%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN204-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:29 AM UTC 2025
% Result : Unsatisfiable 0.52s 0.74s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN204-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 12:30:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.52/0.74 % SZS status Unsatisfiable
% 0.52/0.74 % SZS output start Proof
% 0.52/0.74 tff(q2_type, type, (
% 0.52/0.74 q2: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(b_type, type, (
% 0.52/0.74 b: $i)).
% 0.52/0.74 tff(a_type, type, (
% 0.52/0.74 a: $i)).
% 0.52/0.74 tff(n1_type, type, (
% 0.52/0.74 n1: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(p0_type, type, (
% 0.52/0.74 p0: ( $i * $i ) > $o)).
% 0.52/0.74 tff(s0_type, type, (
% 0.52/0.74 s0: $i > $o)).
% 0.52/0.74 tff(l0_type, type, (
% 0.52/0.74 l0: $i > $o)).
% 0.52/0.74 tff(l1_type, type, (
% 0.52/0.74 l1: ( $i * $i ) > $o)).
% 0.52/0.74 tff(n0_type, type, (
% 0.52/0.74 n0: ( $i * $i ) > $o)).
% 0.52/0.74 tff(s1_type, type, (
% 0.52/0.74 s1: $i > $o)).
% 0.52/0.74 tff(s2_type, type, (
% 0.52/0.74 s2: $i > $o)).
% 0.52/0.74 tff(e_type, type, (
% 0.52/0.74 e: $i)).
% 0.52/0.74 tff(p1_type, type, (
% 0.52/0.74 p1: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(k0_type, type, (
% 0.52/0.74 k0: $i > $o)).
% 0.52/0.74 tff(k1_type, type, (
% 0.52/0.74 k1: $i > $o)).
% 0.52/0.74 tff(m0_type, type, (
% 0.52/0.74 m0: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(r0_type, type, (
% 0.52/0.74 r0: $i > $o)).
% 0.52/0.74 tff(s3_type, type, (
% 0.52/0.74 s3: ( $i * $i ) > $o)).
% 0.52/0.74 tff(c_type, type, (
% 0.52/0.74 c: $i)).
% 0.52/0.74 tff(1,assumption,(~n1(a, b, a)), introduced(assumption)).
% 0.52/0.74 tff(2,assumption,(~p0(b, b)), introduced(assumption)).
% 0.52/0.74 tff(3,plain,
% 0.52/0.74 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(4,plain,
% 0.52/0.74 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.52/0.74 inference(quant_intro,[status(thm)],[3])).
% 0.52/0.74 tff(5,plain,
% 0.52/0.74 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(6,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.52/0.74 tff(7,plain,
% 0.52/0.74 (![X: $i] : p0(b, X)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.52/0.74 tff(8,plain,(
% 0.52/0.74 ![X: $i] : p0(b, X)),
% 0.52/0.74 inference(skolemize,[status(sab)],[7])).
% 0.52/0.74 tff(9,plain,
% 0.52/0.74 (![X: $i] : p0(b, X)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.52/0.74 tff(10,plain,
% 0.52/0.74 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(11,plain,
% 0.52/0.74 ($false),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.52/0.74 tff(12,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.74 tff(13,plain,
% 0.52/0.74 (^[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)))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(14,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[13])).
% 0.52/0.74 tff(15,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(16,plain,
% 0.52/0.74 (^[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))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(17,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[16])).
% 0.52/0.74 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')).
% 0.52/0.74 tff(19,plain,
% 0.52/0.74 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.52/0.74 tff(20,plain,
% 0.52/0.74 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.52/0.74 tff(21,plain,(
% 0.52/0.74 ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.74 inference(skolemize,[status(sab)],[20])).
% 0.52/0.74 tff(22,plain,
% 0.52/0.74 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.52/0.74 tff(23,plain,
% 0.52/0.74 (l0(a) <=> l0(a)),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(24,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.52/0.74 tff(25,plain,
% 0.52/0.74 (l0(a)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.52/0.74 tff(26,plain,
% 0.52/0.74 (s0(b) <=> s0(b)),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(27,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.52/0.74 tff(28,plain,
% 0.52/0.74 (s0(b)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.52/0.74 tff(29,plain,
% 0.52/0.74 (((~![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))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(30,plain,
% 0.52/0.74 ((~![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))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(31,plain,
% 0.52/0.74 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.52/0.74 tff(32,plain,
% 0.52/0.74 ($false),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[31, 28, 25, 22, 12, 1])).
