%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN181-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:26 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.58s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN181-1 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:29:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.41/0.58 % SZS status Unsatisfiable
% 0.41/0.58 % SZS output start Proof
% 0.41/0.58 tff(q2_type, type, (
% 0.41/0.58 q2: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(d_type, type, (
% 0.41/0.58 d: $i)).
% 0.41/0.58 tff(b_type, type, (
% 0.41/0.58 b: $i)).
% 0.41/0.58 tff(l1_type, type, (
% 0.41/0.58 l1: ( $i * $i ) > $o)).
% 0.41/0.58 tff(m0_type, type, (
% 0.41/0.58 m0: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(p0_type, type, (
% 0.41/0.58 p0: ( $i * $i ) > $o)).
% 0.41/0.58 tff(r0_type, type, (
% 0.41/0.58 r0: $i > $o)).
% 0.41/0.58 tff(q4_type, type, (
% 0.41/0.58 q4: ( $i * $i ) > $o)).
% 0.41/0.58 tff(k3_type, type, (
% 0.41/0.58 k3: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(m3_type, type, (
% 0.41/0.58 m3: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(p2_type, type, (
% 0.41/0.58 p2: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(q1_type, type, (
% 0.41/0.58 q1: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(m1_type, type, (
% 0.41/0.58 m1: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(q0_type, type, (
% 0.41/0.58 q0: ( $i * $i ) > $o)).
% 0.41/0.58 tff(e_type, type, (
% 0.41/0.58 e: $i)).
% 0.41/0.58 tff(n1_type, type, (
% 0.41/0.58 n1: ( $i * $i * $i ) > $o)).
% 0.41/0.58 tff(1,assumption,(~m0(b, d, b)), introduced(assumption)).
% 0.41/0.58 tff(2,plain,
% 0.41/0.58 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(3,plain,
% 0.41/0.58 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.41/0.58 inference(quant_intro,[status(thm)],[2])).
% 0.41/0.58 tff(4,plain,
% 0.41/0.58 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.41/0.58 tff(6,plain,
% 0.41/0.58 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.41/0.58 tff(7,plain,(
% 0.41/0.58 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.41/0.58 inference(skolemize,[status(sab)],[6])).
% 0.41/0.58 tff(8,plain,
% 0.41/0.58 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.41/0.58 tff(9,plain,
% 0.41/0.58 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, b)),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(10,plain,
% 0.41/0.58 ($false),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.41/0.58 tff(11,plain,(m0(b, d, b)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.58 tff(12,plain,
% 0.41/0.58 (^[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)))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(13,plain,
% 0.41/0.58 (![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))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[12])).
% 0.41/0.58 tff(14,plain,
% 0.41/0.58 (![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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(15,plain,
% 0.41/0.58 (^[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))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(16,plain,
% 0.41/0.58 (![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))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[15])).
% 0.41/0.58 tff(17,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')).
% 0.41/0.58 tff(18,plain,
% 0.41/0.58 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.41/0.58 tff(19,plain,
% 0.41/0.58 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.41/0.59 tff(20,plain,(
% 0.41/0.59 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.41/0.59 inference(skolemize,[status(sab)],[19])).
% 0.41/0.59 tff(21,plain,
% 0.41/0.59 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.41/0.59 tff(22,plain,
% 0.41/0.59 (p0(b, d) <=> p0(b, d)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(23,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.41/0.59 tff(24,plain,
% 0.41/0.59 (p0(b, d)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.41/0.59 tff(25,plain,
% 0.41/0.59 (r0(b) <=> r0(b)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(26,axiom,(r0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.41/0.59 tff(27,plain,
% 0.41/0.59 (r0(b)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.41/0.59 tff(28,plain,
% 0.41/0.59 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(b, d)) | l1(d, b) | (~m0(b, d, b)))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(b, d)) | l1(d, b) | (~m0(b, d, b)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(29,plain,
% 0.41/0.59 (((~m0(b, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, b)) <=> ((~r0(b)) | (~p0(b, d)) | l1(d, b) | (~m0(b, d, b)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(30,plain,
% 0.41/0.59 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(b, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(b, d)) | l1(d, b) | (~m0(b, d, b))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[29])).
