%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN159-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:23 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN159-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:29:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(p4_type, type, (
% 0.20/0.50 p4: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(e_type, type, (
% 0.20/0.50 e: $i)).
% 0.20/0.50 tff(b_type, type, (
% 0.20/0.50 b: $i)).
% 0.20/0.50 tff(r3_type, type, (
% 0.20/0.50 r3: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(l2_type, type, (
% 0.20/0.50 l2: ( $i * $i ) > $o)).
% 0.20/0.50 tff(s1_type, type, (
% 0.20/0.50 s1: $i > $o)).
% 0.20/0.50 tff(p0_type, type, (
% 0.20/0.50 p0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(m0_type, type, (
% 0.20/0.50 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(p2_type, type, (
% 0.20/0.50 p2: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(n1_type, type, (
% 0.20/0.50 n1: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(k1_type, type, (
% 0.20/0.50 k1: $i > $o)).
% 0.20/0.50 tff(n0_type, type, (
% 0.20/0.50 n0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(d_type, type, (
% 0.20/0.50 d: $i)).
% 0.20/0.50 tff(r0_type, type, (
% 0.20/0.50 r0: $i > $o)).
% 0.20/0.50 tff(q4_type, type, (
% 0.20/0.50 q4: ( $i * $i ) > $o)).
% 0.20/0.50 tff(a_type, type, (
% 0.20/0.50 a: $i)).
% 0.20/0.50 tff(m3_type, type, (
% 0.20/0.50 m3: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(m1_type, type, (
% 0.20/0.50 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(l0_type, type, (
% 0.20/0.50 l0: $i > $o)).
% 0.20/0.50 tff(s0_type, type, (
% 0.20/0.50 s0: $i > $o)).
% 0.20/0.50 tff(q2_type, type, (
% 0.20/0.50 q2: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(p1_type, type, (
% 0.20/0.50 p1: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(k3_type, type, (
% 0.20/0.50 k3: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(r2_type, type, (
% 0.20/0.50 r2: $i > $o)).
% 0.20/0.50 tff(r1_type, type, (
% 0.20/0.50 r1: $i > $o)).
% 0.20/0.50 tff(q1_type, type, (
% 0.20/0.50 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(q0_type, type, (
% 0.20/0.50 q0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(n4_type, type, (
% 0.20/0.50 n4: ( $i * $i ) > $o)).
% 0.20/0.50 tff(k4_type, type, (
% 0.20/0.50 k4: $i > $o)).
% 0.20/0.50 tff(c_type, type, (
% 0.20/0.50 c: $i)).
% 0.20/0.50 tff(n3_type, type, (
% 0.20/0.50 n3: $i > $o)).
% 0.20/0.50 tff(q3_type, type, (
% 0.20/0.50 q3: ( $i * $i ) > $o)).
% 0.20/0.50 tff(l1_type, type, (
% 0.20/0.50 l1: ( $i * $i ) > $o)).
% 0.20/0.50 tff(n5_type, type, (
% 0.20/0.50 n5: ( $i * $i ) > $o)).
% 0.20/0.50 tff(n2_type, type, (
% 0.20/0.50 n2: $i > $o)).
% 0.20/0.50 tff(k0_type, type, (
% 0.20/0.50 k0: $i > $o)).
% 0.20/0.50 tff(m2_type, type, (
% 0.20/0.50 m2: $i > $o)).
% 0.20/0.50 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (![X: $i] : p0(b, X)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.50 tff(7,plain,(
% 0.20/0.50 ![X: $i] : p0(b, X)),
% 0.20/0.50 inference(skolemize,[status(sab)],[6])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (![X: $i] : p0(b, X)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.50 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.50 tff(17,plain,(
% 0.20/0.50 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[16])).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 (s1(b)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (^[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)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.50 tff(28,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.50 tff(31,plain,(
% 0.20/0.50 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.20/0.50 inference(skolemize,[status(sab)],[30])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (m0(b, b, e) <=> m0(b, b, e)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(34,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (m0(b, b, e)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (((~![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (((~![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))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (((~![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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 ((~![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))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 ((~![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 ((~s1(b)) | l2(e, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[41, 35, 32, 11])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (l2(e, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[42, 22])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(47,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.50 tff(49,plain,(
% 0.20/0.50 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[48])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (n0(d, b) <=> n0(d, b)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(52,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (n0(d, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(55,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (k1(b)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[56, 53, 50])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (^[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)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.50 tff(63,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.50 tff(66,plain,(
% 0.20/0.50 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.20/0.50 inference(skolemize,[status(sab)],[65])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))) <=> ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(b)) | (~m0(b, b, e)) | n1(b, e, e)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 ((~k1(b)) | n1(b, e, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[70, 35, 67])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (n1(b, e, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[71, 57])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (^[C: $i] : refl(((~n1(C, e, e)) | p2(C, e, C)) <=> ((~n1(C, e, e)) | p2(C, e, C)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (![C: $i] : ((~n1(C, e, e)) | p2(C, e, C)) <=> ![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (![C: $i] : ((~n1(C, e, e)) | p2(C, e, C)) <=> ![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (^[C: $i] : rewrite((p2(C, e, C) | (~n1(C, e, e))) <=> ((~n1(C, e, e)) | p2(C, e, C)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 (![C: $i] : (p2(C, e, C) | (~n1(C, e, e))) <=> ![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.50 tff(78,axiom,(![C: $i] : (p2(C, e, C) | (~n1(C, e, e)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_170')).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.50 tff(81,plain,(
% 0.20/0.50 ![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(skolemize,[status(sab)],[80])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (((~![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))) | ((~n1(b, e, e)) | p2(b, e, b))) <=> ((~![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))) | (~n1(b, e, e)) | p2(b, e, b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 ((~![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))) | ((~n1(b, e, e)) | p2(b, e, b))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 ((~![C: $i] : ((~n1(C, e, e)) | p2(C, e, C))) | (~n1(b, e, e)) | p2(b, e, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (p2(b, e, b)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[85, 82, 72])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 (^[F: $i] : refl(((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F)) <=> ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F)) <=> ![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F)) <=> ![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (^[F: $i] : trans(monotonicity(trans(monotonicity(rewrite((r3(F, b, F) | (~r0(F))) <=> ((~r0(F)) | r3(F, b, F))), (((r3(F, b, F) | (~r0(F))) | (~p2(b, F, b))) <=> (((~r0(F)) | r3(F, b, F)) | (~p2(b, F, b))))), rewrite((((~r0(F)) | r3(F, b, F)) | (~p2(b, F, b))) <=> ((~r0(F)) | (~p2(b, F, b)) | r3(F, b, F))), (((r3(F, b, F) | (~r0(F))) | (~p2(b, F, b))) <=> ((~r0(F)) | (~p2(b, F, b)) | r3(F, b, F)))), ((((r3(F, b, F) | (~r0(F))) | (~p2(b, F, b))) | (~l2(F, F))) <=> (((~r0(F)) | (~p2(b, F, b)) | r3(F, b, F)) | (~l2(F, F))))), rewrite((((~r0(F)) | (~p2(b, F, b)) | r3(F, b, F)) | (~l2(F, F))) <=> ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))), ((((r3(F, b, F) | (~r0(F))) | (~p2(b, F, b))) | (~l2(F, F))) <=> ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (![F: $i] : (((r3(F, b, F) | (~r0(F))) | (~p2(b, F, b))) | (~l2(F, F))) <=> ![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.50 tff(92,axiom,(![F: $i] : (((r3(F, b, F) | (~r0(F))) | (~p2(b, F, b))) | (~l2(F, F)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_270')).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.50 tff(95,plain,(
