%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN269-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:38 AM UTC 2025
% Result : Unsatisfiable 0.24s 0.50s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYN269-1 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:30:08 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.24/0.50 % SZS status Unsatisfiable
% 0.24/0.50 % SZS output start Proof
% 0.24/0.50 tff(r3_type, type, (
% 0.24/0.50 r3: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(b_type, type, (
% 0.24/0.50 b: $i)).
% 0.24/0.50 tff(a_type, type, (
% 0.24/0.50 a: $i)).
% 0.24/0.50 tff(m3_type, type, (
% 0.24/0.50 m3: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(k3_type, type, (
% 0.24/0.50 k3: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(p2_type, type, (
% 0.24/0.50 p2: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(m1_type, type, (
% 0.24/0.50 m1: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(p0_type, type, (
% 0.24/0.50 p0: ( $i * $i ) > $o)).
% 0.24/0.50 tff(s0_type, type, (
% 0.24/0.50 s0: $i > $o)).
% 0.24/0.50 tff(l1_type, type, (
% 0.24/0.50 l1: ( $i * $i ) > $o)).
% 0.24/0.50 tff(n0_type, type, (
% 0.24/0.50 n0: ( $i * $i ) > $o)).
% 0.24/0.50 tff(p1_type, type, (
% 0.24/0.50 p1: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(l0_type, type, (
% 0.24/0.50 l0: $i > $o)).
% 0.24/0.50 tff(r2_type, type, (
% 0.24/0.50 r2: $i > $o)).
% 0.24/0.50 tff(r1_type, type, (
% 0.24/0.50 r1: $i > $o)).
% 0.24/0.50 tff(q1_type, type, (
% 0.24/0.50 q1: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(d_type, type, (
% 0.24/0.50 d: $i)).
% 0.24/0.50 tff(q0_type, type, (
% 0.24/0.50 q0: ( $i * $i ) > $o)).
% 0.24/0.50 tff(r0_type, type, (
% 0.24/0.50 r0: $i > $o)).
% 0.24/0.50 tff(m2_type, type, (
% 0.24/0.50 m2: $i > $o)).
% 0.24/0.50 tff(k1_type, type, (
% 0.24/0.50 k1: $i > $o)).
% 0.24/0.50 tff(p4_type, type, (
% 0.24/0.50 p4: ( $i * $i * $i ) > $o)).
% 0.24/0.50 tff(1,assumption,(~p0(b, a)), introduced(assumption)).
% 0.24/0.50 tff(2,plain,
% 0.24/0.50 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(3,plain,
% 0.24/0.50 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.24/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.24/0.50 tff(4,plain,
% 0.24/0.50 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.24/0.50 tff(6,plain,
% 0.24/0.50 (![X: $i] : p0(b, X)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.24/0.50 tff(7,plain,(
% 0.24/0.50 ![X: $i] : p0(b, X)),
% 0.24/0.50 inference(skolemize,[status(sab)],[6])).
% 0.24/0.50 tff(8,plain,
% 0.24/0.50 (![X: $i] : p0(b, X)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.24/0.50 tff(9,plain,
% 0.24/0.50 ((~![X: $i] : p0(b, X)) | p0(b, a)),
% 0.24/0.50 inference(quant_inst,[status(thm)],[])).
% 0.24/0.50 tff(10,plain,
% 0.24/0.50 ($false),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.24/0.50 tff(11,plain,(p0(b, a)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.50 tff(12,plain,
% 0.24/0.50 (^[I: $i, H: $i] : refl((m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(13,plain,
% 0.24/0.50 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.24/0.50 tff(14,plain,
% 0.24/0.50 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(15,plain,
% 0.24/0.50 (^[I: $i, H: $i] : trans(monotonicity(rewrite((m1(H, I, H) | (~p0(H, I))) <=> (m1(H, I, H) | (~p0(H, I)))), (((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> ((m1(H, I, H) | (~p0(H, I))) | (~s0(H))))), rewrite(((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))), (((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(16,plain,
% 0.24/0.50 (![I: $i, H: $i] : ((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[15])).
