%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN271-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN271-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:31:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(p4_type, type, (
% 0.20/0.46 p4: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(a_type, type, (
% 0.20/0.46 a: $i)).
% 0.20/0.46 tff(d_type, type, (
% 0.20/0.46 d: $i)).
% 0.20/0.46 tff(r3_type, type, (
% 0.20/0.46 r3: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(m3_type, type, (
% 0.20/0.46 m3: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(b_type, type, (
% 0.20/0.46 b: $i)).
% 0.20/0.46 tff(k3_type, type, (
% 0.20/0.46 k3: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(p2_type, type, (
% 0.20/0.46 p2: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(m1_type, type, (
% 0.20/0.46 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(p0_type, type, (
% 0.20/0.46 p0: ( $i * $i ) > $o)).
% 0.20/0.46 tff(s0_type, type, (
% 0.20/0.46 s0: $i > $o)).
% 0.20/0.46 tff(l1_type, type, (
% 0.20/0.46 l1: ( $i * $i ) > $o)).
% 0.20/0.46 tff(n0_type, type, (
% 0.20/0.46 n0: ( $i * $i ) > $o)).
% 0.20/0.46 tff(p1_type, type, (
% 0.20/0.46 p1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(l0_type, type, (
% 0.20/0.46 l0: $i > $o)).
% 0.20/0.46 tff(r2_type, type, (
% 0.20/0.46 r2: $i > $o)).
% 0.20/0.46 tff(r1_type, type, (
% 0.20/0.46 r1: $i > $o)).
% 0.20/0.46 tff(q1_type, type, (
% 0.20/0.46 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(q0_type, type, (
% 0.20/0.46 q0: ( $i * $i ) > $o)).
% 0.20/0.46 tff(n1_type, type, (
% 0.20/0.46 n1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(m2_type, type, (
% 0.20/0.46 m2: $i > $o)).
% 0.20/0.46 tff(e_type, type, (
% 0.20/0.46 e: $i)).
% 0.20/0.46 tff(r0_type, type, (
% 0.20/0.46 r0: $i > $o)).
% 0.20/0.46 tff(m0_type, type, (
% 0.20/0.46 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(c_type, type, (
% 0.20/0.46 c: $i)).
% 0.20/0.46 tff(1,assumption,(~p0(b, a)), introduced(assumption)).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![X: $i] : p0(b, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.46 tff(7,plain,(
% 0.20/0.46 ![X: $i] : p0(b, X)),
% 0.20/0.46 inference(skolemize,[status(sab)],[6])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (![X: $i] : p0(b, X)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 ((~![X: $i] : p0(b, X)) | p0(b, a)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.46 tff(11,plain,(p0(b, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (^[I: $i, H: $i] : refl((m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.46 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')).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.46 tff(20,plain,(
% 0.20/0.46 ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[19])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (s0(b) <=> s0(b)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(23,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (s0(b)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 ((m1(b, a, b) | (~p0(b, a)) | (~s0(b))) <=> ((~s0(b)) | (~p0(b, a)) | m1(b, a, b))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, a, b) | (~p0(b, a)) | (~s0(b)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, a)) | m1(b, a, b)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (m1(b, a, b)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[30, 24, 21, 11])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.47 tff(37,plain,(
% 0.20/0.47 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[36])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 ((p2(a, b, a) | (~m1(b, a, b))) <=> ((~m1(b, a, b)) | p2(a, b, a))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, b, a) | (~m1(b, a, b)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(b, a, b)) | p2(a, b, a)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (p2(a, b, a)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[44, 38, 31])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.47 tff(51,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.47 tff(54,plain,(
% 0.20/0.47 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(skolemize,[status(sab)],[53])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (n0(b, a) <=> n0(b, a)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(57,axiom,(n0(b, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (n0(b, a)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(b, a)) | l1(a, a))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(b, a)) | l1(a, a)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (l1(a, a)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[61, 58, 55])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.47 tff(71,plain,(
% 0.20/0.47 ![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.20/0.47 inference(skolemize,[status(sab)],[70])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (![D: $i, E: $i, F: $i, C: $i] : ((~p2(C, D, C)) | (~l1(E, F)) | (~p1(C, E, F)) | p2(C, D, D))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (l0(a) <=> l0(a)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(74,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (l0(a)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (((~l0(a)) | p1(a, a, a)) <=> ((~l0(a)) | p1(a, a, a))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(78,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 ((~l0(a)) | p1(a, a, a)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((~l0(a)) | p1(a, a, a)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (p1(a, a, a)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (((~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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 ((~![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)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (p2(a, b, b)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[87, 81, 72, 62, 45])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (^[D: $i, C: $i] : refl(((~p2(D, C, C)) | k3(C, D, C)) <=> ((~p2(D, C, C)) | k3(C, D, C)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C)) <=> ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C)) <=> ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (^[D: $i, C: $i] : rewrite((k3(C, D, C) | (~p2(D, C, C))) <=> ((~p2(D, C, C)) | k3(C, D, C)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![D: $i, C: $i] : (k3(C, D, C) | (~p2(D, C, C))) <=> ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.47 tff(97,plain,(