% 0.20/0.50 ![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(skolemize,[status(sab)],[94])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (r0(e) <=> r0(e)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(98,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (r0(e)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (((~![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))) | ((~r0(e)) | (~l2(e, e)) | (~p2(b, e, b)) | r3(e, b, e))) <=> ((~![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))) | (~r0(e)) | (~l2(e, e)) | (~p2(b, e, b)) | r3(e, b, e))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 ((~![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))) | ((~r0(e)) | (~l2(e, e)) | (~p2(b, e, b)) | r3(e, b, e))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 ((~![F: $i] : ((~r0(F)) | (~l2(F, F)) | (~p2(b, F, b)) | r3(F, b, F))) | (~r0(e)) | (~l2(e, e)) | (~p2(b, e, b)) | r3(e, b, e)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 ((~l2(e, e)) | (~p2(b, e, b)) | r3(e, b, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[102, 99, 96])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 ((~l2(e, e)) | r3(e, b, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[103, 86])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 (r3(e, b, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[104, 43])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (^[H: $i, G: $i] : refl(((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H)) <=> ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 (![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H)) <=> ![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H)) <=> ![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 (^[H: $i, G: $i] : trans(monotonicity(rewrite((p4(G, G, H) | (~r0(G))) <=> ((~r0(G)) | p4(G, G, H))), (((p4(G, G, H) | (~r0(G))) | (~r3(H, G, H))) <=> (((~r0(G)) | p4(G, G, H)) | (~r3(H, G, H))))), rewrite((((~r0(G)) | p4(G, G, H)) | (~r3(H, G, H))) <=> ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))), (((p4(G, G, H) | (~r0(G))) | (~r3(H, G, H))) <=> ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 (![H: $i, G: $i] : ((p4(G, G, H) | (~r0(G))) | (~r3(H, G, H))) <=> ![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.50 tff(111,axiom,(![H: $i, G: $i] : ((p4(G, G, H) | (~r0(G))) | (~r3(H, G, H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_285')).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 (![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 (![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.50 tff(114,plain,(
% 0.20/0.50 ![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(skolemize,[status(sab)],[113])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 (![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.50 tff(116,plain,
% 0.20/0.50 (r0(b) <=> r0(b)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(117,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 (r0(b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (((~![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))) | ((~r0(b)) | (~r3(e, b, e)) | p4(b, b, e))) <=> ((~![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))) | (~r0(b)) | (~r3(e, b, e)) | p4(b, b, e))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 ((~![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))) | ((~r0(b)) | (~r3(e, b, e)) | p4(b, b, e))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 ((~![H: $i, G: $i] : ((~r0(G)) | (~r3(H, G, H)) | p4(G, G, H))) | (~r0(b)) | (~r3(e, b, e)) | p4(b, b, e)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (p4(b, b, e)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[121, 118, 115, 105])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(126,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.50 tff(128,plain,(
% 0.20/0.50 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[127])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(133,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.50 tff(135,plain,(
% 0.20/0.50 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[134])).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (l0(a) <=> l0(a)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(138,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (l0(a)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 (s0(d) <=> s0(d)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(141,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (s0(d)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(146,plain,
% 0.20/0.51 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.51 tff(148,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.20/0.51 tff(149,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[149, 143])).
% 0.20/0.51 tff(151,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[151, 143])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[152, 143])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 (m1(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[153, 142, 139])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (p2(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[157, 154, 136])).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 (((~![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 ((m3(a, a, a) | (~p2(a, a, a))) <=> ((~p2(a, a, a)) | m3(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 (((~![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)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 (((~![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))),
% 0.20/0.51 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 (m3(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[164, 158, 129])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(169,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.51 tff(171,plain,(
% 0.20/0.51 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[170])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(175,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 ((~l0(a)) | p1(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 ((~l0(a)) | p1(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 (p1(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[177, 139])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 ((q2(a, a, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | q2(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[180])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.20/0.51 inference(transitivity,[status(thm)],[181, 179])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 (q2(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[184, 178, 172])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 (^[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)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(189,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(190,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.51 tff(191,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')).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.51 tff(194,plain,(
% 0.20/0.51 ![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))),
% 0.20/0.51 inference(skolemize,[status(sab)],[193])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.51 tff(201,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.20/0.51 tff(204,plain,(
% 0.20/0.51 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(skolemize,[status(sab)],[203])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 (p0(b, d) <=> p0(b, d)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(207,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 (p0(b, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 (q1(d, b, d)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[211, 53, 208, 205])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 (^[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)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[216])).
% 0.20/0.51 tff(218,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')).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.20/0.51 tff(221,plain,(
% 0.20/0.51 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.51 inference(skolemize,[status(sab)],[220])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (q0(a, b) <=> q0(a, b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(224,axiom,(q0(a, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (q0(a, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a)) <=> ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[227])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[228, 226])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 (r1(a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[231, 142, 225, 222, 212])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[233])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[236])).
