%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN253-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:36 AM UTC 2025
% Result : Unsatisfiable 0.59s 0.79s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SYN253-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.10 % Command : run_E %s %d THM
% 0.09/0.31 % Computer : n011.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Fri Jun 20 12:30:12 EDT 2025
% 0.09/0.31 % CPUTime :
% 0.59/0.79 % SZS status Unsatisfiable
% 0.59/0.79 % SZS output start Proof
% 0.59/0.79 tff(m4_type, type, (
% 0.59/0.79 m4: ( $i * $i ) > $o)).
% 0.59/0.79 tff(e_type, type, (
% 0.59/0.79 e: $i)).
% 0.59/0.79 tff(s3_type, type, (
% 0.59/0.79 s3: ( $i * $i ) > $o)).
% 0.59/0.79 tff(a_type, type, (
% 0.59/0.79 a: $i)).
% 0.59/0.79 tff(q2_type, type, (
% 0.59/0.79 q2: ( $i * $i * $i ) > $o)).
% 0.59/0.79 tff(p1_type, type, (
% 0.59/0.79 p1: ( $i * $i * $i ) > $o)).
% 0.59/0.79 tff(k0_type, type, (
% 0.59/0.79 k0: $i > $o)).
% 0.59/0.79 tff(l0_type, type, (
% 0.59/0.79 l0: $i > $o)).
% 0.59/0.79 tff(n1_type, type, (
% 0.59/0.79 n1: ( $i * $i * $i ) > $o)).
% 0.59/0.79 tff(k1_type, type, (
% 0.59/0.79 k1: $i > $o)).
% 0.59/0.79 tff(n0_type, type, (
% 0.59/0.79 n0: ( $i * $i ) > $o)).
% 0.59/0.79 tff(b_type, type, (
% 0.59/0.79 b: $i)).
% 0.59/0.79 tff(m0_type, type, (
% 0.59/0.79 m0: ( $i * $i * $i ) > $o)).
% 0.59/0.79 tff(r0_type, type, (
% 0.59/0.79 r0: $i > $o)).
% 0.59/0.79 tff(s2_type, type, (
% 0.59/0.79 s2: $i > $o)).
% 0.59/0.79 tff(p0_type, type, (
% 0.59/0.79 p0: ( $i * $i ) > $o)).
% 0.59/0.79 tff(s0_type, type, (
% 0.59/0.79 s0: $i > $o)).
% 0.59/0.79 tff(l1_type, type, (
% 0.59/0.79 l1: ( $i * $i ) > $o)).
% 0.59/0.79 tff(c_type, type, (
% 0.59/0.79 c: $i)).
% 0.59/0.79 tff(s1_type, type, (
% 0.59/0.79 s1: $i > $o)).
% 0.59/0.79 tff(d_type, type, (
% 0.59/0.79 d: $i)).
% 0.59/0.79 tff(l2_type, type, (
% 0.59/0.79 l2: ( $i * $i ) > $o)).
% 0.59/0.79 tff(1,assumption,(~s3(a, e)), introduced(assumption)).
% 0.59/0.79 tff(2,assumption,(~q2(a, e, e)), introduced(assumption)).
% 0.59/0.79 tff(3,plain,
% 0.59/0.79 (^[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)))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(4,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[3])).
% 0.59/0.79 tff(5,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(6,plain,
% 0.59/0.79 (^[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))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(7,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[6])).
% 0.59/0.79 tff(8,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')).
% 0.59/0.79 tff(9,plain,
% 0.59/0.79 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.59/0.79 tff(10,plain,
% 0.59/0.79 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.59/0.79 tff(11,plain,(
% 0.59/0.79 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.59/0.79 inference(skolemize,[status(sab)],[10])).
% 0.59/0.79 tff(12,plain,
% 0.59/0.79 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.59/0.79 tff(13,plain,
% 0.59/0.79 (l0(a) <=> l0(a)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(14,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.59/0.79 tff(15,plain,
% 0.59/0.79 (l0(a)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.59/0.79 tff(16,plain,
% 0.59/0.79 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(17,plain,
% 0.59/0.79 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(18,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.59/0.79 tff(19,plain,
% 0.59/0.79 ((~l0(a)) | p1(a, a, a)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.59/0.79 tff(20,plain,
% 0.59/0.79 ((~l0(a)) | p1(a, a, a)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.59/0.79 tff(21,plain,
% 0.59/0.79 (p1(a, a, a)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[20, 15])).