% 0.24/0.50 tff(17,axiom,(![I: $i, H: $i] : ((m1(H, I, H) | (~p0(H, I))) | (~s0(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_029')).
% 0.24/0.50 tff(18,plain,
% 0.24/0.50 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.24/0.50 tff(19,plain,
% 0.24/0.50 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.24/0.50 tff(20,plain,(
% 0.24/0.50 ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(skolemize,[status(sab)],[19])).
% 0.24/0.50 tff(21,plain,
% 0.24/0.50 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.24/0.50 tff(22,plain,
% 0.24/0.50 (s0(b) <=> s0(b)),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(23,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.24/0.50 tff(24,plain,
% 0.24/0.50 (s0(b)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.24/0.50 tff(25,plain,
% 0.24/0.50 (((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | ((~s0(b)) | (~p0(b, a)) | m1(b, a, b))) <=> ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, a)) | m1(b, a, b))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(26,plain,
% 0.24/0.50 ((m1(b, a, b) | (~p0(b, a)) | (~s0(b))) <=> ((~s0(b)) | (~p0(b, a)) | m1(b, a, b))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(27,plain,
% 0.24/0.50 (((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, a, b) | (~p0(b, a)) | (~s0(b)))) <=> ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | ((~s0(b)) | (~p0(b, a)) | m1(b, a, b)))),
% 0.24/0.50 inference(monotonicity,[status(thm)],[26])).
% 0.24/0.50 tff(28,plain,
% 0.24/0.50 (((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, a, b) | (~p0(b, a)) | (~s0(b)))) <=> ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, a)) | m1(b, a, b))),
% 0.24/0.50 inference(transitivity,[status(thm)],[27, 25])).
% 0.24/0.50 tff(29,plain,
% 0.24/0.50 ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, a, b) | (~p0(b, a)) | (~s0(b)))),
% 0.24/0.50 inference(quant_inst,[status(thm)],[])).
% 0.24/0.50 tff(30,plain,
% 0.24/0.50 ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, a)) | m1(b, a, b)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.24/0.50 tff(31,plain,
% 0.24/0.50 (m1(b, a, b)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[30, 24, 21, 11])).
% 0.24/0.50 tff(32,plain,
% 0.24/0.50 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(33,plain,
% 0.24/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.24/0.50 tff(34,plain,
% 0.24/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(35,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.24/0.50 tff(36,plain,
% 0.24/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.24/0.50 tff(37,plain,(
% 0.24/0.50 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.24/0.50 inference(skolemize,[status(sab)],[36])).
% 0.24/0.50 tff(38,plain,
% 0.24/0.50 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.24/0.50 tff(39,plain,
% 0.24/0.50 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(b, a, b)) | p2(a, b, a))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(b, a, b)) | p2(a, b, a))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(40,plain,
% 0.24/0.50 ((p2(a, b, a) | (~m1(b, a, b))) <=> ((~m1(b, a, b)) | p2(a, b, a))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(41,plain,
% 0.24/0.50 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, b, a) | (~m1(b, a, b)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(b, a, b)) | p2(a, b, a)))),
% 0.24/0.50 inference(monotonicity,[status(thm)],[40])).
% 0.24/0.50 tff(42,plain,
% 0.24/0.50 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, b, a) | (~m1(b, a, b)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(b, a, b)) | p2(a, b, a))),
% 0.24/0.50 inference(transitivity,[status(thm)],[41, 39])).
% 0.24/0.50 tff(43,plain,
% 0.24/0.50 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, b, a) | (~m1(b, a, b)))),
% 0.24/0.50 inference(quant_inst,[status(thm)],[])).
% 0.24/0.50 tff(44,plain,
% 0.24/0.50 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(b, a, b)) | p2(a, b, a)),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.24/0.50 tff(45,plain,
% 0.24/0.50 (p2(a, b, a)),
% 0.24/0.50 inference(unit_resolution,[status(thm)],[44, 38, 31])).
% 0.24/0.50 tff(46,plain,
% 0.24/0.50 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(47,plain,
% 0.24/0.50 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[46])).
