%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN205-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.70s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYN205-1 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 12:29:23 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.52/0.70 % SZS status Unsatisfiable
% 0.52/0.70 % SZS output start Proof
% 0.52/0.70 tff(q2_type, type, (
% 0.52/0.70 q2: ( $i * $i * $i ) > $o)).
% 0.52/0.70 tff(b_type, type, (
% 0.52/0.70 b: $i)).
% 0.52/0.70 tff(a_type, type, (
% 0.52/0.70 a: $i)).
% 0.52/0.70 tff(s1_type, type, (
% 0.52/0.70 s1: $i > $o)).
% 0.52/0.70 tff(p0_type, type, (
% 0.52/0.70 p0: ( $i * $i ) > $o)).
% 0.52/0.70 tff(s2_type, type, (
% 0.52/0.70 s2: $i > $o)).
% 0.52/0.70 tff(m0_type, type, (
% 0.52/0.70 m0: ( $i * $i * $i ) > $o)).
% 0.52/0.70 tff(d_type, type, (
% 0.52/0.70 d: $i)).
% 0.52/0.70 tff(e_type, type, (
% 0.52/0.70 e: $i)).
% 0.52/0.70 tff(p1_type, type, (
% 0.52/0.70 p1: ( $i * $i * $i ) > $o)).
% 0.52/0.70 tff(k0_type, type, (
% 0.52/0.70 k0: $i > $o)).
% 0.52/0.70 tff(l0_type, type, (
% 0.52/0.70 l0: $i > $o)).
% 0.52/0.70 tff(n1_type, type, (
% 0.52/0.70 n1: ( $i * $i * $i ) > $o)).
% 0.52/0.70 tff(k1_type, type, (
% 0.52/0.70 k1: $i > $o)).
% 0.52/0.70 tff(n0_type, type, (
% 0.52/0.70 n0: ( $i * $i ) > $o)).
% 0.52/0.70 tff(r0_type, type, (
% 0.52/0.70 r0: $i > $o)).
% 0.52/0.70 tff(s3_type, type, (
% 0.52/0.70 s3: ( $i * $i ) > $o)).
% 0.52/0.70 tff(s0_type, type, (
% 0.52/0.70 s0: $i > $o)).
% 0.52/0.70 tff(l1_type, type, (
% 0.52/0.70 l1: ( $i * $i ) > $o)).
% 0.52/0.70 tff(c_type, type, (
% 0.52/0.70 c: $i)).
% 0.52/0.70 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.52/0.70 tff(2,plain,
% 0.52/0.70 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(3,plain,
% 0.52/0.70 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.52/0.70 inference(quant_intro,[status(thm)],[2])).
% 0.52/0.70 tff(4,plain,
% 0.52/0.70 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.52/0.70 tff(6,plain,
% 0.52/0.70 (![X: $i] : p0(b, X)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.52/0.70 tff(7,plain,(
% 0.52/0.70 ![X: $i] : p0(b, X)),
% 0.52/0.70 inference(skolemize,[status(sab)],[6])).
% 0.52/0.70 tff(8,plain,
% 0.52/0.70 (![X: $i] : p0(b, X)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.52/0.70 tff(9,plain,
% 0.52/0.70 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(10,plain,
% 0.52/0.70 ($false),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.52/0.70 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.70 tff(12,plain,
% 0.52/0.70 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(13,plain,
% 0.52/0.70 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[12])).
% 0.52/0.70 tff(14,plain,
% 0.52/0.70 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.52/0.70 tff(16,plain,
% 0.52/0.70 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.52/0.70 tff(17,plain,(
% 0.52/0.70 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.70 inference(skolemize,[status(sab)],[16])).
% 0.52/0.70 tff(18,plain,
% 0.52/0.70 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.52/0.70 tff(19,plain,
% 0.52/0.70 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(20,plain,
% 0.52/0.70 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(21,plain,
% 0.52/0.70 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.52/0.70 tff(22,plain,
% 0.52/0.70 (s1(b)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.52/0.70 tff(23,assumption,(~m0(e, d, d)), introduced(assumption)).
% 0.52/0.70 tff(24,plain,
% 0.52/0.70 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(25,plain,
% 0.52/0.70 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.52/0.70 inference(quant_intro,[status(thm)],[24])).