% 0.59/0.79 tff(22,plain,
% 0.59/0.79 (k0(e) <=> k0(e)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(23,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.59/0.79 tff(24,plain,
% 0.59/0.79 (k0(e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.59/0.79 tff(25,plain,
% 0.59/0.79 (((~![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(26,plain,
% 0.59/0.79 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(a, a, a)) | q2(a, e, e))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(27,plain,
% 0.59/0.79 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(a, a, a)) | q2(a, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.59/0.79 tff(28,plain,
% 0.59/0.79 ($false),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[27, 24, 21, 12, 2])).
% 0.59/0.79 tff(29,plain,(q2(a, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.79 tff(30,plain,
% 0.59/0.79 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(31,plain,
% 0.59/0.79 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[30])).
% 0.59/0.79 tff(32,plain,
% 0.59/0.79 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(33,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.59/0.79 tff(34,plain,
% 0.59/0.79 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.59/0.79 tff(35,plain,(
% 0.59/0.79 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.79 inference(skolemize,[status(sab)],[34])).
% 0.59/0.79 tff(36,plain,
% 0.59/0.79 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.59/0.79 tff(37,plain,
% 0.59/0.79 (n0(b, a) <=> n0(b, a)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(38,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.59/0.79 tff(39,plain,
% 0.59/0.79 (n0(b, a)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.59/0.79 tff(40,plain,
% 0.59/0.79 (((~![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)))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(41,plain,
% 0.59/0.79 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(42,plain,
% 0.59/0.79 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.59/0.79 tff(43,plain,
% 0.59/0.79 (k1(a)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[42, 39, 36])).
% 0.59/0.79 tff(44,plain,
% 0.59/0.79 (^[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)))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(45,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[44])).
% 0.59/0.79 tff(46,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(47,plain,
% 0.59/0.79 (^[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))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(48,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[47])).
% 0.59/0.79 tff(49,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')).
% 0.59/0.79 tff(50,plain,
% 0.59/0.79 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.59/0.79 tff(51,plain,
% 0.59/0.79 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.59/0.79 tff(52,plain,(
% 0.59/0.79 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.79 inference(skolemize,[status(sab)],[51])).
% 0.59/0.79 tff(53,plain,
% 0.59/0.79 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.59/0.79 tff(54,plain,
% 0.59/0.79 (m0(a, e, e) <=> m0(a, e, e)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(55,axiom,(m0(a, e, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_23')).
% 0.59/0.79 tff(56,plain,
% 0.59/0.79 (m0(a, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.59/0.79 tff(57,plain,
% 0.59/0.79 (((~![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(58,plain,
% 0.59/0.79 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(a)) | (~m0(a, e, e)) | n1(a, e, e))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(59,plain,
% 0.59/0.79 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(a)) | (~m0(a, e, e)) | n1(a, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.59/0.79 tff(60,plain,
% 0.59/0.79 ((~k1(a)) | n1(a, e, e)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[59, 56, 53])).
% 0.59/0.79 tff(61,plain,
% 0.59/0.79 (n1(a, e, e)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[60, 43])).
% 0.59/0.79 tff(62,plain,
% 0.59/0.79 (^[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)))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(63,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[62])).
% 0.59/0.79 tff(64,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(65,plain,
% 0.59/0.79 (^[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))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(66,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[65])).
% 0.59/0.79 tff(67,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')).
% 0.59/0.79 tff(68,plain,
% 0.59/0.79 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.59/0.79 tff(69,plain,
% 0.59/0.79 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.59/0.79 tff(70,plain,(
% 0.59/0.79 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.79 inference(skolemize,[status(sab)],[69])).
% 0.59/0.79 tff(71,plain,
% 0.59/0.79 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.59/0.79 tff(72,plain,
% 0.59/0.79 (r0(e) <=> r0(e)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(73,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.59/0.79 tff(74,plain,
% 0.59/0.79 (r0(e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.59/0.79 tff(75,plain,
% 0.59/0.79 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(76,plain,
% 0.59/0.79 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(77,plain,
% 0.59/0.79 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(78,plain,
% 0.59/0.79 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[77])).