% 0.24/0.50 tff(48,plain,
% 0.24/0.50 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(49,plain,
% 0.24/0.51 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(50,plain,
% 0.24/0.51 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[49])).
% 0.24/0.51 tff(51,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.24/0.51 tff(52,plain,
% 0.24/0.51 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.24/0.51 tff(53,plain,
% 0.24/0.51 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.24/0.51 tff(54,plain,(
% 0.24/0.51 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.51 inference(skolemize,[status(sab)],[53])).
% 0.24/0.51 tff(55,plain,
% 0.24/0.51 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.24/0.51 tff(56,plain,
% 0.24/0.51 (n0(b, a) <=> n0(b, a)),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(57,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.24/0.51 tff(58,plain,
% 0.24/0.51 (n0(b, a)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.24/0.51 tff(59,plain,
% 0.24/0.51 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(60,plain,
% 0.24/0.51 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(61,plain,
% 0.24/0.51 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.24/0.51 tff(62,plain,
% 0.24/0.51 (l1(a, a)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[61, 58, 55])).
% 0.24/0.51 tff(63,plain,
% 0.24/0.51 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)) <=> ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(64,plain,
% 0.24/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[63])).
% 0.24/0.51 tff(65,plain,
% 0.24/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(66,plain,
% 0.24/0.51 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((p2(C, D, D) | (~p1(C, E, F))) <=> ((~p1(C, E, F)) | p2(C, D, D))), (((p2(C, D, D) | (~p1(C, E, F))) | (~l1(E, F))) <=> (((~p1(C, E, F)) | p2(C, D, D)) | (~l1(E, F))))), rewrite((((~p1(C, E, F)) | p2(C, D, D)) | (~l1(E, F))) <=> ((~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))), (((p2(C, D, D) | (~p1(C, E, F))) | (~l1(E, F))) <=> ((~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)))), ((((p2(C, D, D) | (~p1(C, E, F))) | (~l1(E, F))) | (~p2(C, D, C))) <=> (((~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)) | (~p2(C, D, C))))), rewrite((((~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D)) | (~p2(C, D, C))) <=> ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))), ((((p2(C, D, D) | (~p1(C, E, F))) | (~l1(E, F))) | (~p2(C, D, C))) <=> ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(67,plain,
% 0.24/0.51 (![D: $i, E: $i, F: $i, C: $i] : (((p2(C, D, D) | (~p1(C, E, F))) | (~l1(E, F))) | (~p2(C, D, C))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[66])).
% 0.24/0.51 tff(68,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((p2(C, D, D) | (~p1(C, E, F))) | (~l1(E, F))) | (~p2(C, D, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_146')).
% 0.24/0.51 tff(69,plain,
% 0.24/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.24/0.51 tff(70,plain,
% 0.24/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.24/0.51 tff(71,plain,(
% 0.24/0.51 ![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(skolemize,[status(sab)],[70])).
% 0.24/0.51 tff(72,plain,
% 0.24/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.24/0.51 tff(73,plain,
% 0.24/0.51 (l0(a) <=> l0(a)),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(74,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.24/0.51 tff(75,plain,
% 0.24/0.51 (l0(a)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.24/0.51 tff(76,plain,
% 0.24/0.51 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(77,plain,
% 0.24/0.51 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(78,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.24/0.51 tff(79,plain,
% 0.24/0.51 ((~l0(a)) | p1(a, a, a)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.24/0.51 tff(80,plain,
% 0.24/0.51 ((~l0(a)) | p1(a, a, a)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.24/0.51 tff(81,plain,
% 0.24/0.51 (p1(a, a, a)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.24/0.51 tff(82,plain,
% 0.24/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | ((~p1(a, a, a)) | (~l1(a, a)) | (~p2(a, b, a)) | p2(a, b, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | (~p1(a, a, a)) | (~l1(a, a)) | (~p2(a, b, a)) | p2(a, b, b))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(83,plain,
% 0.24/0.51 (((~p2(a, b, a)) | (~l1(a, a)) | (~p1(a, a, a)) | p2(a, b, b)) <=> ((~p1(a, a, a)) | (~l1(a, a)) | (~p2(a, b, a)) | p2(a, b, b))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(84,plain,
% 0.24/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | ((~p2(a, b, a)) | (~l1(a, a)) | (~p1(a, a, a)) | p2(a, b, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | ((~p1(a, a, a)) | (~l1(a, a)) | (~p2(a, b, a)) | p2(a, b, b)))),
% 0.24/0.51 inference(monotonicity,[status(thm)],[83])).
