%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN180-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:26 AM UTC 2025
% Result : Unsatisfiable 0.55s 0.72s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN180-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:28:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.55/0.72 % SZS status Unsatisfiable
% 0.55/0.72 % SZS output start Proof
% 0.55/0.72 tff(q2_type, type, (
% 0.55/0.72 q2: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(a_type, type, (
% 0.55/0.72 a: $i)).
% 0.55/0.72 tff(e_type, type, (
% 0.55/0.72 e: $i)).
% 0.55/0.72 tff(k3_type, type, (
% 0.55/0.72 k3: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(d_type, type, (
% 0.55/0.72 d: $i)).
% 0.55/0.72 tff(k2_type, type, (
% 0.55/0.72 k2: ( $i * $i ) > $o)).
% 0.55/0.72 tff(m1_type, type, (
% 0.55/0.72 m1: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(m0_type, type, (
% 0.55/0.72 m0: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(q1_type, type, (
% 0.55/0.72 q1: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(k0_type, type, (
% 0.55/0.72 k0: $i > $o)).
% 0.55/0.72 tff(s0_type, type, (
% 0.55/0.72 s0: $i > $o)).
% 0.55/0.72 tff(k1_type, type, (
% 0.55/0.72 k1: $i > $o)).
% 0.55/0.72 tff(n0_type, type, (
% 0.55/0.72 n0: ( $i * $i ) > $o)).
% 0.55/0.72 tff(c_type, type, (
% 0.55/0.72 c: $i)).
% 0.55/0.72 tff(m3_type, type, (
% 0.55/0.72 m3: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(p2_type, type, (
% 0.55/0.72 p2: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(l0_type, type, (
% 0.55/0.72 l0: $i > $o)).
% 0.55/0.72 tff(q4_type, type, (
% 0.55/0.72 q4: ( $i * $i ) > $o)).
% 0.55/0.72 tff(p1_type, type, (
% 0.55/0.72 p1: ( $i * $i * $i ) > $o)).
% 0.55/0.72 tff(r0_type, type, (
% 0.55/0.72 r0: $i > $o)).
% 0.55/0.72 tff(r1_type, type, (
% 0.55/0.72 r1: $i > $o)).
% 0.55/0.72 tff(q0_type, type, (
% 0.55/0.72 q0: ( $i * $i ) > $o)).
% 0.55/0.72 tff(1,assumption,(~m0(d, d, a)), introduced(assumption)).
% 0.55/0.72 tff(2,plain,
% 0.55/0.72 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(3,plain,
% 0.55/0.72 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.55/0.72 inference(quant_intro,[status(thm)],[2])).
% 0.55/0.72 tff(4,plain,
% 0.55/0.72 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.55/0.72 tff(6,plain,
% 0.55/0.72 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.55/0.72 tff(7,plain,(
% 0.55/0.72 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.55/0.72 inference(skolemize,[status(sab)],[6])).
% 0.55/0.72 tff(8,plain,
% 0.55/0.72 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.55/0.72 tff(9,plain,
% 0.55/0.72 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, a)),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(10,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.55/0.72 tff(11,plain,(m0(d, d, a)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(12,plain,
% 0.55/0.72 (^[B: $i, C: $i] : refl(((~m0(C, C, B)) | m1(B, C, B)) <=> ((~m0(C, C, B)) | m1(B, C, B)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(13,plain,
% 0.55/0.72 (![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B)) <=> ![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[12])).
% 0.55/0.72 tff(14,plain,
% 0.55/0.72 (![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B)) <=> ![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(15,plain,
% 0.55/0.72 (^[B: $i, C: $i] : rewrite((m1(B, C, B) | (~m0(C, C, B))) <=> ((~m0(C, C, B)) | m1(B, C, B)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(16,plain,
% 0.55/0.72 (![B: $i, C: $i] : (m1(B, C, B) | (~m0(C, C, B))) <=> ![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[15])).
