H, H)) | (~n2(H))))), rewrite((((~k1(H)) | p3(H, H, H)) | (~n2(H))) <=> ((~k1(H)) | (~n2(H)) | p3(H, H, H))), (((p3(H, H, H) | (~k1(H))) | (~n2(H))) <=> ((~k1(H)) | (~n2(H)) | p3(H, H, H))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(121,plain,
% 0.60/0.80 (![H: $i] : ((p3(H, H, H) | (~k1(H))) | (~n2(H))) <=> ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[120])).
% 0.60/0.80 tff(122,axiom,(![H: $i] : ((p3(H, H, H) | (~k1(H))) | (~n2(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_249')).
% 0.60/0.80 tff(123,plain,
% 0.60/0.80 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.60/0.80 tff(124,plain,
% 0.60/0.80 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.60/0.80 tff(125,plain,(
% 0.60/0.80 ![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(skolemize,[status(sab)],[124])).
% 0.60/0.80 tff(126,plain,
% 0.60/0.80 (![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.60/0.80 tff(127,plain,
% 0.60/0.80 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(128,plain,
% 0.60/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[127])).
% 0.60/0.80 tff(129,plain,
% 0.60/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(130,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.60/0.80 tff(131,plain,
% 0.60/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.60/0.80 tff(132,plain,(
% 0.60/0.80 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[131])).
% 0.60/0.80 tff(133,plain,
% 0.60/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.60/0.80 tff(134,plain,
% 0.60/0.80 (n0(c, d) <=> n0(c, d)),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(135,axiom,(n0(c, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.60/0.80 tff(136,plain,
% 0.60/0.80 (n0(c, d)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.60/0.80 tff(137,plain,
% 0.60/0.80 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(138,plain,
% 0.60/0.80 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(139,plain,
% 0.60/0.80 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.60/0.80 tff(140,plain,
% 0.60/0.80 (k1(d)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[139, 136, 133])).
% 0.60/0.80 tff(141,plain,
% 0.60/0.80 (((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | ((~k1(d)) | (~n2(d)) | p3(d, d, d))) <=> ((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | (~k1(d)) | (~n2(d)) | p3(d, d, d))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(142,plain,
% 0.60/0.80 ((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | ((~k1(d)) | (~n2(d)) | p3(d, d, d))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(143,plain,
% 0.60/0.80 ((~![H: $i] : ((~k1(H)) | (~n2(H)) | p3(H, H, H))) | (~k1(d)) | (~n2(d)) | p3(d, d, d)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.60/0.80 tff(144,plain,
% 0.60/0.80 (p3(d, d, d)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[143, 140, 126, 116])).
% 0.60/0.80 tff(145,plain,
% 0.60/0.80 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(c, d)) | l1(d, d))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(c, d)) | l1(d, d))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(146,plain,
% 0.60/0.80 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(c, d)) | l1(d, d))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(147,plain,
% 0.60/0.80 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(c, d)) | l1(d, d)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.60/0.80 tff(148,plain,
% 0.60/0.80 (l1(d, d)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[147, 136, 43])).
% 0.60/0.80 tff(149,plain,
% 0.60/0.80 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~l1(A, C)) | (~p3(B, C, D)) | s4(A)) <=> ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(150,plain,
% 0.60/0.80 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[149])).
% 0.60/0.80 tff(151,plain,
% 0.60/0.80 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(152,plain,
% 0.60/0.80 (^[B: $i, D: $i, A: $i, C: $i] : rewrite(((s4(A) | (~p3(B, C, D))) | (~l1(A, C))) <=> ((~l1(A, C)) | (~p3(B, C, D)) | s4(A)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(153,plain,
% 0.60/0.80 (![B: $i, D: $i, A: $i, C: $i] : ((s4(A) | (~p3(B, C, D))) | (~l1(A, C))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[152])).
% 0.60/0.80 tff(154,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((s4(A) | (~p3(B, C, D))) | (~l1(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_299')).
% 0.60/0.81 tff(155,plain,
% 0.60/0.81 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.60/0.81 tff(156,plain,
% 0.60/0.81 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.60/0.81 tff(157,plain,(
% 0.60/0.81 ![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.81 inference(skolemize,[status(sab)],[156])).