% 0.59/0.79 tff(79,plain,
% 0.59/0.79 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.59/0.79 inference(transitivity,[status(thm)],[78, 76])).
% 0.59/0.79 tff(80,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.59/0.79 tff(81,plain,
% 0.59/0.79 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.59/0.79 tff(82,plain,
% 0.59/0.79 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.59/0.79 tff(83,plain,
% 0.59/0.79 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.59/0.79 tff(84,plain,
% 0.59/0.79 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[83, 75])).
% 0.59/0.79 tff(85,plain,
% 0.59/0.79 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[84, 75])).
% 0.59/0.79 tff(86,plain,
% 0.59/0.79 (p1(e, e, e)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[85, 74, 24])).
% 0.59/0.79 tff(87,plain,
% 0.59/0.79 (((~![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(88,plain,
% 0.59/0.79 (((~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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(89,plain,
% 0.59/0.79 (((~![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)))),
% 0.59/0.79 inference(monotonicity,[status(thm)],[88])).
% 0.59/0.79 tff(90,plain,
% 0.59/0.79 (((~![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))),
% 0.59/0.79 inference(transitivity,[status(thm)],[89, 87])).
% 0.59/0.79 tff(91,plain,
% 0.59/0.79 ((~![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))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(92,plain,
% 0.59/0.79 ((~![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)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.59/0.79 tff(93,plain,
% 0.59/0.79 ((~q2(a, e, e)) | q2(e, a, e)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[92, 86, 71, 61])).
% 0.59/0.79 tff(94,plain,
% 0.59/0.79 (q2(e, a, e)),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[93, 29])).
% 0.59/0.79 tff(95,assumption,(~n1(a, b, a)), introduced(assumption)).
% 0.59/0.79 tff(96,assumption,(~p0(b, b)), introduced(assumption)).
% 0.59/0.79 tff(97,plain,
% 0.59/0.79 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(98,plain,
% 0.59/0.79 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.59/0.79 inference(quant_intro,[status(thm)],[97])).
% 0.59/0.79 tff(99,plain,
% 0.59/0.79 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(100,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.59/0.79 tff(101,plain,
% 0.59/0.79 (![X: $i] : p0(b, X)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.59/0.79 tff(102,plain,(
% 0.59/0.79 ![X: $i] : p0(b, X)),
% 0.59/0.79 inference(skolemize,[status(sab)],[101])).
% 0.59/0.79 tff(103,plain,
% 0.59/0.79 (![X: $i] : p0(b, X)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.59/0.79 tff(104,plain,
% 0.59/0.79 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(105,plain,
% 0.59/0.79 ($false),
% 0.59/0.79 inference(unit_resolution,[status(thm)],[104, 103, 96])).
% 0.59/0.79 tff(106,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.79 tff(107,plain,
% 0.59/0.79 (^[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)))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(108,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[107])).
% 0.59/0.79 tff(109,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(110,plain,
% 0.59/0.79 (^[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))))),
% 0.59/0.79 inference(bind,[status(th)],[])).
% 0.59/0.79 tff(111,plain,
% 0.59/0.79 (![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))),
% 0.59/0.79 inference(quant_intro,[status(thm)],[110])).
% 0.59/0.79 tff(112,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')).
% 0.59/0.79 tff(113,plain,
% 0.59/0.79 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.59/0.79 tff(114,plain,
% 0.59/0.79 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.59/0.79 tff(115,plain,(
% 0.59/0.79 ![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.59/0.79 inference(skolemize,[status(sab)],[114])).
% 0.59/0.79 tff(116,plain,
% 0.59/0.79 (![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.59/0.79 tff(117,plain,
% 0.59/0.79 (s0(b) <=> s0(b)),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(118,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.59/0.79 tff(119,plain,
% 0.59/0.79 (s0(b)),
% 0.59/0.79 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.59/0.79 tff(120,plain,
% 0.59/0.79 (((~![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))),
% 0.59/0.79 inference(rewrite,[status(thm)],[])).
% 0.59/0.79 tff(121,plain,
% 0.59/0.79 ((~![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))),
% 0.59/0.79 inference(quant_inst,[status(thm)],[])).