% 0.55/0.72 tff(17,axiom,(![B: $i, C: $i] : (m1(B, C, B) | (~m0(C, C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_005')).
% 0.55/0.72 tff(18,plain,
% 0.55/0.72 (![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.55/0.72 tff(19,plain,
% 0.55/0.72 (![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.55/0.72 tff(20,plain,(
% 0.55/0.72 ![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(skolemize,[status(sab)],[19])).
% 0.55/0.72 tff(21,plain,
% 0.55/0.72 (![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.55/0.72 tff(22,plain,
% 0.55/0.72 (((~![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))) | ((~m0(d, d, a)) | m1(a, d, a))) <=> ((~![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))) | (~m0(d, d, a)) | m1(a, d, a))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(23,plain,
% 0.55/0.72 ((~![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))) | ((~m0(d, d, a)) | m1(a, d, a))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(24,plain,
% 0.55/0.72 ((~![B: $i, C: $i] : ((~m0(C, C, B)) | m1(B, C, B))) | (~m0(d, d, a)) | m1(a, d, a)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.55/0.72 tff(25,plain,
% 0.55/0.72 (m1(a, d, a)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.55/0.72 tff(26,plain,
% 0.55/0.72 (^[A: $i, J: $i] : refl(((~q1(A, J, J)) | k2(J, J)) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(27,plain,
% 0.55/0.72 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[26])).
% 0.55/0.72 tff(28,plain,
% 0.55/0.72 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(29,plain,
% 0.55/0.72 (^[A: $i, J: $i] : rewrite((k2(J, J) | (~q1(A, J, J))) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(30,plain,
% 0.55/0.72 (![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J))) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[29])).
% 0.55/0.72 tff(31,axiom,(![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_129')).
% 0.55/0.72 tff(32,plain,
% 0.55/0.72 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.55/0.72 tff(33,plain,
% 0.55/0.72 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.55/0.72 tff(34,plain,(
% 0.55/0.72 ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(skolemize,[status(sab)],[33])).
% 0.55/0.72 tff(35,plain,
% 0.55/0.72 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.55/0.72 tff(36,plain,
% 0.55/0.72 (k0(e) <=> k0(e)),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(37,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.55/0.72 tff(38,plain,
% 0.55/0.72 (k0(e)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.55/0.72 tff(39,plain,
% 0.55/0.72 (s0(d) <=> s0(d)),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(40,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.55/0.72 tff(41,plain,
% 0.55/0.72 (s0(d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.55/0.72 tff(42,plain,
% 0.55/0.72 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(43,plain,
% 0.55/0.72 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(44,plain,
% 0.55/0.72 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(45,plain,
% 0.55/0.72 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[44])).
% 0.55/0.72 tff(46,plain,
% 0.55/0.72 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.55/0.72 inference(transitivity,[status(thm)],[45, 43])).
% 0.55/0.72 tff(47,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.55/0.72 tff(48,plain,
% 0.55/0.72 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.55/0.72 tff(49,plain,
% 0.55/0.72 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.55/0.72 tff(50,plain,
% 0.55/0.72 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.55/0.72 tff(51,plain,
% 0.55/0.72 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.55/0.72 tff(52,plain,
% 0.55/0.72 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.55/0.72 tff(53,plain,
% 0.55/0.72 (q1(d, d, d)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[52, 41, 38])).
% 0.55/0.72 tff(54,plain,
% 0.55/0.72 (((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(d, d, d)) | k2(d, d))) <=> ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(d, d, d)) | k2(d, d))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(55,plain,
% 0.55/0.72 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(d, d, d)) | k2(d, d))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(56,plain,
% 0.55/0.72 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(d, d, d)) | k2(d, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.55/0.72 tff(57,plain,
% 0.55/0.72 (k2(d, d)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[56, 53, 35])).
% 0.55/0.72 tff(58,plain,
% 0.55/0.72 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(59,plain,
% 0.55/0.72 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[58])).