% 0.60/0.81 tff(158,plain,
% 0.60/0.81 (![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.60/0.81 tff(159,plain,
% 0.60/0.81 (((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | (~p3(d, d, d)) | s4(d))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | (~l1(d, d)) | (~p3(d, d, d)) | s4(d))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(160,plain,
% 0.60/0.81 ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | ((~l1(d, d)) | (~p3(d, d, d)) | s4(d))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(161,plain,
% 0.60/0.81 ((~![B: $i, D: $i, A: $i, C: $i] : ((~l1(A, C)) | (~p3(B, C, D)) | s4(A))) | (~l1(d, d)) | (~p3(d, d, d)) | s4(d)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.60/0.81 tff(162,plain,
% 0.60/0.81 (s4(d)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[161, 158, 148, 144])).
% 0.60/0.81 tff(163,plain,
% 0.60/0.81 (^[B: $i] : refl((m5(B, B) | (~m4(e, e)) | (~s4(B))) <=> (m5(B, B) | (~m4(e, e)) | (~s4(B))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(164,plain,
% 0.60/0.81 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B))) <=> ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[163])).
% 0.60/0.81 tff(165,plain,
% 0.60/0.81 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B))) <=> ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(166,plain,
% 0.60/0.81 (^[B: $i] : trans(monotonicity(rewrite((m5(B, B) | (~s4(B))) <=> (m5(B, B) | (~s4(B)))), (((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> ((m5(B, B) | (~s4(B))) | (~m4(e, e))))), rewrite(((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> (m5(B, B) | (~m4(e, e)) | (~s4(B)))), (((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> (m5(B, B) | (~m4(e, e)) | (~s4(B)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(167,plain,
% 0.60/0.81 (![B: $i] : ((m5(B, B) | (~s4(B))) | (~m4(e, e))) <=> ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[166])).
% 0.60/0.81 tff(168,axiom,(![B: $i] : ((m5(B, B) | (~s4(B))) | (~m4(e, e)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_305')).
% 0.60/0.81 tff(169,plain,
% 0.60/0.81 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.60/0.81 tff(170,plain,
% 0.60/0.81 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.60/0.81 tff(171,plain,(
% 0.60/0.81 ![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[170])).
% 0.60/0.81 tff(172,plain,
% 0.60/0.81 (![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.60/0.81 tff(173,plain,
% 0.60/0.81 (((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | ((~m4(e, e)) | m5(d, d) | (~s4(d)))) <=> ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (~m4(e, e)) | m5(d, d) | (~s4(d)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(174,plain,
% 0.60/0.81 ((m5(d, d) | (~m4(e, e)) | (~s4(d))) <=> ((~m4(e, e)) | m5(d, d) | (~s4(d)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(175,plain,
% 0.60/0.81 (((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (m5(d, d) | (~m4(e, e)) | (~s4(d)))) <=> ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | ((~m4(e, e)) | m5(d, d) | (~s4(d))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[174])).
% 0.60/0.81 tff(176,plain,
% 0.60/0.81 (((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (m5(d, d) | (~m4(e, e)) | (~s4(d)))) <=> ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (~m4(e, e)) | m5(d, d) | (~s4(d)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[175, 173])).
% 0.60/0.81 tff(177,plain,
% 0.60/0.81 ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (m5(d, d) | (~m4(e, e)) | (~s4(d)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(178,plain,
% 0.60/0.81 ((~![B: $i] : (m5(B, B) | (~m4(e, e)) | (~s4(B)))) | (~m4(e, e)) | m5(d, d) | (~s4(d))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.60/0.81 tff(179,plain,
% 0.60/0.81 ((~m4(e, e)) | m5(d, d)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[178, 172, 162])).
% 0.60/0.81 tff(180,plain,
% 0.60/0.81 (~m4(e, e)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[179, 88])).
% 0.60/0.81 tff(181,plain,
% 0.60/0.81 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(182,plain,
% 0.60/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[181])).
% 0.60/0.81 tff(183,plain,
% 0.60/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(184,plain,
% 0.60/0.81 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(185,plain,
% 0.60/0.81 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[184])).
% 0.60/0.81 tff(186,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.60/0.81 tff(187,plain,
% 0.60/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.60/0.81 tff(188,plain,
% 0.60/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.60/0.81 tff(189,plain,(
% 0.60/0.81 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(skolemize,[status(sab)],[188])).