% 0.20/0.51 tff(238,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[239, 235])).
% 0.20/0.51 tff(241,plain,(
% 0.20/0.51 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(skolemize,[status(sab)],[240])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[241, 234])).
% 0.20/0.51 tff(243,plain,
% 0.20/0.51 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (r2(a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[245, 139, 242, 232])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(249,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 ((~r2(a)) | k3(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 ((~r2(a)) | k3(a, a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 (k3(a, a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[251, 246])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (((~![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))) | ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, 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))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a)) <=> ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (((~![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, a, a)) | (~k3(a, a, a)) | q4(a, 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))) | ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[254])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (((~![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, a, a)) | (~k3(a, a, a)) | q4(a, 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))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(transitivity,[status(thm)],[255, 253])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ((~![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, a, a)) | (~k3(a, a, a)) | q4(a, a))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 ((~![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))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (q4(a, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[258, 252, 195, 185, 165])).
% 0.20/0.51 tff(260,assumption,(~n4(a, a)), introduced(assumption)).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (^[I: $i, H: $i] : refl((n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[261])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 (^[I: $i, H: $i] : trans(monotonicity(rewrite((n4(H, H) | (~k4(I))) <=> (n4(H, H) | (~k4(I)))), (((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> ((n4(H, H) | (~k4(I))) | (~m3(H, H, H))))), rewrite(((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))), (((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 (![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[264])).
% 0.20/0.51 tff(266,axiom,(![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_284')).
% 0.20/0.51 tff(267,plain,
% 0.20/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.20/0.51 tff(269,plain,(
% 0.20/0.51 ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[268])).
% 0.20/0.51 tff(270,plain,
% 0.20/0.51 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 (((~r0(e)) | m1(e, e, e)) <=> ((~r0(e)) | m1(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(272,plain,
% 0.20/0.51 ((m1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | m1(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(273,axiom,(m1(e, e, e) | (~r0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_012')).
% 0.20/0.51 tff(274,plain,
% 0.20/0.51 ((~r0(e)) | m1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.51 tff(275,plain,
% 0.20/0.51 ((~r0(e)) | m1(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[274, 271])).
% 0.20/0.51 tff(276,plain,
% 0.20/0.51 (m1(e, e, e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[275, 99])).
% 0.20/0.51 tff(277,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(e, e, e)) | p2(e, e, e))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(278,plain,
% 0.20/0.51 ((p2(e, e, e) | (~m1(e, e, e))) <=> ((~m1(e, e, e)) | p2(e, e, e))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(279,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(e, e, e)) | p2(e, e, e)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.51 tff(280,plain,
% 0.20/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e))),
% 0.20/0.51 inference(transitivity,[status(thm)],[279, 277])).
% 0.20/0.51 tff(281,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(282,plain,
% 0.20/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.51 tff(283,plain,
% 0.20/0.51 (p2(e, e, e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[282, 276, 136])).
% 0.20/0.51 tff(284,plain,
% 0.20/0.51 (^[D: $i, E: $i, F: $i] : refl((n3(D) | (~p2(E, F, D))) <=> (n3(D) | (~p2(E, F, D))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(285,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[284])).
% 0.20/0.51 tff(286,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(287,axiom,(![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_240')).
% 0.20/0.51 tff(288,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.51 tff(289,plain,(
% 0.20/0.51 ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[288])).
% 0.20/0.51 tff(290,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.20/0.51 tff(291,plain,
% 0.20/0.51 (((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))) <=> ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(292,plain,
% 0.20/0.51 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(293,plain,
% 0.20/0.51 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.51 tff(294,plain,
% 0.20/0.51 (n3(e)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[293, 290, 283])).
% 0.20/0.51 tff(295,plain,
% 0.20/0.51 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(296,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[295])).
% 0.20/0.51 tff(297,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(298,plain,
% 0.20/0.51 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1(C, D) | (~p0(E, C))) <=> ((~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> (((~p0(E, C)) | l1(C, D)) | (~r0(F))))), rewrite((((~p0(E, C)) | l1(C, D)) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D)))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> (((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))))), rewrite((((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(299,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[298])).
% 0.20/0.51 tff(300,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 0.20/0.51 tff(301,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.20/0.51 tff(302,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.20/0.51 tff(303,plain,(
% 0.20/0.51 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(skolemize,[status(sab)],[302])).
% 0.20/0.51 tff(304,plain,
% 0.20/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.20/0.51 tff(305,plain,
% 0.20/0.51 (m0(e, b, c) <=> m0(e, b, c)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(306,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.20/0.51 tff(307,plain,
% 0.20/0.51 (m0(e, b, c)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.52 tff(308,plain,
% 0.20/0.52 (p0(c, b) <=> p0(c, b)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(309,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.20/0.52 tff(310,plain,
% 0.20/0.52 (p0(c, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.20/0.52 tff(311,plain,
% 0.20/0.52 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(312,plain,
% 0.20/0.52 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(313,plain,
% 0.20/0.52 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[312])).
% 0.20/0.52 tff(314,plain,
% 0.20/0.52 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.52 inference(transitivity,[status(thm)],[313, 311])).
% 0.20/0.52 tff(315,plain,
% 0.20/0.52 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(316,plain,
% 0.20/0.52 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.52 tff(317,plain,
% 0.20/0.52 (l1(b, e)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[316, 118, 310, 307, 304])).
% 0.20/0.52 tff(318,plain,
% 0.20/0.52 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(319,plain,
% 0.20/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[318])).
% 0.20/0.52 tff(320,plain,
% 0.20/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(321,plain,
% 0.20/0.52 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(322,plain,
% 0.20/0.52 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[321])).
% 0.20/0.52 tff(323,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 0.20/0.52 tff(324,plain,
% 0.20/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.20/0.52 tff(325,plain,
% 0.20/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.20/0.52 tff(326,plain,(
% 0.20/0.52 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(skolemize,[status(sab)],[325])).
% 0.20/0.52 tff(327,plain,
% 0.20/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.20/0.52 tff(328,plain,
% 0.20/0.52 (((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))) <=> ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(329,plain,
% 0.20/0.52 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(330,plain,
% 0.20/0.52 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.52 tff(331,plain,
% 0.20/0.52 (q2(e, e, b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[330, 327, 317])).