% 0.24/0.51 tff(85,plain,
% 0.24/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | ((~p2(a, b, a)) | (~l1(a, a)) | (~p1(a, a, a)) | p2(a, b, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | (~p1(a, a, a)) | (~l1(a, a)) | (~p2(a, b, a)) | p2(a, b, b))),
% 0.24/0.51 inference(transitivity,[status(thm)],[84, 82])).
% 0.24/0.51 tff(86,plain,
% 0.24/0.51 ((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | ((~p2(a, b, a)) | (~l1(a, a)) | (~p1(a, a, a)) | p2(a, b, b))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(87,plain,
% 0.24/0.51 ((~![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))) | (~p1(a, a, a)) | (~l1(a, a)) | (~p2(a, b, a)) | p2(a, b, b)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.24/0.51 tff(88,plain,
% 0.24/0.51 (p2(a, b, b)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[87, 81, 72, 62, 45])).
% 0.24/0.51 tff(89,plain,
% 0.24/0.51 (^[D: $i, C: $i] : refl(((~p2(D, C, C)) | k3(C, D, C)) <=> ((~p2(D, C, C)) | k3(C, D, C)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(90,plain,
% 0.24/0.51 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C)) <=> ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.24/0.51 tff(91,plain,
% 0.24/0.51 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C)) <=> ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(92,plain,
% 0.24/0.51 (^[D: $i, C: $i] : rewrite((k3(C, D, C) | (~p2(D, C, C))) <=> ((~p2(D, C, C)) | k3(C, D, C)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(93,plain,
% 0.24/0.51 (![D: $i, C: $i] : (k3(C, D, C) | (~p2(D, C, C))) <=> ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[92])).
% 0.24/0.51 tff(94,axiom,(![D: $i, C: $i] : (k3(C, D, C) | (~p2(D, C, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_206')).
% 0.24/0.51 tff(95,plain,
% 0.24/0.51 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.24/0.51 tff(96,plain,
% 0.24/0.51 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.24/0.51 tff(97,plain,(
% 0.24/0.51 ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(skolemize,[status(sab)],[96])).
% 0.24/0.51 tff(98,plain,
% 0.24/0.51 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.24/0.51 tff(99,plain,
% 0.24/0.51 (((~![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))) | ((~p2(a, b, b)) | k3(b, a, b))) <=> ((~![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))) | (~p2(a, b, b)) | k3(b, a, b))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(100,plain,
% 0.24/0.51 ((~![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))) | ((~p2(a, b, b)) | k3(b, a, b))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(101,plain,
% 0.24/0.51 ((~![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))) | (~p2(a, b, b)) | k3(b, a, b)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.24/0.51 tff(102,plain,
% 0.24/0.51 (k3(b, a, b)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.24/0.51 tff(103,plain,
% 0.24/0.51 (^[B: $i, C: $i] : refl(((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)) <=> ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(104,plain,
% 0.24/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)) <=> ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[103])).
% 0.24/0.51 tff(105,plain,
% 0.24/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C)) <=> ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(106,plain,
% 0.24/0.51 (^[B: $i, C: $i] : trans(monotonicity(rewrite((m3(B, B, C) | (~r2(C))) <=> ((~r2(C)) | m3(B, B, C))), (((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B))) <=> (((~r2(C)) | m3(B, B, C)) | (~k3(B, C, B))))), rewrite((((~r2(C)) | m3(B, B, C)) | (~k3(B, C, B))) <=> ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))), (((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B))) <=> ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(107,plain,
% 0.24/0.51 (![B: $i, C: $i] : ((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B))) <=> ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[106])).
% 0.24/0.51 tff(108,axiom,(![B: $i, C: $i] : ((m3(B, B, C) | (~r2(C))) | (~k3(B, C, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_235')).