% 0.20/0.47 ![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(skolemize,[status(sab)],[96])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 ((~![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))) | ((~p2(a, b, b)) | k3(b, a, b))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 ((~![D: $i, C: $i] : ((~p2(D, C, C)) | k3(C, D, C))) | (~p2(a, b, b)) | k3(b, a, b)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (k3(b, a, b)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.47 tff(111,plain,(
% 0.20/0.47 ![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.47 inference(skolemize,[status(sab)],[110])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.47 tff(121,plain,(
% 0.20/0.47 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.47 inference(skolemize,[status(sab)],[120])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (p0(b, d) <=> p0(b, d)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(124,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (p0(b, d)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (n0(d, b) <=> n0(d, b)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(127,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (n0(d, b)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (((~![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 ((~![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)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (q1(d, b, d)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[131, 128, 125, 122])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (^[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))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.47 tff(141,plain,(
% 0.20/0.47 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.47 inference(skolemize,[status(sab)],[140])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (q0(a, b) <=> q0(a, b)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(144,axiom,(q0(a, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (q0(a, b)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (s0(d) <=> s0(d)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(147,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (s0(d)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (((~q0(a, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(a)) <=> ((~s0(d)) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (((~![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))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (r1(a)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[154, 148, 145, 142, 132])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.47 tff(161,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.20/0.47 tff(164,plain,(
% 0.20/0.47 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.47 inference(skolemize,[status(sab)],[163])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (r2(a)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[168, 75, 165, 155])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | ((~r2(a)) | (~k3(b, a, b)) | m3(b, b, a))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 ((~![B: $i, C: $i] : ((~r2(C)) | (~k3(B, C, B)) | m3(B, B, C))) | (~r2(a)) | (~k3(b, a, b)) | m3(b, b, a)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (m3(b, b, a)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 169, 112, 102])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (^[B: $i, D: $i, C: $i] : refl(((~p2(B, D, C)) | r3(B, C, B)) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[174])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (^[B: $i, D: $i, C: $i] : rewrite((r3(B, C, B) | (~p2(B, D, C))) <=> ((~p2(B, D, C)) | r3(B, C, B)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.48 tff(179,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')).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.20/0.48 tff(182,plain,(
% 0.20/0.48 ![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.48 inference(skolemize,[status(sab)],[181])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (^[B: $i] : refl((p2(B, B, B) | (~n1(d, d, B))) <=> (p2(B, B, B) | (~n1(d, d, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[184])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(187,axiom,(![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_153')).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.48 tff(189,plain,(
% 0.20/0.48 ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[188])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (q0(d, d) <=> q0(d, d)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(192,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (q0(d, d)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(195,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[196, 194])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[197, 194])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (n1(d, d, d) | (~q0(d, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[199, 194])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 (n1(d, d, d)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[200, 193])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (p2(d, d, d)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[204, 201, 190])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 (((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(d, d, d)) | r3(d, d, d))) <=> ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(d, d, d)) | r3(d, d, d))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | ((~p2(d, d, d)) | r3(d, d, d))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 ((~![B: $i, D: $i, C: $i] : ((~p2(B, D, C)) | r3(B, C, B))) | (~p2(d, d, d)) | r3(d, d, d)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (r3(d, d, d)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 205, 183])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (^[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)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[210])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.48 tff(215,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')).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.20/0.48 tff(218,plain,(
% 0.20/0.48 ![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.48 inference(skolemize,[status(sab)],[217])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 (![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (^[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)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[220])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[223])).