% 0.20/0.52 tff(332,plain,
% 0.20/0.52 (^[I: $i, H: $i, G: $i] : refl(((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(333,plain,
% 0.20/0.52 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[332])).
% 0.20/0.52 tff(334,plain,
% 0.20/0.52 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(335,plain,
% 0.20/0.52 (^[I: $i, H: $i, G: $i] : trans(monotonicity(rewrite((q3(G, H) | (~q2(I, G, H))) <=> ((~q2(I, G, H)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> (((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))))), rewrite((((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(336,plain,
% 0.20/0.52 (![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[335])).
% 0.20/0.52 tff(337,axiom,(![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_255')).
% 0.20/0.52 tff(338,plain,
% 0.20/0.52 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.20/0.52 tff(339,plain,
% 0.20/0.52 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[338, 334])).
% 0.20/0.52 tff(340,plain,(
% 0.20/0.52 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(skolemize,[status(sab)],[339])).
% 0.20/0.52 tff(341,plain,
% 0.20/0.52 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.20/0.52 tff(342,plain,
% 0.20/0.52 (n0(e, e) <=> n0(e, e)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(343,axiom,(n0(e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_30')).
% 0.20/0.52 tff(344,plain,
% 0.20/0.52 (n0(e, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.20/0.52 tff(345,plain,
% 0.20/0.52 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(346,plain,
% 0.20/0.52 (((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b)) <=> (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(347,plain,
% 0.20/0.52 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[346])).
% 0.20/0.52 tff(348,plain,
% 0.20/0.52 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[347, 345])).
% 0.20/0.52 tff(349,plain,
% 0.20/0.52 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(350,plain,
% 0.20/0.52 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.20/0.52 tff(351,plain,
% 0.20/0.52 (q3(e, b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[350, 344, 341, 331])).
% 0.20/0.52 tff(352,plain,
% 0.20/0.52 (n0(c, d) <=> n0(c, d)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(353,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.20/0.52 tff(354,plain,
% 0.20/0.52 (n0(c, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.20/0.52 tff(355,plain,
% 0.20/0.52 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(356,plain,
% 0.20/0.52 ((((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(357,plain,
% 0.20/0.52 (((k4(c) | (~n0(c, d))) | (~q3(e, b))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(358,plain,
% 0.20/0.52 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> (((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[357])).
% 0.20/0.52 tff(359,plain,
% 0.20/0.52 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[358, 356])).
% 0.20/0.52 tff(360,axiom,(((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_274')).
% 0.20/0.52 tff(361,plain,
% 0.20/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.20/0.52 tff(362,plain,
% 0.20/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[361, 355])).
% 0.20/0.52 tff(363,plain,
% 0.20/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[362, 355])).
% 0.20/0.52 tff(364,plain,
% 0.20/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[363, 355])).
% 0.20/0.52 tff(365,plain,
% 0.20/0.52 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[364, 355])).
% 0.20/0.52 tff(366,plain,
% 0.20/0.52 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[365, 354])).
% 0.20/0.52 tff(367,plain,
% 0.20/0.52 (k4(c)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[366, 351, 294])).
% 0.20/0.52 tff(368,plain,
% 0.20/0.52 (((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(a, a) | (~m3(a, a, a)) | (~k4(c)))) <=> ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(a, a) | (~m3(a, a, a)) | (~k4(c)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(369,plain,
% 0.20/0.52 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(a, a) | (~m3(a, a, a)) | (~k4(c)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(370,plain,
% 0.20/0.52 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(a, a) | (~m3(a, a, a)) | (~k4(c))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.20/0.52 tff(371,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[370, 367, 270, 260, 165])).
% 0.20/0.52 tff(372,plain,(n4(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(373,plain,
% 0.20/0.52 ((~n5(a, e)) <=> (~n5(a, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(374,axiom,(~n5(a, e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.52 tff(375,plain,
% 0.20/0.52 (~n5(a, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.20/0.52 tff(376,plain,
% 0.20/0.52 (^[B: $i, A: $i, C: $i] : refl((n2(A) | (~p1(B, C, A))) <=> (n2(A) | (~p1(B, C, A))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(377,plain,
% 0.20/0.52 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[376])).
% 0.20/0.52 tff(378,plain,
% 0.20/0.52 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(379,axiom,(![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_137')).
% 0.20/0.52 tff(380,plain,
% 0.20/0.52 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.20/0.52 tff(381,plain,(
% 0.20/0.52 ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[380])).
% 0.20/0.52 tff(382,plain,
% 0.20/0.52 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.20/0.52 tff(383,plain,
% 0.20/0.52 (k0(e) <=> k0(e)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(384,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.20/0.52 tff(385,plain,
% 0.20/0.52 (k0(e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.20/0.52 tff(386,plain,
% 0.20/0.52 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(387,plain,
% 0.20/0.52 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(388,plain,
% 0.20/0.52 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(389,plain,
% 0.20/0.52 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[388])).
% 0.20/0.52 tff(390,plain,
% 0.20/0.52 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.20/0.52 inference(transitivity,[status(thm)],[389, 387])).
% 0.20/0.52 tff(391,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.20/0.52 tff(392,plain,
% 0.20/0.52 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.20/0.52 tff(393,plain,
% 0.20/0.52 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[392, 386])).
% 0.20/0.52 tff(394,plain,
% 0.20/0.52 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[393, 386])).
% 0.20/0.52 tff(395,plain,
% 0.20/0.52 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[394, 386])).
% 0.20/0.52 tff(396,plain,
% 0.20/0.52 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[395, 386])).
% 0.20/0.52 tff(397,plain,
% 0.20/0.52 (p1(e, e, e)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[396, 99, 385])).
% 0.20/0.52 tff(398,plain,
% 0.20/0.52 (((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))) <=> ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(399,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(400,plain,
% 0.20/0.52 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.36/0.52 tff(401,plain,
% 0.36/0.52 (n2(e)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[400, 397, 382])).
% 0.36/0.52 tff(402,plain,
% 0.36/0.52 (^[D: $i] : refl(((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(403,plain,
% 0.36/0.52 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[402])).