% 0.24/0.51 tff(109,plain,
% 0.24/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.24/0.51 tff(110,plain,
% 0.24/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.24/0.51 tff(111,plain,(
% 0.24/0.51 ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(skolemize,[status(sab)],[110])).
% 0.24/0.51 tff(112,plain,
% 0.24/0.51 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.24/0.51 tff(113,plain,
% 0.24/0.51 (^[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)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(114,plain,
% 0.24/0.51 (![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))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[113])).
% 0.24/0.51 tff(115,plain,
% 0.24/0.51 (![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))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(116,plain,
% 0.24/0.51 (^[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))))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(117,plain,
% 0.24/0.51 (![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))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[116])).
% 0.24/0.51 tff(118,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.24/0.51 tff(119,plain,
% 0.24/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.24/0.51 tff(120,plain,
% 0.24/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.24/0.51 tff(121,plain,(
% 0.24/0.51 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.24/0.51 inference(skolemize,[status(sab)],[120])).
% 0.24/0.51 tff(122,plain,
% 0.24/0.51 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.24/0.51 tff(123,plain,
% 0.24/0.51 (p0(b, d) <=> p0(b, d)),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(124,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.24/0.51 tff(125,plain,
% 0.24/0.51 (p0(b, d)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.24/0.51 tff(126,plain,
% 0.24/0.51 (n0(d, b) <=> n0(d, b)),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(127,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.24/0.51 tff(128,plain,
% 0.24/0.51 (n0(d, b)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.24/0.51 tff(129,plain,
% 0.24/0.51 (((~![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))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(130,plain,
% 0.24/0.51 ((~![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))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(131,plain,
% 0.24/0.51 ((~![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)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.24/0.51 tff(132,plain,
% 0.24/0.51 (q1(d, b, d)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[131, 128, 125, 122])).
% 0.24/0.51 tff(133,plain,
% 0.24/0.51 (^[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)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(134,plain,
% 0.24/0.51 (![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))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[133])).
% 0.24/0.51 tff(135,plain,
% 0.24/0.51 (![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))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(136,plain,
% 0.24/0.51 (^[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))))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(137,plain,
% 0.24/0.51 (![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))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[136])).
% 0.24/0.51 tff(138,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.24/0.51 tff(139,plain,
% 0.24/0.51 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.24/0.51 tff(140,plain,
% 0.24/0.51 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.24/0.51 tff(141,plain,(
% 0.24/0.51 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.24/0.51 inference(skolemize,[status(sab)],[140])).
% 0.24/0.51 tff(142,plain,
% 0.24/0.51 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.24/0.51 tff(143,plain,
% 0.24/0.51 (q0(a, b) <=> q0(a, b)),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(144,axiom,(q0(a, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.24/0.51 tff(145,plain,
% 0.24/0.51 (q0(a, b)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.24/0.51 tff(146,plain,
% 0.24/0.51 (s0(d) <=> s0(d)),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(147,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.24/0.51 tff(148,plain,
% 0.24/0.51 (s0(d)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.24/0.51 tff(149,plain,
% 0.24/0.51 (((~![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)))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(150,plain,
% 0.24/0.51 (((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a)) <=> ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(151,plain,
% 0.24/0.51 (((~![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))))),
% 0.24/0.51 inference(monotonicity,[status(thm)],[150])).
% 0.24/0.51 tff(152,plain,
% 0.24/0.51 (((~![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)))),
% 0.24/0.51 inference(transitivity,[status(thm)],[151, 149])).
% 0.24/0.51 tff(153,plain,
% 0.24/0.51 ((~![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))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(154,plain,
% 0.24/0.51 ((~![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))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.24/0.51 tff(155,plain,
% 0.24/0.51 (r1(a)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[154, 148, 145, 142, 132])).
% 0.24/0.51 tff(156,plain,
% 0.24/0.51 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(157,plain,
% 0.24/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[156])).
% 0.24/0.51 tff(158,plain,
% 0.24/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(159,plain,
% 0.24/0.51 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.24/0.51 inference(bind,[status(th)],[])).