% 0.55/0.72 tff(60,plain,
% 0.55/0.72 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(61,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.55/0.72 tff(62,plain,
% 0.55/0.72 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.55/0.72 tff(63,plain,(
% 0.55/0.72 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[62])).
% 0.55/0.72 tff(64,plain,
% 0.55/0.72 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.55/0.72 tff(65,plain,
% 0.55/0.72 (n0(c, d) <=> n0(c, d)),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(66,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.55/0.72 tff(67,plain,
% 0.55/0.72 (n0(c, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.55/0.72 tff(68,plain,
% 0.55/0.72 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(69,plain,
% 0.55/0.72 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(d) | (~n0(c, d)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(70,plain,
% 0.55/0.72 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(d) | (~n0(c, d))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.55/0.72 tff(71,plain,
% 0.55/0.72 (k1(d)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[70, 67, 64])).
% 0.55/0.72 tff(72,plain,
% 0.55/0.72 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(73,plain,
% 0.55/0.72 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[72])).
% 0.55/0.72 tff(74,plain,
% 0.55/0.72 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(75,plain,
% 0.55/0.72 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k2(C, D) | (~m1(E, D, C))) <=> ((~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> (((~m1(E, D, C)) | k2(C, D)) | (~k1(F))))), rewrite((((~m1(E, D, C)) | k2(C, D)) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D)))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> (((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))))), rewrite((((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(76,plain,
% 0.55/0.72 (![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[75])).
% 0.55/0.72 tff(77,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_127')).
% 0.55/0.72 tff(78,plain,
% 0.55/0.72 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.55/0.72 tff(79,plain,
% 0.55/0.72 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.55/0.72 tff(80,plain,(
% 0.55/0.72 ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(skolemize,[status(sab)],[79])).
% 0.55/0.72 tff(81,plain,
% 0.55/0.72 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.55/0.72 tff(82,plain,
% 0.55/0.72 (((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(d)) | (~k2(d, d)) | (~m1(a, d, a)) | k2(a, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(d)) | (~k2(d, d)) | (~m1(a, d, a)) | k2(a, d))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(83,plain,
% 0.55/0.72 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(d)) | (~k2(d, d)) | (~m1(a, d, a)) | k2(a, d))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(84,plain,
% 0.55/0.72 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(d)) | (~k2(d, d)) | (~m1(a, d, a)) | k2(a, d)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.55/0.72 tff(85,plain,
% 0.55/0.72 (k2(a, d)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[84, 81, 71, 57, 25])).
% 0.55/0.72 tff(86,plain,
% 0.55/0.72 (^[F: $i, G: $i] : refl(((~k2(G, F)) | k3(F, F, G)) <=> ((~k2(G, F)) | k3(F, F, G)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(87,plain,
% 0.55/0.72 (![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G)) <=> ![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[86])).
% 0.55/0.72 tff(88,plain,
% 0.55/0.72 (![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G)) <=> ![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(89,plain,
% 0.55/0.72 (^[F: $i, G: $i] : rewrite((k3(F, F, G) | (~k2(G, F))) <=> ((~k2(G, F)) | k3(F, F, G)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(90,plain,
% 0.55/0.72 (![F: $i, G: $i] : (k3(F, F, G) | (~k2(G, F))) <=> ![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[89])).
% 0.55/0.72 tff(91,axiom,(![F: $i, G: $i] : (k3(F, F, G) | (~k2(G, F)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_194')).
% 0.55/0.72 tff(92,plain,
% 0.55/0.72 (![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.55/0.73 tff(93,plain,
% 0.55/0.73 (![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.55/0.73 tff(94,plain,(
% 0.55/0.73 ![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.73 inference(skolemize,[status(sab)],[93])).