% 0.36/0.52 tff(404,plain,
% 0.36/0.52 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(405,plain,
% 0.36/0.52 (^[D: $i] : trans(monotonicity(rewrite((m3(D, e, e) | (~n2(e))) <=> ((~n2(e)) | m3(D, e, e))), (((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> (((~n2(e)) | m3(D, e, e)) | (~p2(D, e, e))))), rewrite((((~n2(e)) | m3(D, e, e)) | (~p2(D, e, e))) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))), (((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(406,plain,
% 0.36/0.52 (![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[405])).
% 0.36/0.52 tff(407,axiom,(![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_234')).
% 0.36/0.52 tff(408,plain,
% 0.36/0.52 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.36/0.52 tff(409,plain,
% 0.36/0.52 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[408, 404])).
% 0.36/0.52 tff(410,plain,(
% 0.36/0.52 ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(skolemize,[status(sab)],[409])).
% 0.36/0.52 tff(411,plain,
% 0.36/0.52 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[410, 403])).
% 0.36/0.52 tff(412,plain,
% 0.36/0.52 (((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))) <=> ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(413,plain,
% 0.36/0.52 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(414,plain,
% 0.36/0.52 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e)),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.36/0.52 tff(415,plain,
% 0.36/0.52 (m3(e, e, e)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[414, 411, 283, 401])).
% 0.36/0.52 tff(416,plain,
% 0.36/0.52 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(417,plain,
% 0.36/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[416])).
% 0.36/0.52 tff(418,plain,
% 0.36/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(419,plain,
% 0.36/0.52 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(420,plain,
% 0.36/0.52 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[419])).
% 0.36/0.52 tff(421,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.36/0.52 tff(422,plain,
% 0.36/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.36/0.52 tff(423,plain,
% 0.36/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.36/0.52 tff(424,plain,(
% 0.36/0.52 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(skolemize,[status(sab)],[423])).
% 0.36/0.52 tff(425,plain,
% 0.36/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[424, 417])).
% 0.36/0.52 tff(426,plain,
% 0.36/0.52 (((~![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))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(427,plain,
% 0.36/0.52 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(428,plain,
% 0.36/0.52 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.36/0.52 tff(429,plain,
% 0.36/0.52 (p1(b, b, b)),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[428, 310, 425])).
% 0.36/0.52 tff(430,plain,
% 0.36/0.52 (^[B: $i, D: $i, E: $i, C: $i] : refl(((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(431,plain,
% 0.36/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[430])).
% 0.36/0.52 tff(432,plain,
% 0.36/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(433,plain,
% 0.36/0.52 (^[B: $i, D: $i, E: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k3(B, B, C) | (~p1(C, D, B))) <=> ((~p1(C, D, B)) | k3(B, B, C))), (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) <=> (((~p1(C, D, B)) | k3(B, B, C)) | (~m2(E))))), rewrite((((~p1(C, D, B)) | k3(B, B, C)) | (~m2(E))) <=> ((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))), (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) <=> ((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)))), ((((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> (((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) | (~m2(D))))), rewrite((((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) | (~m2(D))) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))), ((((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(434,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[433])).
% 0.36/0.53 tff(435,axiom,(![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_201')).
% 0.36/0.53 tff(436,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.36/0.53 tff(437,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.36/0.53 tff(438,plain,(
% 0.36/0.53 ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.53 inference(skolemize,[status(sab)],[437])).
% 0.36/0.53 tff(439,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.36/0.53 tff(440,plain,
% 0.36/0.53 ((m2(b) | (~k1(b))) <=> (m2(b) | (~k1(b)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(441,axiom,(m2(b) | (~k1(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_136')).
% 0.36/0.53 tff(442,plain,
% 0.36/0.53 (m2(b) | (~k1(b))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.36/0.53 tff(443,plain,
% 0.36/0.53 (m2(b)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[442, 57])).
% 0.36/0.53 tff(444,plain,
% 0.36/0.53 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(445,plain,
% 0.36/0.53 (((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b)) <=> ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(446,plain,
% 0.36/0.53 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[445])).
% 0.36/0.53 tff(447,plain,
% 0.36/0.53 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.36/0.53 inference(transitivity,[status(thm)],[446, 444])).
% 0.36/0.53 tff(448,plain,
% 0.36/0.53 ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(449,plain,
% 0.36/0.53 ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.36/0.53 tff(450,plain,
% 0.36/0.53 (k3(b, b, b)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[449, 443, 439, 429])).
% 0.36/0.53 tff(451,plain,
% 0.36/0.53 (((~![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))) | ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, 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))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(452,plain,
% 0.36/0.53 (((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e)) <=> ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(453,plain,
% 0.36/0.53 (((~![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(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, 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))) | ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[452])).
% 0.36/0.53 tff(454,plain,
% 0.36/0.53 (((~![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(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, 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))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.36/0.53 inference(transitivity,[status(thm)],[453, 451])).
% 0.36/0.53 tff(455,plain,
% 0.36/0.53 ((~![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(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(456,plain,
% 0.36/0.53 ((~![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))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.36/0.53 tff(457,plain,
% 0.36/0.53 (q4(b, e)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[456, 195, 450, 331, 415])).
% 0.36/0.53 tff(458,plain,
% 0.36/0.53 (^[D: $i, C: $i] : refl((n5(C, C) | (~q4(D, C))) <=> (n5(C, C) | (~q4(D, C))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(459,plain,
% 0.36/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[458])).
% 0.36/0.53 tff(460,plain,
% 0.36/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(461,axiom,(![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_313')).
% 0.36/0.53 tff(462,plain,
% 0.36/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.36/0.53 tff(463,plain,(
% 0.36/0.53 ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.36/0.53 inference(skolemize,[status(sab)],[462])).
% 0.36/0.53 tff(464,plain,
% 0.36/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[463, 459])).
% 0.36/0.53 tff(465,plain,
% 0.36/0.53 (((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(e, e) | (~q4(b, e)))) <=> ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(e, e) | (~q4(b, e)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(466,plain,
% 0.36/0.53 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(e, e) | (~q4(b, e)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(467,plain,
% 0.36/0.53 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(e, e) | (~q4(b, e))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.36/0.53 tff(468,plain,
% 0.36/0.53 (n5(e, e)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[467, 464, 457])).