% 0.52/0.70 tff(26,plain,
% 0.52/0.70 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(27,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.52/0.70 tff(28,plain,
% 0.52/0.70 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.52/0.70 tff(29,plain,(
% 0.52/0.70 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.52/0.70 inference(skolemize,[status(sab)],[28])).
% 0.52/0.70 tff(30,plain,
% 0.52/0.70 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.52/0.70 tff(31,plain,
% 0.52/0.70 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(e, d, d)),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(32,plain,
% 0.52/0.70 ($false),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.52/0.70 tff(33,plain,(m0(e, d, d)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.70 tff(34,assumption,(~q2(a, e, e)), introduced(assumption)).
% 0.52/0.70 tff(35,plain,
% 0.52/0.70 (^[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)))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(36,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[35])).
% 0.52/0.70 tff(37,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(38,plain,
% 0.52/0.70 (^[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))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(39,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[38])).
% 0.52/0.70 tff(40,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')).
% 0.52/0.70 tff(41,plain,
% 0.52/0.70 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.52/0.70 tff(42,plain,
% 0.52/0.70 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.52/0.70 tff(43,plain,(
% 0.52/0.70 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.70 inference(skolemize,[status(sab)],[42])).
% 0.52/0.70 tff(44,plain,
% 0.52/0.70 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.52/0.70 tff(45,plain,
% 0.52/0.70 (l0(a) <=> l0(a)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(46,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.52/0.70 tff(47,plain,
% 0.52/0.70 (l0(a)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.52/0.70 tff(48,plain,
% 0.52/0.70 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(49,plain,
% 0.52/0.70 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(50,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.52/0.70 tff(51,plain,
% 0.52/0.70 ((~l0(a)) | p1(a, a, a)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.52/0.70 tff(52,plain,
% 0.52/0.70 ((~l0(a)) | p1(a, a, a)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.52/0.70 tff(53,plain,
% 0.52/0.70 (p1(a, a, a)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.52/0.70 tff(54,plain,
% 0.52/0.70 (k0(e) <=> k0(e)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(55,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.52/0.70 tff(56,plain,
% 0.52/0.70 (k0(e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.52/0.70 tff(57,plain,
% 0.52/0.70 (((~![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(58,plain,
% 0.52/0.70 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(59,plain,
% 0.52/0.70 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.52/0.70 tff(60,plain,
% 0.52/0.70 ($false),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[59, 56, 53, 44, 34])).
% 0.52/0.70 tff(61,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.70 tff(62,plain,
% 0.52/0.70 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(63,plain,
% 0.52/0.70 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[62])).
% 0.52/0.70 tff(64,plain,
% 0.52/0.70 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(65,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.52/0.70 tff(66,plain,
% 0.52/0.70 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.52/0.70 tff(67,plain,(
% 0.52/0.70 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.52/0.70 inference(skolemize,[status(sab)],[66])).
% 0.52/0.70 tff(68,plain,
% 0.52/0.70 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.52/0.70 tff(69,plain,
% 0.52/0.70 (n0(b, a) <=> n0(b, a)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(70,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.52/0.70 tff(71,plain,
% 0.52/0.70 (n0(b, a)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.52/0.70 tff(72,plain,
% 0.52/0.70 (((~![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)))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(73,plain,
% 0.52/0.70 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(74,plain,
% 0.52/0.70 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.52/0.70 tff(75,plain,
% 0.52/0.70 (k1(a)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[74, 71, 68])).
% 0.52/0.70 tff(76,plain,
% 0.52/0.70 (^[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)))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(77,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[76])).
% 0.52/0.70 tff(78,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(79,plain,
% 0.52/0.70 (^[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))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(80,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[79])).
% 0.52/0.70 tff(81,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')).
% 0.52/0.70 tff(82,plain,
% 0.52/0.70 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.52/0.70 tff(83,plain,
% 0.52/0.70 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.52/0.70 tff(84,plain,(
% 0.52/0.70 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.52/0.70 inference(skolemize,[status(sab)],[83])).
% 0.52/0.70 tff(85,plain,
% 0.52/0.70 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.52/0.70 tff(86,plain,
% 0.52/0.70 (m0(a, e, e) <=> m0(a, e, e)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(87,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 0.52/0.70 tff(88,plain,
% 0.52/0.70 (m0(a, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.52/0.70 tff(89,plain,
% 0.52/0.70 (((~![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(90,plain,
% 0.52/0.70 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(91,plain,
% 0.52/0.70 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.52/0.70 tff(92,plain,
% 0.52/0.70 ((~k1(a)) | n1(a, e, e)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[91, 88, 85])).