% 0.59/0.79 tff(122,plain,
% 0.59/0.79 ((~![D: $i, E: $i] : ((~l0(D)) | (~s0(b)) | (~p0(b, E)) | n1(D, E, D))) | (~l0(a)) | (~s0(b)) | (~p0(b, b)) | n1(a, b, a)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.59/0.80 tff(123,plain,
% 0.59/0.80 ($false),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[122, 119, 15, 116, 106, 95])).
% 0.59/0.80 tff(124,plain,(n1(a, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.80 tff(125,plain,
% 0.59/0.80 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(126,plain,
% 0.59/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[125])).
% 0.59/0.80 tff(127,plain,
% 0.59/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(128,plain,
% 0.59/0.80 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(129,plain,
% 0.59/0.80 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[128])).
% 0.59/0.80 tff(130,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.59/0.80 tff(131,plain,
% 0.59/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.59/0.80 tff(132,plain,
% 0.59/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.59/0.80 tff(133,plain,(
% 0.59/0.80 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(skolemize,[status(sab)],[132])).
% 0.59/0.80 tff(134,plain,
% 0.59/0.80 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.59/0.80 tff(135,plain,
% 0.59/0.80 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(136,plain,
% 0.59/0.80 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(137,plain,
% 0.59/0.80 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.59/0.80 tff(138,plain,
% 0.59/0.80 (l1(a, a)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[137, 39, 134])).
% 0.59/0.80 tff(139,plain,
% 0.59/0.80 (^[E: $i, F: $i, G: $i] : refl(((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(140,plain,
% 0.59/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[139])).
% 0.59/0.80 tff(141,plain,
% 0.59/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F)) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(142,plain,
% 0.59/0.80 (^[E: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((n1(E, F, F) | (~l0(G))) <=> ((~l0(G)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> (((~l0(G)) | n1(E, F, F)) | (~l1(G, E))))), rewrite((((~l0(G)) | n1(E, F, F)) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F))), (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) <=> ((~l0(G)) | (~l1(G, E)) | n1(E, F, F)))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> (((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))))), rewrite((((~l0(G)) | (~l1(G, E)) | n1(E, F, F)) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))), ((((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(143,plain,
% 0.59/0.80 (![E: $i, F: $i, G: $i] : (((n1(E, F, F) | (~l0(G))) | (~l1(G, E))) | (~n1(E, F, E))) <=> ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[142])).
% 0.59/0.80 tff(144,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')).
% 0.59/0.80 tff(145,plain,
% 0.59/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.59/0.80 tff(146,plain,
% 0.59/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.59/0.80 tff(147,plain,(
% 0.59/0.80 ![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(skolemize,[status(sab)],[146])).
% 0.59/0.80 tff(148,plain,
% 0.59/0.80 (![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.59/0.80 tff(149,plain,
% 0.59/0.80 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(150,plain,
% 0.59/0.80 (((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b)) <=> ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(151,plain,
% 0.59/0.80 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))))),
% 0.59/0.80 inference(monotonicity,[status(thm)],[150])).
% 0.59/0.80 tff(152,plain,
% 0.59/0.80 (((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))) <=> ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a)))),
% 0.59/0.80 inference(transitivity,[status(thm)],[151, 149])).
% 0.59/0.80 tff(153,plain,
% 0.59/0.80 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | ((~l0(a)) | (~n1(a, b, a)) | (~l1(a, a)) | n1(a, b, b))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(154,plain,
% 0.59/0.80 ((~![E: $i, F: $i, G: $i] : ((~l0(G)) | (~n1(E, F, E)) | (~l1(G, E)) | n1(E, F, F))) | (~l0(a)) | n1(a, b, b) | (~l1(a, a)) | (~n1(a, b, a))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.59/0.80 tff(155,plain,
% 0.59/0.80 (n1(a, b, b) | (~n1(a, b, a))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[154, 15, 148, 138])).
% 0.59/0.80 tff(156,plain,
% 0.59/0.80 (n1(a, b, b)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[155, 124])).
% 0.59/0.80 tff(157,assumption,(~q2(a, b, b)), introduced(assumption)).