% 0.41/0.59 tff(31,plain,
% 0.41/0.59 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(b, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(b, d)) | l1(d, b) | (~m0(b, d, b)))),
% 0.41/0.59 inference(transitivity,[status(thm)],[30, 28])).
% 0.41/0.59 tff(32,plain,
% 0.41/0.59 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(b, d, b)) | (~r0(b)) | (~p0(b, d)) | l1(d, b))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(33,plain,
% 0.41/0.59 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(b, d)) | l1(d, b) | (~m0(b, d, b))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.41/0.59 tff(34,plain,
% 0.41/0.59 (l1(d, b) | (~m0(b, d, b))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[33, 27, 24, 21])).
% 0.41/0.59 tff(35,plain,
% 0.41/0.59 (l1(d, b)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[34, 11])).
% 0.41/0.59 tff(36,plain,
% 0.41/0.59 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(37,plain,
% 0.41/0.59 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[36])).
% 0.41/0.59 tff(38,plain,
% 0.41/0.59 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(39,plain,
% 0.41/0.59 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(40,plain,
% 0.41/0.59 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[39])).
% 0.41/0.59 tff(41,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 0.41/0.59 tff(42,plain,
% 0.41/0.59 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.41/0.59 tff(43,plain,
% 0.41/0.59 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.41/0.59 tff(44,plain,(
% 0.41/0.59 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(skolemize,[status(sab)],[43])).
% 0.41/0.59 tff(45,plain,
% 0.41/0.59 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.41/0.59 tff(46,plain,
% 0.41/0.59 (((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(d, b)) | q2(b, b, d))) <=> ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(d, b)) | q2(b, b, d))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(47,plain,
% 0.41/0.59 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(d, b)) | q2(b, b, d))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(48,plain,
% 0.41/0.59 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(d, b)) | q2(b, b, d)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.41/0.59 tff(49,plain,
% 0.41/0.59 (q2(b, b, d)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 0.41/0.59 tff(50,plain,
% 0.41/0.59 ((~q4(d, b)) <=> (~q4(d, b))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(51,axiom,(~q4(d, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.41/0.59 tff(52,plain,
% 0.41/0.59 (~q4(d, b)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.41/0.59 tff(53,plain,
% 0.41/0.59 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(54,plain,
% 0.41/0.59 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[53])).
% 0.41/0.59 tff(55,plain,
% 0.41/0.59 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(56,plain,
% 0.41/0.59 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q4(B, C) | (~k3(D, D, B))) <=> ((~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> (((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))))), rewrite((((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> (((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))))), rewrite((((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(57,plain,
% 0.41/0.59 (![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[56])).
% 0.41/0.59 tff(58,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 0.41/0.59 tff(59,plain,
% 0.41/0.59 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.41/0.59 tff(60,plain,
% 0.41/0.59 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.41/0.59 tff(61,plain,(
% 0.41/0.59 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(skolemize,[status(sab)],[60])).
% 0.41/0.59 tff(62,plain,
% 0.41/0.59 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.41/0.59 tff(63,plain,
% 0.41/0.59 (^[A: $i] : refl((p2(A, A, A) | (~q1(A, A, A))) <=> (p2(A, A, A) | (~q1(A, A, A))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(64,plain,
% 0.41/0.59 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[63])).
% 0.41/0.59 tff(65,plain,
% 0.41/0.59 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A))) <=> ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(66,axiom,(![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_154')).
% 0.41/0.59 tff(67,plain,
% 0.41/0.59 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.41/0.59 tff(68,plain,(
% 0.41/0.59 ![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[67])).
% 0.41/0.59 tff(69,plain,
% 0.41/0.59 (![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.41/0.59 tff(70,plain,
% 0.41/0.59 (((~r0(b)) | q1(b, b, b)) <=> ((~r0(b)) | q1(b, b, b))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(71,plain,
% 0.41/0.59 ((q1(b, b, b) | (~r0(b))) <=> ((~r0(b)) | q1(b, b, b))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(72,axiom,(q1(b, b, b) | (~r0(b))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_120')).
% 0.41/0.59 tff(73,plain,
% 0.41/0.59 ((~r0(b)) | q1(b, b, b)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.41/0.59 tff(74,plain,
% 0.41/0.59 ((~r0(b)) | q1(b, b, b)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.41/0.59 tff(75,plain,
% 0.41/0.59 (q1(b, b, b)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[74, 27])).