% 0.24/0.51 tff(160,plain,
% 0.24/0.51 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(quant_intro,[status(thm)],[159])).
% 0.24/0.51 tff(161,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.24/0.51 tff(162,plain,
% 0.24/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.24/0.51 tff(163,plain,
% 0.24/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.24/0.51 tff(164,plain,(
% 0.24/0.51 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(skolemize,[status(sab)],[163])).
% 0.24/0.51 tff(165,plain,
% 0.24/0.51 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.24/0.51 tff(166,plain,
% 0.24/0.51 (((~![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))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(167,plain,
% 0.24/0.51 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(168,plain,
% 0.24/0.51 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.24/0.51 tff(169,plain,
% 0.24/0.51 (r2(a)),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[168, 75, 165, 155])).
% 0.24/0.51 tff(170,plain,
% 0.24/0.51 (((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | ((~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))) <=> ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | (~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(171,plain,
% 0.24/0.51 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | ((~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(172,plain,
% 0.24/0.51 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | (~r2(a)) | (~k3(b, a, b)) | m3(b, b, a)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.24/0.52 tff(173,plain,
% 0.24/0.52 (m3(b, b, a)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[172, 169, 112, 102])).
% 0.24/0.52 tff(174,plain,
% 0.24/0.52 (^[A: $i] : refl((p2(A, A, A) | (~q1(A, A, A))) <=> (p2(A, A, A) | (~q1(A, A, A))))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(175,plain,
% 0.24/0.52 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[174])).
% 0.24/0.52 tff(176,plain,
% 0.24/0.52 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(177,axiom,(![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_154')).
% 0.24/0.52 tff(178,plain,
% 0.24/0.52 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.24/0.52 tff(179,plain,(
% 0.24/0.52 ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.24/0.52 inference(skolemize,[status(sab)],[178])).
% 0.24/0.52 tff(180,plain,
% 0.24/0.52 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.24/0.52 tff(181,plain,
% 0.24/0.52 (r0(b) <=> r0(b)),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(182,axiom,(r0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.24/0.52 tff(183,plain,
% 0.24/0.52 (r0(b)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.24/0.52 tff(184,plain,
% 0.24/0.52 (((~r0(b)) | q1(b, b, b)) <=> ((~r0(b)) | q1(b, b, b))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(185,plain,
% 0.24/0.52 ((q1(b, b, b) | (~r0(b))) <=> ((~r0(b)) | q1(b, b, b))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(186,axiom,(q1(b, b, b) | (~r0(b))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_120')).
% 0.24/0.52 tff(187,plain,
% 0.24/0.52 ((~r0(b)) | q1(b, b, b)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.24/0.52 tff(188,plain,
% 0.24/0.52 ((~r0(b)) | q1(b, b, b)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.24/0.52 tff(189,plain,
% 0.24/0.52 (q1(b, b, b)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[188, 183])).
% 0.24/0.52 tff(190,plain,
% 0.24/0.52 (((~![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)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(191,plain,
% 0.24/0.52 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | (p2(b, b, b) | (~q1(b, b, b)))),
% 0.24/0.52 inference(quant_inst,[status(thm)],[])).
% 0.24/0.52 tff(192,plain,
% 0.24/0.52 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | p2(b, b, b) | (~q1(b, b, b))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.24/0.52 tff(193,plain,
% 0.24/0.52 (p2(b, b, b)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[192, 189, 180])).
% 0.24/0.52 tff(194,plain,
% 0.24/0.52 (^[B: $i, D: $i, C: $i] : refl(((~p2(B, D, C)) | r3(B, C, B)) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(195,plain,
% 0.24/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B)) <=> ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[194])).
% 0.24/0.52 tff(196,plain,
% 0.24/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B)) <=> ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(197,plain,
% 0.24/0.52 (^[B: $i, D: $i, C: $i] : rewrite((r3(B, C, B) | (~p2(B, D, C))) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(198,plain,
% 0.24/0.52 (![B: $i, D: $i, C: $i] : (r3(B, C, B) | (~p2(B, D, C))) <=> ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[197])).