% 0.52/0.74 tff(33,plain,(n1(a, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.74 tff(34,plain,
% 0.52/0.74 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(35,plain,
% 0.52/0.74 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[34])).
% 0.52/0.74 tff(36,plain,
% 0.52/0.74 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(37,plain,
% 0.52/0.74 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(38,plain,
% 0.52/0.74 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[37])).
% 0.52/0.74 tff(39,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.52/0.74 tff(40,plain,
% 0.52/0.74 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.52/0.74 tff(41,plain,
% 0.52/0.74 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.52/0.74 tff(42,plain,(
% 0.52/0.74 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(skolemize,[status(sab)],[41])).
% 0.52/0.74 tff(43,plain,
% 0.52/0.74 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.52/0.74 tff(44,plain,
% 0.52/0.74 (n0(b, a) <=> n0(b, a)),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(45,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.52/0.74 tff(46,plain,
% 0.52/0.74 (n0(b, a)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.52/0.74 tff(47,plain,
% 0.52/0.74 (((~![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))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(48,plain,
% 0.52/0.74 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(49,plain,
% 0.52/0.74 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.52/0.74 tff(50,plain,
% 0.52/0.74 (l1(a, a)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[49, 46, 43])).
% 0.52/0.74 tff(51,plain,
% 0.52/0.74 (^[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)))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(52,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[51])).
% 0.52/0.74 tff(53,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(54,plain,
% 0.52/0.74 (^[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))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(55,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[54])).
% 0.52/0.74 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')).
% 0.52/0.74 tff(57,plain,
% 0.52/0.74 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.52/0.74 tff(58,plain,
% 0.52/0.74 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.52/0.74 tff(59,plain,(
% 0.52/0.74 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.74 inference(skolemize,[status(sab)],[58])).
% 0.52/0.74 tff(60,plain,
% 0.52/0.74 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.52/0.74 tff(61,plain,
% 0.52/0.74 (((~![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)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(62,plain,
% 0.52/0.74 (((~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)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(63,plain,
% 0.52/0.74 (((~![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))))),
% 0.52/0.74 inference(monotonicity,[status(thm)],[62])).
% 0.52/0.74 tff(64,plain,
% 0.52/0.74 (((~![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)))),
% 0.52/0.74 inference(transitivity,[status(thm)],[63, 61])).
% 0.52/0.74 tff(65,plain,
% 0.52/0.74 ((~![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))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(66,plain,
% 0.52/0.74 ((~![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))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.52/0.74 tff(67,plain,
% 0.52/0.74 (n1(a, b, b)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[66, 25, 60, 50, 33])).
% 0.52/0.74 tff(68,plain,
% 0.52/0.74 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(69,plain,
% 0.52/0.74 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[68])).
% 0.52/0.74 tff(70,plain,
% 0.52/0.74 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(71,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.52/0.74 tff(72,plain,
% 0.52/0.74 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.52/0.74 tff(73,plain,(
% 0.52/0.74 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.74 inference(skolemize,[status(sab)],[72])).
% 0.52/0.74 tff(74,plain,
% 0.52/0.74 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.52/0.74 tff(75,plain,
% 0.52/0.74 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(76,plain,
% 0.52/0.74 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.52/0.74 inference(quant_inst,[status(thm)],[])).
% 0.52/0.74 tff(77,plain,
% 0.52/0.74 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.52/0.74 tff(78,plain,
% 0.52/0.74 (s1(b)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[77, 74, 12])).
% 0.52/0.74 tff(79,assumption,(~q2(a, e, e)), introduced(assumption)).
% 0.52/0.74 tff(80,plain,
% 0.52/0.74 (^[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)))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(81,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[80])).
% 0.52/0.74 tff(82,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(83,plain,
% 0.52/0.74 (^[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))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(84,plain,
% 0.52/0.74 (![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))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[83])).
% 0.52/0.74 tff(85,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')).
% 0.52/0.74 tff(86,plain,
% 0.52/0.74 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.52/0.74 tff(87,plain,
% 0.52/0.74 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.52/0.74 tff(88,plain,(
% 0.52/0.74 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.74 inference(skolemize,[status(sab)],[87])).