% 0.41/0.59 tff(76,plain,
% 0.41/0.59 (((~![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)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(77,plain,
% 0.41/0.59 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | (p2(b, b, b) | (~q1(b, b, b)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(78,plain,
% 0.41/0.59 ((~![A: $i] : (p2(A, A, A) | (~q1(A, A, A)))) | p2(b, b, b) | (~q1(b, b, b))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.41/0.59 tff(79,plain,
% 0.41/0.59 (p2(b, b, b)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[78, 75, 69])).
% 0.41/0.59 tff(80,plain,
% 0.41/0.59 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(81,plain,
% 0.41/0.59 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[80])).
% 0.41/0.59 tff(82,plain,
% 0.41/0.59 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(83,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 0.41/0.59 tff(84,plain,
% 0.41/0.59 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.41/0.59 tff(85,plain,(
% 0.41/0.59 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[84])).
% 0.41/0.59 tff(86,plain,
% 0.41/0.59 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.41/0.59 tff(87,plain,
% 0.41/0.59 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(b, b, b) | (~p2(b, b, b)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | m3(b, b, b) | (~p2(b, b, b)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(88,plain,
% 0.41/0.59 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(b, b, b) | (~p2(b, b, b)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(89,plain,
% 0.41/0.59 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | m3(b, b, b) | (~p2(b, b, b))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.41/0.59 tff(90,plain,
% 0.41/0.59 (m3(b, b, b)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[89, 86, 79])).
% 0.41/0.59 tff(91,plain,
% 0.41/0.59 (^[D: $i, E: $i, C: $i] : refl((m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))) <=> (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(92,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))) <=> ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[91])).
% 0.41/0.59 tff(93,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E))) <=> ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(94,plain,
% 0.41/0.59 (^[D: $i, E: $i, C: $i] : trans(monotonicity(rewrite((m1(C, C, C) | (~q0(D, E))) <=> (m1(C, C, C) | (~q0(D, E)))), (((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> ((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))))), rewrite(((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))), (((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(95,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C))) <=> ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[94])).
% 0.41/0.59 tff(96,axiom,(![D: $i, E: $i, C: $i] : ((m1(C, C, C) | (~q0(D, E))) | (~q0(D, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_018')).
% 0.41/0.59 tff(97,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.41/0.59 tff(98,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.41/0.59 tff(99,plain,(
% 0.41/0.59 ![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[98])).
% 0.41/0.59 tff(100,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.41/0.59 tff(101,plain,
% 0.41/0.59 (q0(e, d) <=> q0(e, d)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(102,axiom,(q0(e, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.41/0.59 tff(103,plain,
% 0.41/0.59 (q0(e, d)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.41/0.59 tff(104,plain,
% 0.41/0.59 (((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | ((~q0(e, d)) | m1(d, d, d))) <=> ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (~q0(e, d)) | m1(d, d, d))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(105,plain,
% 0.41/0.59 ((m1(d, d, d) | (~q0(e, d)) | (~q0(e, d))) <=> ((~q0(e, d)) | m1(d, d, d))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(106,plain,
% 0.41/0.59 (((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (m1(d, d, d) | (~q0(e, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | ((~q0(e, d)) | m1(d, d, d)))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[105])).
% 0.41/0.59 tff(107,plain,
% 0.41/0.59 (((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (m1(d, d, d) | (~q0(e, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (~q0(e, d)) | m1(d, d, d))),
% 0.41/0.59 inference(transitivity,[status(thm)],[106, 104])).
% 0.41/0.59 tff(108,plain,
% 0.41/0.59 ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (m1(d, d, d) | (~q0(e, d)) | (~q0(e, d)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(109,plain,
% 0.41/0.59 ((~![D: $i, E: $i, C: $i] : (m1(C, C, C) | (~q0(D, C)) | (~q0(D, E)))) | (~q0(e, d)) | m1(d, d, d)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.41/0.59 tff(110,plain,
% 0.41/0.59 (m1(d, d, d)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[109, 103, 100])).
% 0.41/0.59 tff(111,plain,
% 0.41/0.59 (^[D: $i, E: $i, C: $i] : refl(((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)) <=> ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(112,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)) <=> ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[111])).