% 0.24/0.52 tff(199,axiom,(![B: $i, D: $i, C: $i] : (r3(B, C, B) | (~p2(B, D, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_267')).
% 0.24/0.52 tff(200,plain,
% 0.24/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.24/0.52 tff(201,plain,
% 0.24/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.24/0.52 tff(202,plain,(
% 0.24/0.52 ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(skolemize,[status(sab)],[201])).
% 0.24/0.52 tff(203,plain,
% 0.24/0.52 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.24/0.52 tff(204,plain,
% 0.24/0.52 (((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(b, b, b)) | r3(b, b, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(b, b, b)) | r3(b, b, b))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(205,plain,
% 0.24/0.52 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(b, b, b)) | r3(b, b, b))),
% 0.24/0.52 inference(quant_inst,[status(thm)],[])).
% 0.24/0.52 tff(206,plain,
% 0.24/0.52 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(b, b, b)) | r3(b, b, b)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.24/0.52 tff(207,plain,
% 0.24/0.52 (r3(b, b, b)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[206, 203, 193])).
% 0.24/0.52 tff(208,plain,
% 0.24/0.52 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) <=> ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(209,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[208])).
% 0.24/0.52 tff(210,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(211,plain,
% 0.24/0.52 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(trans(monotonicity(rewrite((r3(H, H, I) | (~m2(I))) <=> ((~m2(I)) | r3(H, H, I))), (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) <=> (((~m2(I)) | r3(H, H, I)) | (~m3(J, b, H))))), rewrite((((~m2(I)) | r3(H, H, I)) | (~m3(J, b, H))) <=> ((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))), (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) <=> ((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)))), ((((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A))) <=> (((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) | (~r3(I, A, A))))), rewrite((((~m3(J, b, H)) | (~m2(I)) | r3(H, H, I)) | (~r3(I, A, A))) <=> ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))), ((((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A))) <=> ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(212,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[211])).
% 0.24/0.52 tff(213,axiom,(![I: $i, A: $i, J: $i, H: $i] : (((r3(H, H, I) | (~m2(I))) | (~m3(J, b, H))) | (~r3(I, A, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_268')).
% 0.24/0.52 tff(214,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.24/0.52 tff(215,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.24/0.52 tff(216,plain,(
% 0.24/0.52 ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(skolemize,[status(sab)],[215])).
% 0.24/0.52 tff(217,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.24/0.52 tff(218,plain,
% 0.24/0.52 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(219,plain,
% 0.24/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[218])).
% 0.24/0.52 tff(220,plain,
% 0.24/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(221,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.24/0.52 tff(222,plain,
% 0.24/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.24/0.52 tff(223,plain,(
% 0.24/0.52 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.24/0.52 inference(skolemize,[status(sab)],[222])).
% 0.24/0.52 tff(224,plain,
% 0.24/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.24/0.52 tff(225,plain,
% 0.24/0.52 (((~![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)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(226,plain,
% 0.24/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.24/0.52 inference(quant_inst,[status(thm)],[])).
% 0.24/0.52 tff(227,plain,
% 0.24/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.24/0.52 tff(228,plain,
% 0.24/0.52 (k1(b)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[227, 128, 224])).
% 0.24/0.52 tff(229,plain,
% 0.24/0.52 ((m2(b) | (~k1(b))) <=> (m2(b) | (~k1(b)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(230,axiom,(m2(b) | (~k1(b))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_136')).
% 0.24/0.52 tff(231,plain,
% 0.24/0.52 (m2(b) | (~k1(b))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.24/0.52 tff(232,plain,
% 0.24/0.52 (m2(b)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[231, 228])).
% 0.24/0.52 tff(233,plain,
% 0.24/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(234,plain,
% 0.24/0.52 (((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b)) <=> ((~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(235,plain,
% 0.24/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b)))),
% 0.24/0.52 inference(monotonicity,[status(thm)],[234])).
% 0.24/0.52 tff(236,plain,
% 0.24/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b))),
% 0.24/0.52 inference(transitivity,[status(thm)],[235, 233])).