% 0.52/0.74 tff(89,plain,
% 0.52/0.74 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.52/0.74 tff(90,plain,
% 0.52/0.74 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(91,plain,
% 0.52/0.74 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(92,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.52/0.74 tff(93,plain,
% 0.52/0.74 ((~l0(a)) | p1(a, a, a)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.52/0.74 tff(94,plain,
% 0.52/0.74 ((~l0(a)) | p1(a, a, a)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.52/0.74 tff(95,plain,
% 0.52/0.74 (p1(a, a, a)),
% 0.52/0.74 inference(unit_resolution,[status(thm)],[94, 25])).
% 0.52/0.74 tff(96,plain,
% 0.52/0.74 (k0(e) <=> k0(e)),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(97,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.52/0.74 tff(98,plain,
% 0.52/0.74 (k0(e)),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.52/0.74 tff(99,plain,
% 0.52/0.74 (((~![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))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(100,plain,
% 0.59/0.74 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 0.59/0.74 inference(quant_inst,[status(thm)],[])).
% 0.59/0.74 tff(101,plain,
% 0.59/0.74 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.59/0.74 tff(102,plain,
% 0.59/0.74 ($false),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[101, 98, 95, 89, 79])).
% 0.59/0.74 tff(103,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.74 tff(104,plain,
% 0.59/0.74 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.59/0.74 inference(bind,[status(th)],[])).
% 0.59/0.74 tff(105,plain,
% 0.59/0.74 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.74 inference(quant_intro,[status(thm)],[104])).
% 0.59/0.74 tff(106,plain,
% 0.59/0.74 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(107,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.59/0.74 tff(108,plain,
% 0.59/0.74 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.59/0.74 tff(109,plain,(
% 0.59/0.74 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.74 inference(skolemize,[status(sab)],[108])).
% 0.59/0.74 tff(110,plain,
% 0.59/0.74 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.59/0.74 tff(111,plain,
% 0.59/0.74 (((~![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)))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(112,plain,
% 0.59/0.74 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.59/0.74 inference(quant_inst,[status(thm)],[])).
% 0.59/0.74 tff(113,plain,
% 0.59/0.74 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.59/0.74 tff(114,plain,
% 0.59/0.74 (k1(a)),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[113, 46, 110])).
% 0.59/0.74 tff(115,plain,
% 0.59/0.74 (^[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)))),
% 0.59/0.74 inference(bind,[status(th)],[])).
% 0.59/0.74 tff(116,plain,
% 0.59/0.74 (![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))),
% 0.59/0.74 inference(quant_intro,[status(thm)],[115])).
% 0.59/0.74 tff(117,plain,
% 0.59/0.74 (![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))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(118,plain,
% 0.59/0.74 (^[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))))),
% 0.59/0.74 inference(bind,[status(th)],[])).
% 0.59/0.74 tff(119,plain,
% 0.59/0.74 (![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))),
% 0.59/0.74 inference(quant_intro,[status(thm)],[118])).
% 0.59/0.74 tff(120,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')).
% 0.59/0.74 tff(121,plain,
% 0.59/0.74 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.59/0.74 tff(122,plain,
% 0.59/0.74 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.59/0.74 tff(123,plain,(
% 0.59/0.74 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.74 inference(skolemize,[status(sab)],[122])).
% 0.59/0.74 tff(124,plain,
% 0.59/0.74 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.59/0.75 tff(125,plain,
% 0.59/0.75 (m0(a, e, e) <=> m0(a, e, e)),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(126,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 0.59/0.75 tff(127,plain,
% 0.59/0.75 (m0(a, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.59/0.75 tff(128,plain,
% 0.59/0.75 (((~![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))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(129,plain,
% 0.59/0.75 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(130,plain,
% 0.59/0.75 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.59/0.75 tff(131,plain,
% 0.59/0.75 ((~k1(a)) | n1(a, e, e)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[130, 127, 124])).
% 0.59/0.75 tff(132,plain,
% 0.59/0.75 (n1(a, e, e)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[131, 114])).
% 0.59/0.75 tff(133,plain,
% 0.59/0.75 (^[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)))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(134,plain,
% 0.59/0.75 (![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))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[133])).