% 0.52/0.70 tff(93,plain,
% 0.52/0.70 (n1(a, e, e)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[92, 75])).
% 0.52/0.70 tff(94,plain,
% 0.52/0.70 (^[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)))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(95,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[94])).
% 0.52/0.70 tff(96,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(97,plain,
% 0.52/0.70 (^[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))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(98,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[97])).
% 0.52/0.70 tff(99,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')).
% 0.52/0.70 tff(100,plain,
% 0.52/0.70 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.52/0.70 tff(101,plain,
% 0.52/0.70 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.52/0.70 tff(102,plain,(
% 0.52/0.70 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.52/0.70 inference(skolemize,[status(sab)],[101])).
% 0.52/0.70 tff(103,plain,
% 0.52/0.70 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.52/0.70 tff(104,plain,
% 0.52/0.70 (r0(e) <=> r0(e)),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(105,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.52/0.70 tff(106,plain,
% 0.52/0.70 (r0(e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.52/0.70 tff(107,plain,
% 0.52/0.70 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(108,plain,
% 0.52/0.70 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(109,plain,
% 0.52/0.70 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(110,plain,
% 0.52/0.70 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.52/0.70 inference(monotonicity,[status(thm)],[109])).
% 0.52/0.70 tff(111,plain,
% 0.52/0.70 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.52/0.70 inference(transitivity,[status(thm)],[110, 108])).
% 0.52/0.70 tff(112,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.52/0.70 tff(113,plain,
% 0.52/0.70 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.52/0.70 tff(114,plain,
% 0.52/0.70 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[113, 107])).
% 0.52/0.70 tff(115,plain,
% 0.52/0.70 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.52/0.70 tff(116,plain,
% 0.52/0.70 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[115, 107])).
% 0.52/0.70 tff(117,plain,
% 0.52/0.70 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[116, 107])).
% 0.52/0.70 tff(118,plain,
% 0.52/0.70 (p1(e, e, e)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[117, 106, 56])).
% 0.52/0.70 tff(119,plain,
% 0.52/0.70 (((~![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(120,plain,
% 0.52/0.70 (((~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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(121,plain,
% 0.52/0.70 (((~![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)))),
% 0.52/0.70 inference(monotonicity,[status(thm)],[120])).
% 0.52/0.70 tff(122,plain,
% 0.52/0.70 (((~![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))),
% 0.52/0.70 inference(transitivity,[status(thm)],[121, 119])).
% 0.52/0.70 tff(123,plain,
% 0.52/0.70 ((~![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))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(124,plain,
% 0.52/0.70 ((~![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)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.52/0.70 tff(125,plain,
% 0.52/0.70 ((~q2(a, e, e)) | q2(e, a, e)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[124, 118, 103, 93])).
% 0.52/0.70 tff(126,plain,
% 0.52/0.70 (q2(e, a, e)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[125, 61])).
% 0.52/0.70 tff(127,plain,
% 0.52/0.70 ((~s3(a, d)) <=> (~s3(a, d))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(128,axiom,(~s3(a, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.52/0.70 tff(129,plain,
% 0.52/0.70 (~s3(a, d)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.52/0.70 tff(130,plain,
% 0.52/0.70 (^[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)))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(131,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[130])).
% 0.52/0.70 tff(132,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(133,plain,
% 0.52/0.70 (^[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))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.70 tff(134,plain,
% 0.52/0.70 (![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))),
% 0.52/0.70 inference(quant_intro,[status(thm)],[133])).
% 0.52/0.70 tff(135,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')).
% 0.52/0.70 tff(136,plain,
% 0.52/0.70 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.52/0.70 tff(137,plain,
% 0.52/0.70 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.52/0.70 tff(138,plain,(
% 0.52/0.70 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.52/0.70 inference(skolemize,[status(sab)],[137])).
% 0.52/0.70 tff(139,plain,
% 0.52/0.70 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.52/0.70 tff(140,plain,
% 0.52/0.70 (((~![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, d)) | (~q2(e, a, e)) | s3(a, d))) <=> ((~![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, d)) | (~q2(e, a, e)) | s3(a, d))),
% 0.52/0.70 inference(rewrite,[status(thm)],[])).