% 0.55/0.73 tff(95,plain,
% 0.55/0.73 (![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.55/0.73 tff(96,plain,
% 0.55/0.73 (((~![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))) | ((~k2(a, d)) | k3(d, d, a))) <=> ((~![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))) | (~k2(a, d)) | k3(d, d, a))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(97,plain,
% 0.55/0.73 ((~![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))) | ((~k2(a, d)) | k3(d, d, a))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(98,plain,
% 0.55/0.73 ((~![F: $i, G: $i] : ((~k2(G, F)) | k3(F, F, G))) | (~k2(a, d)) | k3(d, d, a)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.55/0.73 tff(99,plain,
% 0.55/0.73 (k3(d, d, a)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[98, 95, 85])).
% 0.55/0.73 tff(100,plain,
% 0.55/0.73 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(101,plain,
% 0.55/0.73 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[100])).
% 0.55/0.73 tff(102,plain,
% 0.55/0.73 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(103,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 0.55/0.73 tff(104,plain,
% 0.55/0.73 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.55/0.73 tff(105,plain,(
% 0.55/0.73 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[104])).
% 0.55/0.73 tff(106,plain,
% 0.55/0.73 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.55/0.73 tff(107,plain,
% 0.55/0.73 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(108,plain,
% 0.55/0.73 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[107])).
% 0.55/0.73 tff(109,plain,
% 0.55/0.73 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(110,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.55/0.73 tff(111,plain,
% 0.55/0.73 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.55/0.73 tff(112,plain,(
% 0.55/0.73 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[111])).
% 0.55/0.73 tff(113,plain,
% 0.55/0.73 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.55/0.73 tff(114,plain,
% 0.55/0.73 (l0(a) <=> l0(a)),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(115,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.55/0.73 tff(116,plain,
% 0.55/0.73 (l0(a)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.55/0.73 tff(117,plain,
% 0.55/0.73 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(118,plain,
% 0.55/0.73 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(119,plain,
% 0.55/0.73 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(120,plain,
% 0.55/0.73 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[119])).
% 0.55/0.73 tff(121,plain,
% 0.55/0.73 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[120, 118])).
% 0.55/0.73 tff(122,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.55/0.73 tff(123,plain,
% 0.55/0.73 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.55/0.73 tff(124,plain,
% 0.55/0.73 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[123, 117])).
% 0.55/0.73 tff(125,plain,
% 0.55/0.73 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.55/0.73 tff(126,plain,
% 0.55/0.73 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[125, 117])).
% 0.55/0.73 tff(127,plain,
% 0.55/0.73 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[126, 117])).
% 0.55/0.73 tff(128,plain,
% 0.55/0.73 (m1(a, a, a)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[127, 41, 116])).
% 0.55/0.73 tff(129,plain,
% 0.55/0.73 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(130,plain,
% 0.55/0.73 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(131,plain,
% 0.55/0.73 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.55/0.73 tff(132,plain,
% 0.55/0.73 (p2(a, a, a)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[131, 128, 113])).
% 0.55/0.73 tff(133,plain,
% 0.55/0.73 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(134,plain,
% 0.55/0.73 ((m3(a, a, a) | (~p2(a, a, a))) <=> ((~p2(a, a, a)) | m3(a, a, a))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(135,plain,
% 0.55/0.73 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[134])).
% 0.55/0.73 tff(136,plain,
% 0.55/0.73 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 0.55/0.73 inference(transitivity,[status(thm)],[135, 133])).
% 0.55/0.73 tff(137,plain,
% 0.55/0.73 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(138,plain,
% 0.55/0.73 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.55/0.73 tff(139,plain,
% 0.55/0.73 (m3(a, a, a)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[138, 132, 106])).
% 0.55/0.73 tff(140,plain,
% 0.55/0.73 ((~q4(a, e)) <=> (~q4(a, e))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(141,axiom,(~q4(a, e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.55/0.73 tff(142,plain,
% 0.55/0.73 (~q4(a, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.55/0.73 tff(143,plain,
% 0.55/0.73 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(144,plain,
% 0.55/0.73 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[143])).