% 0.59/0.75 tff(135,plain,
% 0.59/0.75 (![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))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(136,plain,
% 0.59/0.75 (^[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))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(137,plain,
% 0.59/0.75 (![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))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[136])).
% 0.59/0.75 tff(138,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')).
% 0.59/0.75 tff(139,plain,
% 0.59/0.75 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.59/0.75 tff(140,plain,
% 0.59/0.75 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.59/0.75 tff(141,plain,(
% 0.59/0.75 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.75 inference(skolemize,[status(sab)],[140])).
% 0.59/0.75 tff(142,plain,
% 0.59/0.75 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.59/0.75 tff(143,plain,
% 0.59/0.75 (r0(e) <=> r0(e)),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(144,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.59/0.75 tff(145,plain,
% 0.59/0.75 (r0(e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.59/0.75 tff(146,plain,
% 0.59/0.75 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(147,plain,
% 0.59/0.75 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(148,plain,
% 0.59/0.75 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(149,plain,
% 0.59/0.75 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[148])).
% 0.59/0.75 tff(150,plain,
% 0.59/0.75 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.59/0.75 inference(transitivity,[status(thm)],[149, 147])).
% 0.59/0.75 tff(151,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.59/0.75 tff(152,plain,
% 0.59/0.75 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.59/0.75 tff(153,plain,
% 0.59/0.75 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[152, 146])).
% 0.59/0.75 tff(154,plain,
% 0.59/0.75 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.59/0.75 tff(155,plain,
% 0.59/0.75 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[154, 146])).
% 0.59/0.75 tff(156,plain,
% 0.59/0.75 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[155, 146])).
% 0.59/0.75 tff(157,plain,
% 0.59/0.75 (p1(e, e, e)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[156, 145, 98])).
% 0.59/0.75 tff(158,plain,
% 0.59/0.75 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(159,plain,
% 0.59/0.75 (((~q2(a, e, e)) | (~n1(a, e, e)) | (~p1(e, e, e)) | q2(e, a, e)) <=> (q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(160,plain,
% 0.59/0.75 (((~![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))) | (q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[159])).
% 0.59/0.75 tff(161,plain,
% 0.59/0.75 (((~![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))) | q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e)))),
% 0.59/0.75 inference(transitivity,[status(thm)],[160, 158])).
% 0.59/0.75 tff(162,plain,
% 0.59/0.75 ((~![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))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(163,plain,
% 0.59/0.75 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | q2(e, a, e) | (~p1(e, e, e)) | (~n1(a, e, e)) | (~q2(a, e, e))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.59/0.75 tff(164,plain,
% 0.59/0.75 (q2(e, a, e) | (~q2(a, e, e))),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[163, 157, 142, 132])).
% 0.59/0.75 tff(165,plain,
% 0.59/0.75 (q2(e, a, e)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[164, 103])).
% 0.59/0.75 tff(166,plain,
% 0.59/0.75 ((~s3(a, c)) <=> (~s3(a, c))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(167,axiom,(~s3(a, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.59/0.75 tff(168,plain,
% 0.59/0.75 (~s3(a, c)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.59/0.75 tff(169,plain,
% 0.59/0.75 (^[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)))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(170,plain,
% 0.59/0.75 (![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))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[169])).
% 0.59/0.75 tff(171,plain,
% 0.59/0.75 (![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))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(172,plain,
% 0.59/0.75 (^[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))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(173,plain,
% 0.59/0.75 (![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))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[172])).
% 0.59/0.75 tff(174,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')).
% 0.59/0.75 tff(175,plain,
% 0.59/0.75 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.59/0.75 tff(176,plain,
% 0.59/0.75 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.59/0.75 tff(177,plain,(
% 0.59/0.75 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.75 inference(skolemize,[status(sab)],[176])).
% 0.59/0.75 tff(178,plain,
% 0.59/0.75 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.59/0.75 tff(179,plain,
% 0.59/0.75 (m0(e, b, c) <=> m0(e, b, c)),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(180,axiom,(m0(e, b, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.59/0.75 tff(181,plain,
% 0.59/0.75 (m0(e, b, c)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.59/0.75 tff(182,plain,
% 0.59/0.75 (((~![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, b, c)) | (~q2(e, a, e)) | s3(a, c))) <=> ((~![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, b, c)) | (~q2(e, a, e)) | s3(a, c))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(183,plain,
% 0.59/0.75 ((~![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, b, c)) | (~q2(e, a, e)) | s3(a, c))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(184,plain,
% 0.59/0.75 ((~![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, b, c)) | (~q2(e, a, e)) | s3(a, c)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.59/0.75 tff(185,plain,
% 0.59/0.75 ((~s2(a)) | (~q2(e, a, e))),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[184, 181, 178, 168])).