% 0.52/0.70 tff(141,plain,
% 0.52/0.70 ((~![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, d)) | (~q2(e, a, e)) | s3(a, d))),
% 0.52/0.70 inference(quant_inst,[status(thm)],[])).
% 0.52/0.70 tff(142,plain,
% 0.52/0.70 ((~![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, d)) | (~q2(e, a, e)) | s3(a, d)),
% 0.52/0.70 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.52/0.70 tff(143,plain,
% 0.52/0.70 (~s2(a)),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[142, 139, 129, 126, 33])).
% 0.52/0.70 tff(144,plain,
% 0.52/0.70 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.52/0.70 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(145,plain,
% 0.52/0.71 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[144])).
% 0.52/0.71 tff(146,plain,
% 0.52/0.71 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(147,plain,
% 0.52/0.71 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(148,plain,
% 0.52/0.71 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[147])).
% 0.52/0.71 tff(149,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.52/0.71 tff(150,plain,
% 0.52/0.71 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.52/0.71 tff(151,plain,
% 0.52/0.71 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.52/0.71 tff(152,plain,(
% 0.52/0.71 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(skolemize,[status(sab)],[151])).
% 0.52/0.71 tff(153,plain,
% 0.52/0.71 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.52/0.71 tff(154,plain,
% 0.52/0.71 (((~![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)))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(155,plain,
% 0.52/0.71 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
% 0.52/0.71 tff(156,plain,
% 0.52/0.71 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.52/0.71 tff(157,plain,
% 0.52/0.71 (~q2(b, a, b)),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[156, 153, 143, 22])).
% 0.52/0.71 tff(158,assumption,(~n1(a, b, a)), introduced(assumption)).
% 0.52/0.71 tff(159,plain,
% 0.52/0.71 (^[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)))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(160,plain,
% 0.52/0.71 (![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))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[159])).
% 0.52/0.71 tff(161,plain,
% 0.52/0.71 (![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))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(162,plain,
% 0.52/0.71 (^[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))))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(163,plain,
% 0.52/0.71 (![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))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[162])).
% 0.52/0.71 tff(164,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')).
% 0.52/0.71 tff(165,plain,
% 0.52/0.71 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.52/0.71 tff(166,plain,
% 0.52/0.71 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.52/0.71 tff(167,plain,(
% 0.52/0.71 ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.71 inference(skolemize,[status(sab)],[166])).
% 0.52/0.71 tff(168,plain,
% 0.52/0.71 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.52/0.71 tff(169,plain,
% 0.52/0.71 (s0(b) <=> s0(b)),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(170,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.52/0.71 tff(171,plain,
% 0.52/0.71 (s0(b)),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.52/0.71 tff(172,plain,
% 0.52/0.71 (((~![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))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(173,plain,
% 0.52/0.71 ((~![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))),
% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
% 0.52/0.71 tff(174,plain,
% 0.52/0.71 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a)),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.52/0.71 tff(175,plain,
% 0.52/0.71 ($false),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[174, 171, 47, 168, 11, 158])).
% 0.52/0.71 tff(176,plain,(n1(a, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.71 tff(177,plain,
% 0.52/0.71 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(178,plain,
% 0.52/0.71 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[177])).
% 0.52/0.71 tff(179,plain,
% 0.52/0.71 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(180,plain,
% 0.52/0.71 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(181,plain,
% 0.52/0.71 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[180])).
% 0.52/0.71 tff(182,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.52/0.71 tff(183,plain,
% 0.52/0.71 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.52/0.71 tff(184,plain,
% 0.52/0.71 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.52/0.71 tff(185,plain,(
% 0.52/0.71 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(skolemize,[status(sab)],[184])).
% 0.52/0.71 tff(186,plain,
% 0.52/0.71 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.52/0.71 tff(187,plain,
% 0.52/0.71 (((~![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))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(188,plain,
% 0.52/0.71 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
% 0.52/0.71 tff(189,plain,
% 0.52/0.71 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.52/0.71 tff(190,plain,
% 0.52/0.71 (l1(a, a)),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[189, 71, 186])).
% 0.52/0.71 tff(191,plain,
% 0.52/0.71 (^[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)))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(192,plain,
% 0.52/0.71 (![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))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[191])).
% 0.52/0.71 tff(193,plain,
% 0.52/0.71 (![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))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(194,plain,
% 0.52/0.71 (^[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))))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(195,plain,
% 0.52/0.71 (![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))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[194])).