% 0.55/0.73 tff(145,plain,
% 0.55/0.73 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(146,plain,
% 0.55/0.73 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q4(B, C) | (~k3(D, D, B))) <=> ((~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> (((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))))), rewrite((((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> (((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))))), rewrite((((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(147,plain,
% 0.55/0.73 (![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[146])).
% 0.55/0.73 tff(148,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 0.55/0.73 tff(149,plain,
% 0.55/0.73 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.55/0.73 tff(150,plain,
% 0.55/0.73 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.55/0.73 tff(151,plain,(
% 0.55/0.73 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(skolemize,[status(sab)],[150])).
% 0.55/0.73 tff(152,plain,
% 0.55/0.73 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.55/0.73 tff(153,plain,
% 0.55/0.73 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(a, e) | (~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(a, e) | (~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(154,plain,
% 0.55/0.73 (((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)) | q4(a, e)) <=> (q4(a, e) | (~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(155,plain,
% 0.55/0.73 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)) | q4(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(a, e) | (~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[154])).
% 0.55/0.73 tff(156,plain,
% 0.55/0.73 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)) | q4(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(a, e) | (~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[155, 153])).
% 0.55/0.73 tff(157,plain,
% 0.55/0.73 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a)) | q4(a, e))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(158,plain,
% 0.55/0.73 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(a, e) | (~m3(a, a, a)) | (~q2(a, e, a)) | (~k3(d, d, a))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.55/0.73 tff(159,plain,
% 0.55/0.73 (~q2(a, e, a)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[158, 152, 142, 139, 99])).
% 0.55/0.73 tff(160,plain,
% 0.55/0.73 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(161,plain,
% 0.55/0.73 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[160])).
% 0.55/0.73 tff(162,plain,
% 0.55/0.73 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(163,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.55/0.73 tff(164,plain,
% 0.55/0.73 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.55/0.73 tff(165,plain,(
% 0.55/0.73 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[164])).
% 0.55/0.73 tff(166,plain,
% 0.55/0.73 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.55/0.73 tff(167,plain,
% 0.55/0.73 (r0(e) <=> r0(e)),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(168,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.55/0.73 tff(169,plain,
% 0.55/0.73 (r0(e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.55/0.73 tff(170,plain,
% 0.55/0.73 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(171,plain,
% 0.55/0.73 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(172,plain,
% 0.55/0.73 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(173,plain,
% 0.55/0.73 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[172])).
% 0.55/0.73 tff(174,plain,
% 0.55/0.73 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.55/0.73 inference(transitivity,[status(thm)],[173, 171])).
% 0.55/0.73 tff(175,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.55/0.73 tff(176,plain,
% 0.55/0.73 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.55/0.73 tff(177,plain,
% 0.55/0.73 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[176, 170])).
% 0.55/0.73 tff(178,plain,
% 0.55/0.73 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.55/0.73 tff(179,plain,
% 0.55/0.73 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[178, 170])).
% 0.55/0.73 tff(180,plain,
% 0.55/0.73 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[179, 170])).
% 0.55/0.73 tff(181,plain,
% 0.55/0.73 (p1(e, e, e)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[180, 169, 38])).
% 0.55/0.73 tff(182,plain,
% 0.55/0.73 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(183,plain,
% 0.55/0.73 ((q2(e, e, e) | (~p1(e, e, e))) <=> ((~p1(e, e, e)) | q2(e, e, e))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(184,plain,
% 0.55/0.73 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[183])).
% 0.55/0.73 tff(185,plain,
% 0.55/0.73 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 0.55/0.73 inference(transitivity,[status(thm)],[184, 182])).
% 0.55/0.73 tff(186,plain,
% 0.55/0.73 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(187,plain,
% 0.55/0.73 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.55/0.73 tff(188,plain,
% 0.55/0.73 (q2(e, e, e)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[187, 181, 166])).
% 0.55/0.73 tff(189,plain,
% 0.55/0.73 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(190,plain,
% 0.55/0.73 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[189])).