% 0.59/0.75 tff(186,plain,
% 0.59/0.75 (~s2(a)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[185, 165])).
% 0.59/0.75 tff(187,plain,
% 0.59/0.75 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(188,plain,
% 0.59/0.75 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[187])).
% 0.59/0.75 tff(189,plain,
% 0.59/0.75 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(190,plain,
% 0.59/0.75 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(191,plain,
% 0.59/0.75 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[190])).
% 0.59/0.75 tff(192,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.59/0.75 tff(193,plain,
% 0.59/0.75 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.59/0.75 tff(194,plain,
% 0.59/0.75 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.59/0.75 tff(195,plain,(
% 0.59/0.75 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(skolemize,[status(sab)],[194])).
% 0.59/0.75 tff(196,plain,
% 0.59/0.75 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.59/0.75 tff(197,plain,
% 0.59/0.75 (((~![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)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(198,plain,
% 0.59/0.75 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(199,plain,
% 0.59/0.75 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.59/0.75 tff(200,plain,
% 0.59/0.75 (~q2(b, a, b)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[199, 196, 186, 78])).
% 0.59/0.75 tff(201,plain,
% 0.59/0.75 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(202,plain,
% 0.59/0.75 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[201])).
% 0.59/0.75 tff(203,plain,
% 0.59/0.75 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(204,plain,
% 0.59/0.75 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.59/0.75 inference(bind,[status(th)],[])).
% 0.59/0.75 tff(205,plain,
% 0.59/0.75 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(quant_intro,[status(thm)],[204])).
% 0.59/0.75 tff(206,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.59/0.75 tff(207,plain,
% 0.59/0.75 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.59/0.75 tff(208,plain,
% 0.59/0.75 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.59/0.75 tff(209,plain,(
% 0.59/0.75 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(skolemize,[status(sab)],[208])).
% 0.59/0.75 tff(210,plain,
% 0.59/0.75 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.59/0.75 tff(211,plain,
% 0.59/0.75 (p0(c, b) <=> p0(c, b)),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(212,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.59/0.75 tff(213,plain,
% 0.59/0.75 (p0(c, b)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.59/0.75 tff(214,plain,
% 0.59/0.75 (((~![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))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(215,plain,
% 0.59/0.75 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(216,plain,
% 0.59/0.75 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.59/0.75 tff(217,plain,
% 0.59/0.75 (p1(b, b, b)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[216, 213, 210])).
% 0.59/0.76 tff(218,plain,
% 0.59/0.76 (((~![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)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(219,plain,
% 0.59/0.76 (((~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)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(220,plain,
% 0.59/0.76 (((~![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))))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[219])).
% 0.59/0.76 tff(221,plain,
% 0.59/0.76 (((~![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)))),
% 0.59/0.76 inference(transitivity,[status(thm)],[220, 218])).
% 0.59/0.76 tff(222,plain,
% 0.59/0.76 ((~![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))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(223,plain,
% 0.59/0.76 ((~![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))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.59/0.76 tff(224,plain,
% 0.59/0.76 ((~q2(a, b, b)) | (~n1(a, b, b))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[223, 142, 217, 200])).
% 0.59/0.76 tff(225,plain,
% 0.59/0.76 (~q2(a, b, b)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[224, 67])).
% 0.59/0.76 tff(226,plain,
% 0.59/0.76 (k0(b) <=> k0(b)),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(227,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.59/0.76 tff(228,plain,
% 0.59/0.76 (k0(b)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.59/0.76 tff(229,plain,
% 0.59/0.76 (((~![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))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(230,plain,
% 0.59/0.76 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(231,plain,
% 0.59/0.76 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.59/0.76 tff(232,plain,
% 0.59/0.76 ($false),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[231, 228, 95, 89, 225])).
% 0.59/0.76 % SZS output end Proof
% 0.59/0.76 % E exiting
%------------------------------------------------------------------------------