% 0.52/0.71 tff(196,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')).
% 0.52/0.71 tff(197,plain,
% 0.52/0.71 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.52/0.71 tff(198,plain,
% 0.52/0.71 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.52/0.71 tff(199,plain,(
% 0.52/0.71 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.71 inference(skolemize,[status(sab)],[198])).
% 0.52/0.71 tff(200,plain,
% 0.52/0.71 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.52/0.71 tff(201,plain,
% 0.52/0.71 (((~![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)))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(202,plain,
% 0.52/0.71 (((~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)))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(203,plain,
% 0.52/0.71 (((~![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))))),
% 0.52/0.71 inference(monotonicity,[status(thm)],[202])).
% 0.52/0.71 tff(204,plain,
% 0.52/0.71 (((~![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)))),
% 0.52/0.71 inference(transitivity,[status(thm)],[203, 201])).
% 0.52/0.71 tff(205,plain,
% 0.52/0.71 ((~![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))),
% 0.52/0.71 inference(quant_inst,[status(thm)],[])).
% 0.52/0.71 tff(206,plain,
% 0.52/0.71 ((~![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))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.52/0.71 tff(207,plain,
% 0.52/0.71 (n1(a, b, b)),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[206, 47, 200, 190, 176])).
% 0.52/0.71 tff(208,plain,
% 0.52/0.71 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(209,plain,
% 0.52/0.71 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[208])).
% 0.52/0.71 tff(210,plain,
% 0.52/0.71 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(211,plain,
% 0.52/0.71 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.52/0.71 inference(bind,[status(th)],[])).
% 0.52/0.71 tff(212,plain,
% 0.52/0.71 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(quant_intro,[status(thm)],[211])).
% 0.52/0.71 tff(213,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.52/0.71 tff(214,plain,
% 0.52/0.71 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.52/0.71 tff(215,plain,
% 0.52/0.71 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.52/0.71 tff(216,plain,(
% 0.52/0.71 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(skolemize,[status(sab)],[215])).
% 0.52/0.71 tff(217,plain,
% 0.52/0.71 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.52/0.71 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.52/0.71 tff(218,plain,
% 0.52/0.71 (p0(c, b) <=> p0(c, b)),
% 0.52/0.71 inference(rewrite,[status(thm)],[])).
% 0.52/0.71 tff(219,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.52/0.72 tff(220,plain,
% 0.52/0.72 (p0(c, b)),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.52/0.72 tff(221,plain,
% 0.52/0.72 (((~![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))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(222,plain,
% 0.52/0.72 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
% 0.52/0.72 tff(223,plain,
% 0.52/0.72 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.52/0.72 tff(224,plain,
% 0.52/0.72 (p1(b, b, b)),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[223, 220, 217])).
% 0.52/0.72 tff(225,plain,
% 0.52/0.72 (((~![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)))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(226,plain,
% 0.52/0.72 (((~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)))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(227,plain,
% 0.52/0.72 (((~![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))))),
% 0.52/0.72 inference(monotonicity,[status(thm)],[226])).
% 0.52/0.72 tff(228,plain,
% 0.52/0.72 (((~![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)))),
% 0.52/0.72 inference(transitivity,[status(thm)],[227, 225])).
% 0.52/0.72 tff(229,plain,
% 0.52/0.72 ((~![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))),
% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
% 0.52/0.72 tff(230,plain,
% 0.52/0.72 ((~![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))),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.52/0.72 tff(231,plain,
% 0.52/0.72 (~q2(a, b, b)),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[230, 103, 224, 207, 157])).
% 0.52/0.72 tff(232,plain,
% 0.52/0.72 (k0(b) <=> k0(b)),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(233,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.52/0.72 tff(234,plain,
% 0.52/0.72 (k0(b)),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.52/0.72 tff(235,plain,
% 0.52/0.72 (((~![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))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(236,plain,
% 0.52/0.72 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.52/0.72 inference(quant_inst,[status(thm)],[])).
% 0.52/0.72 tff(237,plain,
% 0.52/0.72 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 0.52/0.72 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.52/0.72 tff(238,plain,
% 0.52/0.72 ($false),
% 0.52/0.72 inference(unit_resolution,[status(thm)],[237, 234, 53, 44, 231])).
% 0.52/0.72 % SZS output end Proof
% 0.52/0.73 % E exiting
%------------------------------------------------------------------------------