% 0.24/0.52 tff(237,plain,
% 0.24/0.52 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(b, b, b)) | (~m3(b, b, a)) | (~m2(b)) | r3(a, a, b))),
% 0.24/0.52 inference(quant_inst,[status(thm)],[])).
% 0.24/0.52 tff(238,plain,
% 0.24/0.52 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(b)) | (~r3(b, b, b)) | (~m3(b, b, a)) | r3(a, a, b)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.24/0.52 tff(239,plain,
% 0.24/0.52 (r3(a, a, b)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[238, 232, 217, 207, 173])).
% 0.24/0.52 tff(240,plain,
% 0.24/0.52 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(241,plain,
% 0.24/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[240])).
% 0.24/0.52 tff(242,plain,
% 0.24/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(243,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.24/0.52 tff(244,plain,
% 0.24/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.24/0.52 tff(245,plain,(
% 0.24/0.52 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.24/0.52 inference(skolemize,[status(sab)],[244])).
% 0.24/0.52 tff(246,plain,
% 0.24/0.52 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.24/0.52 tff(247,plain,
% 0.24/0.52 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(248,plain,
% 0.24/0.52 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(249,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.24/0.52 tff(250,plain,
% 0.24/0.52 ((~r2(a)) | k3(a, a, a)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.24/0.52 tff(251,plain,
% 0.24/0.52 ((~r2(a)) | k3(a, a, a)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.24/0.52 tff(252,plain,
% 0.24/0.52 (k3(a, a, a)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[251, 169])).
% 0.24/0.52 tff(253,plain,
% 0.24/0.52 (((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))) <=> ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(254,plain,
% 0.24/0.52 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))),
% 0.24/0.52 inference(quant_inst,[status(thm)],[])).
% 0.24/0.52 tff(255,plain,
% 0.24/0.52 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.24/0.52 tff(256,plain,
% 0.24/0.52 (p4(a, a, a)),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[255, 252, 246])).
% 0.24/0.52 tff(257,plain,
% 0.24/0.52 ((~p4(b, a, a)) <=> (~p4(b, a, a))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(258,axiom,(~p4(b, a, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.24/0.52 tff(259,plain,
% 0.24/0.52 (~p4(b, a, a)),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.24/0.52 tff(260,plain,
% 0.24/0.52 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)) <=> ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(261,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.24/0.52 inference(quant_intro,[status(thm)],[260])).
% 0.24/0.52 tff(262,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(263,plain,
% 0.24/0.52 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(rewrite((p4(H, I, I) | (~r3(I, I, H))) <=> ((~r3(I, I, H)) | p4(H, I, I))), (((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A))) <=> (((~r3(I, I, H)) | p4(H, I, I)) | (~p4(J, J, A))))), rewrite((((~r3(I, I, H)) | p4(H, I, I)) | (~p4(J, J, A))) <=> ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))), (((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A))) <=> ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))))),
% 0.24/0.52 inference(bind,[status(th)],[])).
% 0.24/0.52 tff(264,plain,
% 0.24/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.38/0.53 inference(quant_intro,[status(thm)],[263])).
% 0.38/0.53 tff(265,axiom,(![I: $i, A: $i, J: $i, H: $i] : ((p4(H, I, I) | (~r3(I, I, H))) | (~p4(J, J, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_288')).
% 0.38/0.53 tff(266,plain,
% 0.38/0.53 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.38/0.53 tff(267,plain,
% 0.38/0.53 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.38/0.53 tff(268,plain,(
% 0.38/0.53 ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.38/0.53 inference(skolemize,[status(sab)],[267])).
% 0.38/0.53 tff(269,plain,
% 0.38/0.53 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.38/0.53 tff(270,plain,
% 0.38/0.53 (((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | ((~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | (~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(271,plain,
% 0.38/0.53 ((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | ((~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(272,plain,
% 0.38/0.53 ((~![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))) | (~p4(a, a, a)) | (~r3(a, a, b)) | p4(b, a, a)),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.38/0.53 tff(273,plain,
% 0.38/0.53 ($false),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[272, 269, 259, 256, 239])).
% 0.38/0.53 % SZS output end Proof
% 0.38/0.54 % E exiting
%------------------------------------------------------------------------------