% 0.36/0.53 tff(469,assumption,(~n4(b, b)), introduced(assumption)).
% 0.36/0.53 tff(470,plain,
% 0.36/0.53 (^[A: $i] : refl((p2(A, A, A) | (~q1(A, A, A))) <=> (p2(A, A, A) | (~q1(A, A, A))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(471,plain,
% 0.36/0.53 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[470])).
% 0.36/0.53 tff(472,plain,
% 0.36/0.53 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(473,axiom,(![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_154')).
% 0.36/0.53 tff(474,plain,
% 0.36/0.53 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.36/0.53 tff(475,plain,(
% 0.36/0.53 ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.36/0.53 inference(skolemize,[status(sab)],[474])).
% 0.36/0.53 tff(476,plain,
% 0.36/0.53 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[475, 471])).
% 0.36/0.53 tff(477,plain,
% 0.36/0.53 (((~r0(b)) | q1(b, b, b)) <=> ((~r0(b)) | q1(b, b, b))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(478,plain,
% 0.36/0.53 ((q1(b, b, b) | (~r0(b))) <=> ((~r0(b)) | q1(b, b, b))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(479,axiom,(q1(b, b, b) | (~r0(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_120')).
% 0.36/0.53 tff(480,plain,
% 0.36/0.53 ((~r0(b)) | q1(b, b, b)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.36/0.53 tff(481,plain,
% 0.36/0.53 ((~r0(b)) | q1(b, b, b)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[480, 477])).
% 0.36/0.53 tff(482,plain,
% 0.36/0.53 (q1(b, b, b)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[481, 118])).
% 0.36/0.53 tff(483,plain,
% 0.36/0.53 (((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | (p2(b, b, b) | (~q1(b, b, b)))) <=> ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | p2(b, b, b) | (~q1(b, b, b)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(484,plain,
% 0.36/0.53 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | (p2(b, b, b) | (~q1(b, b, b)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(485,plain,
% 0.36/0.53 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | p2(b, b, b) | (~q1(b, b, b))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.36/0.53 tff(486,plain,
% 0.36/0.53 (p2(b, b, b)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[485, 482, 476])).
% 0.36/0.53 tff(487,plain,
% 0.36/0.53 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(b, b, b) | (~p2(b, b, b)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | m3(b, b, b) | (~p2(b, b, b)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(488,plain,
% 0.36/0.53 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(b, b, b) | (~p2(b, b, b)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(489,plain,
% 0.36/0.53 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | m3(b, b, b) | (~p2(b, b, b))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.36/0.53 tff(490,plain,
% 0.36/0.53 (m3(b, b, b)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[489, 129, 486])).
% 0.36/0.53 tff(491,plain,
% 0.36/0.53 (((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(b, b) | (~m3(b, b, b)) | (~k4(c)))) <=> ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(b, b) | (~m3(b, b, b)) | (~k4(c)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(492,plain,
% 0.36/0.53 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(b, b) | (~m3(b, b, b)) | (~k4(c)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(493,plain,
% 0.36/0.53 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(b, b) | (~m3(b, b, b)) | (~k4(c))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.36/0.53 tff(494,plain,
% 0.36/0.53 ($false),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[493, 490, 367, 270, 469])).
% 0.36/0.53 tff(495,plain,(n4(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.36/0.53 tff(496,plain,
% 0.36/0.53 (^[I: $i, A: $i, J: $i] : refl(((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)) <=> ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(497,plain,
% 0.36/0.53 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)) <=> ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[496])).
% 0.36/0.53 tff(498,plain,
% 0.36/0.53 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)) <=> ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(499,plain,
% 0.36/0.53 (^[I: $i, A: $i, J: $i] : trans(monotonicity(rewrite((k3(I, I, I) | (~r1(I))) <=> ((~r1(I)) | k3(I, I, I))), (((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A))) <=> (((~r1(I)) | k3(I, I, I)) | (~p2(J, A, A))))), rewrite((((~r1(I)) | k3(I, I, I)) | (~p2(J, A, A))) <=> ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))), (((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A))) <=> ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(500,plain,
% 0.36/0.53 (![I: $i, A: $i, J: $i] : ((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A))) <=> ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[499])).
% 0.36/0.53 tff(501,axiom,(![I: $i, A: $i, J: $i] : ((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_213')).
% 0.36/0.53 tff(502,plain,
% 0.36/0.53 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.36/0.53 tff(503,plain,
% 0.36/0.53 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.36/0.53 tff(504,plain,(
% 0.36/0.53 ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(skolemize,[status(sab)],[503])).
% 0.36/0.53 tff(505,plain,
% 0.36/0.53 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[504, 497])).
% 0.36/0.53 tff(506,plain,
% 0.36/0.53 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(507,plain,
% 0.36/0.53 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(508,plain,
% 0.36/0.53 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(509,plain,
% 0.36/0.53 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[508])).
% 0.36/0.53 tff(510,plain,
% 0.36/0.53 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.36/0.53 inference(transitivity,[status(thm)],[509, 507])).
% 0.36/0.53 tff(511,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.36/0.53 tff(512,plain,
% 0.36/0.53 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.36/0.53 tff(513,plain,
% 0.36/0.53 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[512, 506])).
% 0.36/0.53 tff(514,plain,
% 0.36/0.53 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[513, 506])).
% 0.36/0.53 tff(515,plain,
% 0.36/0.53 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[514, 506])).
% 0.36/0.53 tff(516,plain,
% 0.36/0.53 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[515, 506])).
% 0.36/0.53 tff(517,plain,
% 0.36/0.53 (q1(d, d, d)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[516, 142, 385])).
% 0.36/0.53 tff(518,plain,
% 0.36/0.53 (q0(e, d) <=> q0(e, d)),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(519,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.36/0.53 tff(520,plain,
% 0.36/0.53 (q0(e, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.36/0.53 tff(521,plain,
% 0.36/0.53 (((~![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)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(522,plain,
% 0.36/0.53 (((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e)) <=> ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(523,plain,
% 0.36/0.53 (((~![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))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[522])).
% 0.36/0.53 tff(524,plain,
% 0.36/0.53 (((~![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)))),
% 0.36/0.53 inference(transitivity,[status(thm)],[523, 521])).