% 0.59/0.80 tff(158,plain,
% 0.59/0.80 (k0(b) <=> k0(b)),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(159,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.59/0.80 tff(160,plain,
% 0.59/0.80 (k0(b)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.59/0.80 tff(161,plain,
% 0.59/0.80 (((~![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))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(162,plain,
% 0.59/0.80 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(b)) | (~p1(a, a, a)) | q2(a, b, b))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(163,plain,
% 0.59/0.80 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(b)) | (~p1(a, a, a)) | q2(a, b, b)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.59/0.80 tff(164,plain,
% 0.59/0.80 ($false),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[163, 160, 21, 12, 157])).
% 0.59/0.80 tff(165,plain,(q2(a, b, b)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.80 tff(166,plain,
% 0.59/0.80 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(167,plain,
% 0.59/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[166])).
% 0.59/0.80 tff(168,plain,
% 0.59/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(169,plain,
% 0.59/0.80 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(170,plain,
% 0.59/0.80 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[169])).
% 0.59/0.80 tff(171,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.59/0.80 tff(172,plain,
% 0.59/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.59/0.80 tff(173,plain,
% 0.59/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.59/0.80 tff(174,plain,(
% 0.59/0.80 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(skolemize,[status(sab)],[173])).
% 0.59/0.80 tff(175,plain,
% 0.59/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.59/0.80 tff(176,plain,
% 0.59/0.80 (p0(c, b) <=> p0(c, b)),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(177,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.59/0.80 tff(178,plain,
% 0.59/0.80 (p0(c, b)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.59/0.80 tff(179,plain,
% 0.59/0.80 (((~![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))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(180,plain,
% 0.59/0.80 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(181,plain,
% 0.59/0.80 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.59/0.80 tff(182,plain,
% 0.59/0.80 (p1(b, b, b)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[181, 178, 175])).
% 0.59/0.80 tff(183,plain,
% 0.59/0.80 (((~![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)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(184,plain,
% 0.59/0.80 (((~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)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(185,plain,
% 0.59/0.80 (((~![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))))),
% 0.59/0.80 inference(monotonicity,[status(thm)],[184])).
% 0.59/0.80 tff(186,plain,
% 0.59/0.80 (((~![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)))),
% 0.59/0.80 inference(transitivity,[status(thm)],[185, 183])).
% 0.59/0.80 tff(187,plain,
% 0.59/0.80 ((~![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))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(188,plain,
% 0.59/0.80 ((~![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))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.59/0.80 tff(189,plain,
% 0.59/0.80 (q2(b, a, b) | (~q2(a, b, b)) | (~n1(a, b, b))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[188, 71, 182])).
% 0.59/0.80 tff(190,plain,
% 0.59/0.80 (q2(b, a, b) | (~n1(a, b, b))),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[189, 165])).
% 0.59/0.80 tff(191,plain,
% 0.59/0.80 (q2(b, a, b)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[190, 156])).
% 0.59/0.80 tff(192,plain,
% 0.59/0.80 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(193,plain,
% 0.59/0.80 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[192])).
% 0.59/0.80 tff(194,plain,
% 0.59/0.80 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(195,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.59/0.80 tff(196,plain,
% 0.59/0.80 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.59/0.80 tff(197,plain,(
% 0.59/0.80 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.59/0.80 inference(skolemize,[status(sab)],[196])).
% 0.59/0.80 tff(198,plain,
% 0.59/0.80 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.59/0.80 tff(199,plain,
% 0.59/0.80 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(200,plain,
% 0.59/0.80 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(201,plain,
% 0.59/0.80 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.59/0.80 tff(202,plain,
% 0.59/0.80 (s1(b)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[201, 198, 106])).
% 0.59/0.80 tff(203,plain,
% 0.59/0.80 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(204,plain,
% 0.59/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[203])).
% 0.59/0.80 tff(205,plain,
% 0.59/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(206,plain,
% 0.59/0.80 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(207,plain,
% 0.59/0.80 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[206])).
% 0.59/0.80 tff(208,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.59/0.80 tff(209,plain,
% 0.59/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.59/0.80 tff(210,plain,
% 0.59/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.59/0.80 tff(211,plain,(
% 0.59/0.80 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(skolemize,[status(sab)],[210])).