% 0.20/0.48 tff(225,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.20/0.48 tff(228,plain,(
% 0.20/0.48 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.48 inference(skolemize,[status(sab)],[227])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (m0(e, b, c) <=> m0(e, b, c)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(231,axiom,(m0(e, b, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (m0(e, b, c)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (p0(c, b) <=> p0(c, b)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(234,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 (p0(c, b)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (r0(b) <=> r0(b)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(237,axiom,(r0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 (r0(b)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (((~![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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.48 inference(transitivity,[status(thm)],[241, 239])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 ((~![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))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 ((~![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)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (l1(b, e)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[244, 238, 235, 232, 229])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (^[H: $i, F: $i, G: $i] : refl(((~s0(F)) | (~l1(G, H)) | m2(F)) <=> ((~s0(F)) | (~l1(G, H)) | m2(F)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F)) <=> ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[246])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F)) <=> ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (^[H: $i, F: $i, G: $i] : rewrite(((m2(F) | (~s0(F))) | (~l1(G, H))) <=> ((~s0(F)) | (~l1(G, H)) | m2(F)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((m2(F) | (~s0(F))) | (~l1(G, H))) <=> ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[249])).
% 0.20/0.48 tff(251,axiom,(![H: $i, F: $i, G: $i] : ((m2(F) | (~s0(F))) | (~l1(G, H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_135')).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.20/0.48 tff(254,plain,(
% 0.20/0.48 ![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(skolemize,[status(sab)],[253])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 (((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | m2(d) | (~l1(b, e)))) <=> ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | (~s0(d)) | m2(d) | (~l1(b, e)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (((~s0(d)) | (~l1(b, e)) | m2(d)) <=> ((~s0(d)) | m2(d) | (~l1(b, e)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | (~l1(b, e)) | m2(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | m2(d) | (~l1(b, e))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[257])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | (~l1(b, e)) | m2(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | (~s0(d)) | m2(d) | (~l1(b, e)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[258, 256])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | ((~s0(d)) | (~l1(b, e)) | m2(d))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 ((~![H: $i, F: $i, G: $i] : ((~s0(F)) | (~l1(G, H)) | m2(F))) | (~s0(d)) | m2(d) | (~l1(b, e))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (m2(d)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[261, 148, 255, 245])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d)) <=> ((~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d))),
% 0.20/0.48 inference(transitivity,[status(thm)],[265, 263])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | ((~r3(d, d, d)) | (~m3(b, b, a)) | (~m2(d)) | r3(a, a, d))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 ((~![I: $i, A: $i, J: $i, H: $i] : ((~r3(I, A, A)) | (~m3(J, b, H)) | (~m2(I)) | r3(H, H, I))) | (~m2(d)) | (~r3(d, d, d)) | (~m3(b, b, a)) | r3(a, a, d)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (r3(a, a, d)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[268, 262, 219, 209, 173])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[270])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(273,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.48 tff(275,plain,(
% 0.20/0.48 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[274])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(279,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 ((~r2(a)) | k3(a, a, a)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 ((~r2(a)) | k3(a, a, a)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[280, 277])).
% 0.20/0.49 tff(282,plain,
% 0.20/0.49 (k3(a, a, a)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[281, 169])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 (((~![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(a, a, a) | (~k3(a, a, a)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(a, a, a) | (~k3(a, a, a))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (p4(a, a, a)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[285, 282, 276])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 (^[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)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[287])).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[290])).
% 0.20/0.49 tff(292,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')).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.20/0.49 tff(295,plain,(
% 0.20/0.49 ![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.20/0.49 inference(skolemize,[status(sab)],[294])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 (![I: $i, A: $i, J: $i, H: $i] : ((~p4(J, J, A)) | (~r3(I, I, H)) | p4(H, I, I))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.20/0.49 tff(297,plain,
% 0.20/0.49 (((~![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, d)) | p4(d, 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, d)) | p4(d, a, a))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 ((~![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, d)) | p4(d, a, a))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 ((~![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, d)) | p4(d, a, a)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (p4(d, a, a)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[299, 296, 286, 269])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 (^[X: $i] : refl((~p4(d, X, a)) <=> (~p4(d, X, a)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 (![X: $i] : (~p4(d, X, a)) <=> ![X: $i] : (~p4(d, X, a))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[301])).
% 0.20/0.50 tff(303,plain,
% 0.20/0.50 (![X: $i] : (~p4(d, X, a)) <=> ![X: $i] : (~p4(d, X, a))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(304,axiom,(![X: $i] : (~p4(d, X, a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.50 tff(305,plain,
% 0.20/0.50 (![X: $i] : (~p4(d, X, a))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.50 tff(306,plain,(
% 0.20/0.50 ![X: $i] : (~p4(d, X, a))),
% 0.20/0.50 inference(skolemize,[status(sab)],[305])).
% 0.20/0.50 tff(307,plain,
% 0.20/0.50 (![X: $i] : (~p4(d, X, a))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[306, 302])).
% 0.20/0.50 tff(308,plain,
% 0.20/0.50 ((~![X: $i] : (~p4(d, X, a))) | (~p4(d, a, a))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[308, 307, 300])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------