% 0.36/0.53 tff(525,plain,
% 0.36/0.53 ((~![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))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(526,plain,
% 0.36/0.53 ((~![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))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.36/0.53 tff(527,plain,
% 0.36/0.53 (r1(e)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[526, 142, 520, 517, 222])).
% 0.36/0.53 tff(528,plain,
% 0.36/0.53 (^[B: $i] : refl((p2(B, B, B) | (~n1(d, d, B))) <=> (p2(B, B, B) | (~n1(d, d, B))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(529,plain,
% 0.36/0.53 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[528])).
% 0.36/0.53 tff(530,plain,
% 0.36/0.53 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(531,axiom,(![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_153')).
% 0.36/0.53 tff(532,plain,
% 0.36/0.53 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.36/0.53 tff(533,plain,(
% 0.36/0.53 ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.36/0.53 inference(skolemize,[status(sab)],[532])).
% 0.36/0.53 tff(534,plain,
% 0.36/0.53 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[533, 529])).
% 0.36/0.53 tff(535,plain,
% 0.36/0.53 (q0(d, d) <=> q0(d, d)),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(536,axiom,(q0(d, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.36/0.53 tff(537,plain,
% 0.36/0.53 (q0(d, d)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.36/0.53 tff(538,plain,
% 0.36/0.53 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(539,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 0.36/0.53 tff(540,plain,
% 0.36/0.53 (n1(d, d, d) | (~q0(d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.36/0.53 tff(541,plain,
% 0.36/0.53 (n1(d, d, d) | (~q0(d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[540, 538])).
% 0.36/0.53 tff(542,plain,
% 0.36/0.53 (n1(d, d, d) | (~q0(d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[541, 538])).
% 0.36/0.53 tff(543,plain,
% 0.36/0.53 (n1(d, d, d) | (~q0(d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[542, 538])).
% 0.36/0.53 tff(544,plain,
% 0.36/0.53 (n1(d, d, d) | (~q0(d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[543, 538])).
% 0.36/0.53 tff(545,plain,
% 0.36/0.53 (n1(d, d, d)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[544, 537])).
% 0.36/0.53 tff(546,plain,
% 0.36/0.53 (((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))) <=> ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(547,plain,
% 0.36/0.53 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(548,plain,
% 0.36/0.53 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.36/0.53 tff(549,plain,
% 0.36/0.53 (p2(d, d, d)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[548, 545, 534])).
% 0.36/0.53 tff(550,plain,
% 0.36/0.53 (((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))) <=> ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | (~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(551,plain,
% 0.36/0.53 (((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e)) <=> ((~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(552,plain,
% 0.36/0.53 (((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e))) <=> ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~r1(e)) | k3(e, e, e) | (~p2(d, d, d))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[551])).
% 0.36/0.53 tff(553,plain,
% 0.36/0.53 (((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e))) <=> ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | (~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))),
% 0.36/0.53 inference(transitivity,[status(thm)],[552, 550])).
% 0.36/0.53 tff(554,plain,
% 0.36/0.53 ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(555,plain,
% 0.36/0.53 ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | (~r1(e)) | k3(e, e, e) | (~p2(d, d, d))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.36/0.53 tff(556,plain,
% 0.36/0.53 (k3(e, e, e)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[555, 549, 527, 505])).
% 0.36/0.53 tff(557,plain,
% 0.36/0.53 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(558,plain,
% 0.36/0.53 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[557])).
% 0.36/0.53 tff(559,plain,
% 0.36/0.53 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(560,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.36/0.53 tff(561,plain,
% 0.36/0.53 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.36/0.53 tff(562,plain,(
% 0.36/0.53 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.36/0.53 inference(skolemize,[status(sab)],[561])).
% 0.36/0.53 tff(563,plain,
% 0.36/0.53 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[562, 558])).
% 0.36/0.53 tff(564,plain,
% 0.36/0.53 (((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(e, e, e) | (~k3(e, e, e)))) <=> ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(e, e, e) | (~k3(e, e, e)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(565,plain,
% 0.36/0.53 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(e, e, e) | (~k3(e, e, e)))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(566,plain,
% 0.36/0.53 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(e, e, e) | (~k3(e, e, e))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.36/0.53 tff(567,plain,
% 0.36/0.53 (p4(e, e, e)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[566, 563, 556])).
% 0.36/0.53 tff(568,plain,
% 0.36/0.53 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(569,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[568])).
% 0.36/0.53 tff(570,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(571,plain,
% 0.36/0.53 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((n5(B, C) | (~q4(D, E))) <=> ((~q4(D, E)) | n5(B, C))), (((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) <=> (((~q4(D, E)) | n5(B, C)) | (~n4(B, E))))), rewrite((((~q4(D, E)) | n5(B, C)) | (~n4(B, E))) <=> ((~n4(B, E)) | (~q4(D, E)) | n5(B, C))), (((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) <=> ((~n4(B, E)) | (~q4(D, E)) | n5(B, C)))), ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) <=> (((~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~p4(F, F, C))))), rewrite((((~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~p4(F, F, C))) <=> ((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))), ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) <=> ((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)))), (((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> (((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~n5(F, C))))), rewrite((((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~n5(F, C))) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))), (((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(572,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[571])).
% 0.36/0.53 tff(573,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_307')).
% 0.36/0.53 tff(574,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.36/0.53 tff(575,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.36/0.53 tff(576,plain,(
% 0.36/0.53 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(skolemize,[status(sab)],[575])).
% 0.36/0.53 tff(577,plain,
% 0.36/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[576, 569])).
% 0.36/0.53 tff(578,plain,
% 0.36/0.53 (n0(d, c) <=> n0(d, c)),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(579,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.36/0.53 tff(580,plain,
% 0.36/0.53 (n0(d, c)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.36/0.53 tff(581,plain,
% 0.36/0.53 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(582,plain,
% 0.36/0.53 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(583,plain,
% 0.36/0.53 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b)),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.36/0.53 tff(584,plain,
% 0.36/0.53 (q1(b, c, b)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[583, 310, 580, 205])).
% 0.36/0.53 tff(585,plain,
% 0.36/0.53 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(586,plain,
% 0.36/0.53 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[585])).