% 0.60/0.81 tff(190,plain,
% 0.60/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.60/0.81 tff(191,plain,
% 0.60/0.81 (m0(b, b, e) <=> m0(b, b, e)),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(192,axiom,(m0(b, b, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.60/0.81 tff(193,plain,
% 0.60/0.81 (m0(b, b, e)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.60/0.81 tff(194,plain,
% 0.60/0.81 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(195,plain,
% 0.60/0.81 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(196,plain,
% 0.60/0.81 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[195])).
% 0.60/0.81 tff(197,plain,
% 0.60/0.81 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[196, 194])).
% 0.60/0.81 tff(198,plain,
% 0.60/0.81 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(199,plain,
% 0.60/0.81 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.60/0.81 tff(200,plain,
% 0.60/0.81 ((~s1(b)) | l2(e, e)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[199, 193, 190, 12])).
% 0.60/0.81 tff(201,plain,
% 0.60/0.81 (l2(e, e)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[200, 79])).
% 0.60/0.81 tff(202,plain,
% 0.60/0.81 (^[E: $i, F: $i, G: $i] : refl(((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(203,plain,
% 0.60/0.81 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[202])).
% 0.60/0.81 tff(204,plain,
% 0.60/0.81 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(205,plain,
% 0.60/0.81 (^[E: $i, F: $i, G: $i] : trans(monotonicity(rewrite((m4(E, F) | (~l2(G, F))) <=> ((~l2(G, F)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> (((~l2(G, F)) | m4(E, F)) | (~s3(a, E))))), rewrite((((~l2(G, F)) | m4(E, F)) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(206,plain,
% 0.60/0.81 (![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[205])).
% 0.60/0.81 tff(207,axiom,(![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_279')).
% 0.60/0.81 tff(208,plain,
% 0.60/0.81 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.60/0.81 tff(209,plain,
% 0.60/0.81 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.60/0.81 tff(210,plain,(
% 0.60/0.81 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(skolemize,[status(sab)],[209])).
% 0.60/0.81 tff(211,plain,
% 0.60/0.81 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.60/0.81 tff(212,plain,
% 0.60/0.81 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(213,plain,
% 0.60/0.81 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(214,plain,
% 0.60/0.81 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.60/0.81 tff(215,plain,
% 0.60/0.81 (~s3(a, e)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[214, 211, 201, 180])).
% 0.60/0.81 tff(216,assumption,(~q2(a, e, e)), introduced(assumption)).
% 0.60/0.81 tff(217,plain,
% 0.60/0.81 (^[E: $i, F: $i] : refl(((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(218,plain,
% 0.60/0.81 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[217])).
% 0.60/0.81 tff(219,plain,
% 0.60/0.81 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(220,plain,
% 0.60/0.81 (^[E: $i, F: $i] : trans(monotonicity(rewrite((q2(E, F, F) | (~k0(F))) <=> ((~k0(F)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> (((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))))), rewrite((((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(221,plain,
% 0.60/0.81 (![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[220])).
% 0.60/0.81 tff(222,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 0.60/0.81 tff(223,plain,
% 0.60/0.81 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.60/0.81 tff(224,plain,
% 0.60/0.81 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.60/0.81 tff(225,plain,(
% 0.60/0.81 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(skolemize,[status(sab)],[224])).
% 0.60/0.81 tff(226,plain,
% 0.60/0.81 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.60/0.81 tff(227,plain,
% 0.60/0.81 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(228,plain,
% 0.60/0.81 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(229,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.60/0.81 tff(230,plain,
% 0.60/0.81 ((~l0(a)) | p1(a, a, a)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.60/0.81 tff(231,plain,
% 0.60/0.81 ((~l0(a)) | p1(a, a, a)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.60/0.81 tff(232,plain,
% 0.60/0.81 (p1(a, a, a)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[231, 25])).
% 0.60/0.81 tff(233,plain,
% 0.60/0.81 (k0(e) <=> k0(e)),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(234,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.60/0.81 tff(235,plain,
% 0.60/0.81 (k0(e)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.60/0.81 tff(236,plain,
% 0.60/0.81 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(237,plain,
% 0.60/0.81 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(238,plain,
% 0.60/0.81 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.60/0.81 tff(239,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[238, 235, 232, 226, 216])).
% 0.60/0.81 tff(240,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(241,plain,
% 0.60/0.81 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(242,plain,
% 0.60/0.81 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(243,plain,
% 0.60/0.81 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.60/0.81 tff(244,plain,
% 0.60/0.81 (k1(a)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[243, 46, 133])).