% 0.59/0.80 tff(212,plain,
% 0.59/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.59/0.80 tff(213,plain,
% 0.59/0.80 (((~![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)))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(214,plain,
% 0.59/0.80 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(a) | (~q2(b, a, b)))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(215,plain,
% 0.59/0.80 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(a) | (~q2(b, a, b))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.59/0.80 tff(216,plain,
% 0.59/0.80 (s2(a)),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[215, 212, 202, 191])).
% 0.59/0.80 tff(217,plain,
% 0.59/0.80 (^[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)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(218,plain,
% 0.59/0.80 (![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))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[217])).
% 0.59/0.80 tff(219,plain,
% 0.59/0.80 (![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))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(220,plain,
% 0.59/0.80 (^[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))))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(221,plain,
% 0.59/0.80 (![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))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[220])).
% 0.59/0.80 tff(222,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')).
% 0.59/0.80 tff(223,plain,
% 0.59/0.80 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.59/0.80 tff(224,plain,
% 0.59/0.80 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.59/0.80 tff(225,plain,(
% 0.59/0.80 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.80 inference(skolemize,[status(sab)],[224])).
% 0.59/0.80 tff(226,plain,
% 0.59/0.80 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.59/0.80 tff(227,plain,
% 0.59/0.80 (m0(e, d, e) <=> m0(e, d, e)),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(228,axiom,(m0(e, d, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_8')).
% 0.59/0.80 tff(229,plain,
% 0.59/0.80 (m0(e, d, e)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.59/0.80 tff(230,plain,
% 0.59/0.80 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(231,plain,
% 0.59/0.80 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e))),
% 0.59/0.80 inference(quant_inst,[status(thm)],[])).
% 0.59/0.80 tff(232,plain,
% 0.59/0.80 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(a)) | (~m0(e, d, e)) | (~q2(e, a, e)) | s3(a, e)),
% 0.59/0.80 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.59/0.80 tff(233,plain,
% 0.59/0.80 ($false),
% 0.59/0.80 inference(unit_resolution,[status(thm)],[232, 229, 226, 216, 94, 1])).
% 0.59/0.80 tff(234,plain,(s3(a, e)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.80 tff(235,assumption,(~m4(e, e)), introduced(assumption)).
% 0.59/0.80 tff(236,plain,
% 0.59/0.80 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.59/0.80 inference(bind,[status(th)],[])).
% 0.59/0.80 tff(237,plain,
% 0.59/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.80 inference(quant_intro,[status(thm)],[236])).
% 0.59/0.80 tff(238,plain,
% 0.59/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.80 inference(rewrite,[status(thm)],[])).
% 0.59/0.80 tff(239,plain,
% 0.59/0.80 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.59/0.81 inference(bind,[status(th)],[])).
% 0.59/0.81 tff(240,plain,
% 0.59/0.81 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.81 inference(quant_intro,[status(thm)],[239])).
% 0.59/0.81 tff(241,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.59/0.81 tff(242,plain,
% 0.59/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.59/0.81 tff(243,plain,
% 0.59/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.59/0.81 tff(244,plain,(
% 0.59/0.81 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.81 inference(skolemize,[status(sab)],[243])).
% 0.59/0.81 tff(245,plain,
% 0.59/0.81 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.59/0.81 tff(246,plain,
% 0.59/0.81 (m0(b, b, e) <=> m0(b, b, e)),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(247,axiom,(m0(b, b, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.59/0.81 tff(248,plain,
% 0.59/0.81 (m0(b, b, e)),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.59/0.81 tff(249,plain,
% 0.59/0.81 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(250,plain,
% 0.59/0.81 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(251,plain,
% 0.59/0.81 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))))),
% 0.59/0.81 inference(monotonicity,[status(thm)],[250])).
% 0.59/0.81 tff(252,plain,
% 0.59/0.81 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.59/0.81 inference(transitivity,[status(thm)],[251, 249])).
% 0.59/0.81 tff(253,plain,
% 0.59/0.81 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))),
% 0.59/0.81 inference(quant_inst,[status(thm)],[])).