% 0.36/0.53 tff(587,plain,
% 0.36/0.53 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(588,plain,
% 0.36/0.53 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.36/0.53 inference(bind,[status(th)],[])).
% 0.36/0.53 tff(589,plain,
% 0.36/0.53 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[588])).
% 0.36/0.53 tff(590,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 0.36/0.53 tff(591,plain,
% 0.36/0.53 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.36/0.53 tff(592,plain,
% 0.36/0.53 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[591, 587])).
% 0.36/0.53 tff(593,plain,(
% 0.36/0.53 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(skolemize,[status(sab)],[592])).
% 0.36/0.53 tff(594,plain,
% 0.36/0.53 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[593, 586])).
% 0.36/0.53 tff(595,plain,
% 0.36/0.53 (((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))) <=> ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(596,plain,
% 0.36/0.54 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(597,plain,
% 0.36/0.54 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.36/0.54 tff(598,plain,
% 0.36/0.54 (q2(b, b, b)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[597, 594, 584])).
% 0.36/0.54 tff(599,plain,
% 0.36/0.54 (((~![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(b, b) | (~k3(b, b, b)) | (~m3(b, b, b)) | (~q2(b, b, b)))) <=> ((~![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(b, b) | (~k3(b, b, b)) | (~m3(b, b, b)) | (~q2(b, b, b)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(600,plain,
% 0.36/0.54 (((~m3(b, b, b)) | (~q2(b, b, b)) | (~k3(b, b, b)) | q4(b, b)) <=> (q4(b, b) | (~k3(b, b, b)) | (~m3(b, b, b)) | (~q2(b, b, b)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(601,plain,
% 0.36/0.54 (((~![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(b, b, b)) | (~q2(b, b, b)) | (~k3(b, b, b)) | q4(b, b))) <=> ((~![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(b, b) | (~k3(b, b, b)) | (~m3(b, b, b)) | (~q2(b, b, b))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[600])).
% 0.36/0.54 tff(602,plain,
% 0.36/0.54 (((~![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(b, b, b)) | (~q2(b, b, b)) | (~k3(b, b, b)) | q4(b, b))) <=> ((~![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(b, b) | (~k3(b, b, b)) | (~m3(b, b, b)) | (~q2(b, b, b)))),
% 0.36/0.54 inference(transitivity,[status(thm)],[601, 599])).
% 0.36/0.54 tff(603,plain,
% 0.36/0.54 ((~![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(b, b, b)) | (~q2(b, b, b)) | (~k3(b, b, b)) | q4(b, b))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(604,plain,
% 0.36/0.54 ((~![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(b, b) | (~k3(b, b, b)) | (~m3(b, b, b)) | (~q2(b, b, b))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.36/0.54 tff(605,plain,
% 0.36/0.54 (q4(b, b)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[604, 490, 195, 598, 450])).
% 0.36/0.54 tff(606,plain,
% 0.36/0.54 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(b, e) | (~n4(b, b)) | (~q4(b, b)) | (~p4(e, e, e)) | (~n5(e, e)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(b, e) | (~n4(b, b)) | (~q4(b, b)) | (~p4(e, e, e)) | (~n5(e, e)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(607,plain,
% 0.36/0.54 (((~n5(e, e)) | (~p4(e, e, e)) | (~n4(b, b)) | (~q4(b, b)) | n5(b, e)) <=> (n5(b, e) | (~n4(b, b)) | (~q4(b, b)) | (~p4(e, e, e)) | (~n5(e, e)))),
% 0.36/0.54 inference(rewrite,[status(thm)],[])).
% 0.36/0.54 tff(608,plain,
% 0.36/0.54 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(e, e)) | (~p4(e, e, e)) | (~n4(b, b)) | (~q4(b, b)) | n5(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(b, e) | (~n4(b, b)) | (~q4(b, b)) | (~p4(e, e, e)) | (~n5(e, e))))),
% 0.36/0.54 inference(monotonicity,[status(thm)],[607])).
% 0.36/0.54 tff(609,plain,
% 0.36/0.54 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(e, e)) | (~p4(e, e, e)) | (~n4(b, b)) | (~q4(b, b)) | n5(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(b, e) | (~n4(b, b)) | (~q4(b, b)) | (~p4(e, e, e)) | (~n5(e, e)))),
% 0.36/0.54 inference(transitivity,[status(thm)],[608, 606])).
% 0.36/0.54 tff(610,plain,
% 0.36/0.54 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(e, e)) | (~p4(e, e, e)) | (~n4(b, b)) | (~q4(b, b)) | n5(b, e))),
% 0.36/0.54 inference(quant_inst,[status(thm)],[])).
% 0.36/0.54 tff(611,plain,
% 0.36/0.54 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(b, e) | (~n4(b, b)) | (~q4(b, b)) | (~p4(e, e, e)) | (~n5(e, e))),
% 0.36/0.54 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.36/0.54 tff(612,plain,
% 0.36/0.54 (n5(b, e)),
% 0.36/0.54 inference(unit_resolution,[status(thm)],[611, 605, 577, 567, 495, 468])).
% 0.36/0.54 tff(613,plain,
% 0.36/0.54 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~n5(b, e)) | (~p4(b, b, e)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~n5(b, e)) | (~p4(b, b, e)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(614,plain,
% 0.38/0.55 (((~n5(b, e)) | (~p4(b, b, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e)) <=> (n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~n5(b, e)) | (~p4(b, b, e)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(615,plain,
% 0.38/0.55 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(b, e)) | (~p4(b, b, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~n5(b, e)) | (~p4(b, b, e))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[614])).
% 0.38/0.55 tff(616,plain,
% 0.38/0.55 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(b, e)) | (~p4(b, b, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~n5(b, e)) | (~p4(b, b, e)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[615, 613])).
% 0.38/0.55 tff(617,plain,
% 0.38/0.55 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(b, e)) | (~p4(b, b, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(618,plain,
% 0.38/0.55 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~n5(b, e)) | (~p4(b, b, e))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.38/0.55 tff(619,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[618, 577, 612, 375, 372, 259, 122])).
% 0.38/0.55 % SZS output end Proof
% 0.38/0.55 % E exiting
%------------------------------------------------------------------------------