% 0.60/0.81 tff(245,plain,
% 0.60/0.81 (^[D: $i, C: $i] : refl(((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(246,plain,
% 0.60/0.81 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[245])).
% 0.60/0.81 tff(247,plain,
% 0.60/0.81 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(248,plain,
% 0.60/0.81 (^[D: $i, C: $i] : trans(monotonicity(rewrite((n1(C, e, e) | (~m0(C, D, e))) <=> ((~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> (((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))))), rewrite((((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(249,plain,
% 0.60/0.81 (![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[248])).
% 0.60/0.81 tff(250,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 0.60/0.81 tff(251,plain,
% 0.60/0.81 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.60/0.81 tff(252,plain,
% 0.60/0.81 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.60/0.81 tff(253,plain,(
% 0.60/0.81 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(skolemize,[status(sab)],[252])).
% 0.60/0.81 tff(254,plain,
% 0.60/0.81 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.60/0.81 tff(255,plain,
% 0.60/0.81 (m0(a, e, e) <=> m0(a, e, e)),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(256,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 0.60/0.81 tff(257,plain,
% 0.60/0.81 (m0(a, e, e)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.60/0.81 tff(258,plain,
% 0.60/0.81 (((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))) <=> ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(259,plain,
% 0.60/0.81 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(260,plain,
% 0.60/0.81 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.60/0.81 tff(261,plain,
% 0.60/0.81 ((~k1(a)) | n1(a, e, e)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[260, 257, 254])).
% 0.60/0.81 tff(262,plain,
% 0.60/0.81 (n1(a, e, e)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[261, 244])).
% 0.60/0.81 tff(263,plain,
% 0.60/0.81 (^[H: $i, F: $i, G: $i] : refl(((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(264,plain,
% 0.60/0.81 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[263])).
% 0.60/0.81 tff(265,plain,
% 0.60/0.81 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(266,plain,
% 0.60/0.81 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(F, G, F) | (~p1(F, F, H))) <=> ((~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> (((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))))), rewrite((((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> (((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))))), rewrite((((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(267,plain,
% 0.60/0.82 (![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[266])).
% 0.60/0.82 tff(268,axiom,(![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 0.60/0.82 tff(269,plain,
% 0.60/0.82 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.60/0.82 tff(270,plain,
% 0.60/0.82 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.60/0.82 tff(271,plain,(
% 0.60/0.82 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.82 inference(skolemize,[status(sab)],[270])).
% 0.60/0.82 tff(272,plain,
% 0.60/0.82 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.60/0.82 tff(273,plain,
% 0.60/0.82 (r0(e) <=> r0(e)),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(274,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.60/0.82 tff(275,plain,
% 0.60/0.82 (r0(e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.60/0.82 tff(276,plain,
% 0.60/0.82 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(277,plain,
% 0.60/0.82 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(278,plain,
% 0.60/0.82 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(279,plain,
% 0.60/0.82 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[278])).
% 0.60/0.82 tff(280,plain,
% 0.60/0.82 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.60/0.82 inference(transitivity,[status(thm)],[279, 277])).
% 0.60/0.82 tff(281,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.60/0.82 tff(282,plain,
% 0.60/0.82 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.60/0.82 tff(283,plain,
% 0.60/0.82 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[282, 276])).
% 0.60/0.82 tff(284,plain,
% 0.60/0.82 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[283, 276])).
% 0.60/0.82 tff(285,plain,
% 0.60/0.82 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[284, 276])).
% 0.60/0.82 tff(286,plain,
% 0.60/0.82 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[285, 276])).
% 0.60/0.82 tff(287,plain,
% 0.60/0.82 (p1(e, e, e)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[286, 275, 235])).
% 0.60/0.82 tff(288,plain,
% 0.60/0.82 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(289,plain,
% 0.60/0.82 (((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e)) <=> ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(290,plain,
% 0.60/0.82 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[289])).
% 0.60/0.82 tff(291,plain,
% 0.60/0.82 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e))),
% 0.60/0.82 inference(transitivity,[status(thm)],[290, 288])).
% 0.60/0.82 tff(292,plain,
% 0.60/0.82 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(293,plain,
% 0.60/0.82 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)) | q2(e, a, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.60/0.82 tff(294,plain,
% 0.60/0.82 ((~q2(a, e, e)) | q2(e, a, e)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[293, 287, 272, 262])).