% 0.59/0.81 tff(254,plain,
% 0.59/0.81 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.59/0.81 tff(255,plain,
% 0.59/0.81 ((~s1(b)) | l2(e, e)),
% 0.59/0.81 inference(unit_resolution,[status(thm)],[254, 248, 245, 106])).
% 0.59/0.81 tff(256,plain,
% 0.59/0.81 (l2(e, e)),
% 0.59/0.81 inference(unit_resolution,[status(thm)],[255, 202])).
% 0.59/0.81 tff(257,plain,
% 0.59/0.81 (^[E: $i, F: $i, G: $i] : refl(((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(258,plain,
% 0.66/0.82 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[257])).
% 0.66/0.82 tff(259,plain,
% 0.66/0.82 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F)) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(260,plain,
% 0.66/0.82 (^[E: $i, F: $i, G: $i] : trans(monotonicity(rewrite((m4(E, F) | (~l2(G, F))) <=> ((~l2(G, F)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> (((~l2(G, F)) | m4(E, F)) | (~s3(a, E))))), rewrite((((~l2(G, F)) | m4(E, F)) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))), (((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(261,plain,
% 0.66/0.82 (![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E))) <=> ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[260])).
% 0.66/0.82 tff(262,axiom,(![E: $i, F: $i, G: $i] : ((m4(E, F) | (~l2(G, F))) | (~s3(a, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_279')).
% 0.66/0.82 tff(263,plain,
% 0.66/0.82 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.66/0.82 tff(264,plain,
% 0.66/0.82 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.66/0.82 tff(265,plain,(
% 0.66/0.82 ![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(skolemize,[status(sab)],[264])).
% 0.66/0.82 tff(266,plain,
% 0.66/0.82 (![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.66/0.82 tff(267,plain,
% 0.66/0.82 (((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))) <=> ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(268,plain,
% 0.66/0.82 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | ((~l2(e, e)) | (~s3(a, e)) | m4(e, e))),
% 0.66/0.82 inference(quant_inst,[status(thm)],[])).
% 0.66/0.82 tff(269,plain,
% 0.66/0.82 ((~![E: $i, F: $i, G: $i] : ((~l2(G, F)) | (~s3(a, E)) | m4(E, F))) | (~l2(e, e)) | (~s3(a, e)) | m4(e, e)),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.66/0.82 tff(270,plain,
% 0.66/0.82 ($false),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[269, 266, 256, 235, 234])).
% 0.66/0.82 tff(271,plain,(m4(e, e)), inference(lemma,lemma(discharge,[]))).
% 0.66/0.82 tff(272,plain,
% 0.66/0.82 (^[X: $i] : refl((~m4(e, X)) <=> (~m4(e, X)))),
% 0.66/0.82 inference(bind,[status(th)],[])).
% 0.66/0.82 tff(273,plain,
% 0.66/0.82 (![X: $i] : (~m4(e, X)) <=> ![X: $i] : (~m4(e, X))),
% 0.66/0.82 inference(quant_intro,[status(thm)],[272])).
% 0.66/0.82 tff(274,plain,
% 0.66/0.82 (![X: $i] : (~m4(e, X)) <=> ![X: $i] : (~m4(e, X))),
% 0.66/0.82 inference(rewrite,[status(thm)],[])).
% 0.66/0.82 tff(275,axiom,(![X: $i] : (~m4(e, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.66/0.82 tff(276,plain,
% 0.66/0.82 (![X: $i] : (~m4(e, X))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.66/0.82 tff(277,plain,(
% 0.66/0.82 ![X: $i] : (~m4(e, X))),
% 0.66/0.82 inference(skolemize,[status(sab)],[276])).
% 0.66/0.82 tff(278,plain,
% 0.66/0.82 (![X: $i] : (~m4(e, X))),
% 0.66/0.82 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.66/0.82 tff(279,plain,
% 0.66/0.82 ((~![X: $i] : (~m4(e, X))) | (~m4(e, e))),
% 0.66/0.82 inference(quant_inst,[status(thm)],[])).
% 0.66/0.82 tff(280,plain,
% 0.66/0.82 ($false),
% 0.66/0.82 inference(unit_resolution,[status(thm)],[279, 278, 271])).
% 0.66/0.82 % SZS output end Proof
% 0.66/0.82 % E exiting
%------------------------------------------------------------------------------