% 0.55/0.73 tff(191,plain,
% 0.55/0.73 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(192,plain,
% 0.55/0.73 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((q2(C, D, C) | (~r1(D))) <=> ((~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> (((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))))), rewrite((((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> (((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))))), rewrite((((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> (((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))))), rewrite((((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(193,plain,
% 0.55/0.73 (![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[192])).
% 0.55/0.73 tff(194,axiom,(![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 0.55/0.73 tff(195,plain,
% 0.55/0.73 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.55/0.73 tff(196,plain,
% 0.55/0.73 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.55/0.73 tff(197,plain,(
% 0.55/0.73 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(skolemize,[status(sab)],[196])).
% 0.55/0.73 tff(198,plain,
% 0.55/0.73 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.55/0.73 tff(199,plain,
% 0.55/0.73 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(200,plain,
% 0.55/0.73 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[199])).
% 0.55/0.73 tff(201,plain,
% 0.55/0.73 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(202,plain,
% 0.55/0.73 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(203,plain,
% 0.55/0.73 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[202])).
% 0.55/0.73 tff(204,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.55/0.73 tff(205,plain,
% 0.55/0.73 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.55/0.73 tff(206,plain,
% 0.55/0.73 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.55/0.73 tff(207,plain,(
% 0.55/0.73 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(skolemize,[status(sab)],[206])).
% 0.55/0.73 tff(208,plain,
% 0.55/0.73 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.55/0.73 tff(209,plain,
% 0.55/0.73 (q0(e, d) <=> q0(e, d)),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(210,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.55/0.73 tff(211,plain,
% 0.55/0.73 (q0(e, d)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.55/0.73 tff(212,plain,
% 0.55/0.73 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(213,plain,
% 0.55/0.74 (((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e)) <=> ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(214,plain,
% 0.55/0.74 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[213])).
% 0.55/0.74 tff(215,plain,
% 0.55/0.74 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[214, 212])).
% 0.55/0.74 tff(216,plain,
% 0.55/0.74 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(217,plain,
% 0.55/0.75 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.55/0.75 tff(218,plain,
% 0.55/0.75 (r1(e)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[217, 41, 211, 53, 208])).
% 0.55/0.75 tff(219,plain,
% 0.55/0.75 (m0(e, d, a) <=> m0(e, d, a)),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(220,axiom,(m0(e, d, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_4')).
% 0.55/0.75 tff(221,plain,
% 0.55/0.75 (m0(e, d, a)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.55/0.75 tff(222,plain,
% 0.55/0.75 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(e)) | (~r1(e)) | (~m0(e, d, a)) | (~q2(e, e, e)) | q2(a, e, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~m0(e, d, a)) | (~q2(e, e, e)) | q2(a, e, a))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(223,plain,
% 0.55/0.75 (((~m0(e, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a)) <=> ((~k0(e)) | (~r1(e)) | (~m0(e, d, a)) | (~q2(e, e, e)) | q2(a, e, a))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(224,plain,
% 0.55/0.75 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(e, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(e)) | (~r1(e)) | (~m0(e, d, a)) | (~q2(e, e, e)) | q2(a, e, a)))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[223])).
% 0.55/0.75 tff(225,plain,
% 0.55/0.75 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(e, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~m0(e, d, a)) | (~q2(e, e, e)) | q2(a, e, a))),
% 0.55/0.75 inference(transitivity,[status(thm)],[224, 222])).
% 0.55/0.75 tff(226,plain,
% 0.55/0.75 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(e, d, a)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(a, e, a))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(227,plain,
% 0.55/0.75 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~m0(e, d, a)) | (~q2(e, e, e)) | q2(a, e, a)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.55/0.75 tff(228,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[227, 221, 38, 218, 198, 188, 159])).
% 0.55/0.75 % SZS output end Proof
% 0.55/0.75 % E exiting
%------------------------------------------------------------------------------