% 0.60/0.82 tff(295,plain,
% 0.60/0.82 (q2(e, a, e)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[294, 240])).
% 0.60/0.82 tff(296,plain,
% 0.60/0.82 (^[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)))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(297,plain,
% 0.60/0.82 (![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))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[296])).
% 0.60/0.82 tff(298,plain,
% 0.60/0.82 (![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))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(299,plain,
% 0.60/0.82 (^[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))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(300,plain,
% 0.60/0.82 (![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))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[299])).
% 0.60/0.82 tff(301,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')).
% 0.60/0.82 tff(302,plain,
% 0.60/0.82 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.60/0.82 tff(303,plain,
% 0.60/0.82 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.60/0.82 tff(304,plain,(
% 0.60/0.82 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.60/0.82 inference(skolemize,[status(sab)],[303])).
% 0.60/0.82 tff(305,plain,
% 0.60/0.82 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.60/0.82 tff(306,plain,
% 0.60/0.82 (m0(e, d, e) <=> m0(e, d, e)),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(307,axiom,(m0(e, d, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_8')).
% 0.60/0.82 tff(308,plain,
% 0.60/0.82 (m0(e, d, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.60/0.82 tff(309,plain,
% 0.60/0.82 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(310,plain,
% 0.60/0.82 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(311,plain,
% 0.60/0.82 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.60/0.82 tff(312,plain,
% 0.60/0.82 (~s2(a)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[311, 308, 305, 295, 215])).
% 0.60/0.82 tff(313,plain,
% 0.60/0.82 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(314,plain,
% 0.60/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[313])).
% 0.60/0.82 tff(315,plain,
% 0.60/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(316,plain,
% 0.60/0.82 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(317,plain,
% 0.60/0.82 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[316])).
% 0.60/0.82 tff(318,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.60/0.82 tff(319,plain,
% 0.60/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.60/0.82 tff(320,plain,
% 0.60/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[319, 315])).
% 0.60/0.82 tff(321,plain,(
% 0.60/0.82 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[320])).
% 0.60/0.82 tff(322,plain,
% 0.60/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[321, 314])).
% 0.60/0.82 tff(323,plain,
% 0.60/0.82 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(324,plain,
% 0.60/0.82 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(325,plain,
% 0.60/0.82 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.60/0.82 tff(326,plain,
% 0.60/0.82 (~q2(b, a, b)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[325, 322, 312, 79])).
% 0.60/0.82 tff(327,plain,
% 0.60/0.82 (p0(c, b) <=> p0(c, b)),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(328,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.60/0.82 tff(329,plain,
% 0.60/0.82 (p0(c, b)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.60/0.82 tff(330,plain,
% 0.60/0.82 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(331,plain,
% 0.60/0.82 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(332,plain,
% 0.60/0.82 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.60/0.82 tff(333,plain,
% 0.60/0.82 (p1(b, b, b)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[332, 329, 98])).
% 0.60/0.82 tff(334,plain,
% 0.60/0.82 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(335,plain,
% 0.60/0.83 (((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b)) <=> ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(336,plain,
% 0.60/0.83 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[335])).
% 0.60/0.83 tff(337,plain,
% 0.60/0.83 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[336, 334])).
% 0.60/0.83 tff(338,plain,
% 0.60/0.83 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(a, b, b)) | (~n1(a, b, b)) | (~p1(b, b, b)) | q2(b, a, b))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(339,plain,
% 0.60/0.83 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(b, b, b)) | q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.60/0.83 tff(340,plain,
% 0.60/0.83 ((~q2(a, b, b)) | (~n1(a, b, b))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[339, 272, 333, 326])).
% 0.60/0.83 tff(341,plain,
% 0.60/0.83 (~q2(a, b, b)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[340, 68])).
% 0.60/0.83 tff(342,plain,
% 0.60/0.83 (k0(b) <=> k0(b)),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(343,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.60/0.83 tff(344,plain,
% 0.60/0.83 (k0(b)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.60/0.83 tff(345,plain,
% 0.60/0.83 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(346,plain,
% 0.60/0.83 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(347,plain,
% 0.60/0.83 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.60/0.83 tff(348,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[347, 344, 232, 226, 341])).
% 0.60/0.83 % SZS output end Proof
% 0.68/0.83 % E exiting
%------------------------------------------------------------------------------