% 0.41/0.59 tff(113,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C)) <=> ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(114,plain,
% 0.41/0.59 (^[D: $i, E: $i, C: $i] : trans(monotonicity(rewrite((k3(C, C, C) | (~p2(D, E, D))) <=> ((~p2(D, E, D)) | k3(C, C, C))), (((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E))) <=> (((~p2(D, E, D)) | k3(C, C, C)) | (~m1(C, C, E))))), rewrite((((~p2(D, E, D)) | k3(C, C, C)) | (~m1(C, C, E))) <=> ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))), (((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E))) <=> ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(115,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E))) <=> ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[114])).
% 0.41/0.59 tff(116,axiom,(![D: $i, E: $i, C: $i] : ((k3(C, C, C) | (~p2(D, E, D))) | (~m1(C, C, E)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_196')).
% 0.41/0.59 tff(117,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.41/0.59 tff(118,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.41/0.59 tff(119,plain,(
% 0.41/0.59 ![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(skolemize,[status(sab)],[118])).
% 0.41/0.59 tff(120,plain,
% 0.41/0.59 (![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.41/0.59 tff(121,plain,
% 0.41/0.59 (^[B: $i] : refl((p2(B, B, B) | (~n1(d, d, B))) <=> (p2(B, B, B) | (~n1(d, d, B))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(122,plain,
% 0.41/0.59 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[121])).
% 0.41/0.59 tff(123,plain,
% 0.41/0.59 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(124,axiom,(![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_153')).
% 0.41/0.59 tff(125,plain,
% 0.41/0.59 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.41/0.59 tff(126,plain,(
% 0.41/0.59 ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[125])).
% 0.41/0.59 tff(127,plain,
% 0.41/0.59 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.41/0.59 tff(128,plain,
% 0.41/0.59 (q0(d, d) <=> q0(d, d)),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(129,axiom,(q0(d, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.41/0.59 tff(130,plain,
% 0.41/0.59 (q0(d, d)),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.41/0.59 tff(131,plain,
% 0.41/0.59 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(132,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 0.41/0.59 tff(133,plain,
% 0.41/0.59 (n1(d, d, d) | (~q0(d, d))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.41/0.59 tff(134,plain,
% 0.41/0.59 (n1(d, d, d) | (~q0(d, d))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.41/0.59 tff(135,plain,
% 0.41/0.59 (n1(d, d, d) | (~q0(d, d))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[134, 131])).
% 0.41/0.59 tff(136,plain,
% 0.41/0.59 (n1(d, d, d) | (~q0(d, d))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.41/0.59 tff(137,plain,
% 0.41/0.59 (n1(d, d, d) | (~q0(d, d))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[136, 131])).
% 0.41/0.59 tff(138,plain,
% 0.41/0.59 (n1(d, d, d)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[137, 130])).
% 0.41/0.59 tff(139,plain,
% 0.41/0.59 (((~![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)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(140,plain,
% 0.41/0.59 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(141,plain,
% 0.41/0.59 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.41/0.59 tff(142,plain,
% 0.41/0.59 (p2(d, d, d)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[141, 138, 127])).
% 0.41/0.59 tff(143,plain,
% 0.41/0.59 (((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | ((~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d))) <=> ((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | (~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(144,plain,
% 0.41/0.59 ((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | ((~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(145,plain,
% 0.41/0.60 ((~![D: $i, E: $i, C: $i] : ((~m1(C, C, E)) | (~p2(D, E, D)) | k3(C, C, C))) | (~m1(d, d, d)) | (~p2(d, d, d)) | k3(d, d, d)),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.41/0.60 tff(146,plain,
% 0.41/0.60 (k3(d, d, d)),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[145, 142, 120, 110])).
% 0.41/0.60 tff(147,plain,
% 0.41/0.60 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(d, b) | (~k3(d, d, d)) | (~m3(b, b, b)) | (~q2(b, b, d)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(d, b) | (~k3(d, d, d)) | (~m3(b, b, b)) | (~q2(b, b, d)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(148,plain,
% 0.41/0.60 (((~m3(b, b, b)) | (~q2(b, b, d)) | (~k3(d, d, d)) | q4(d, b)) <=> (q4(d, b) | (~k3(d, d, d)) | (~m3(b, b, b)) | (~q2(b, b, d)))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(149,plain,
% 0.41/0.60 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(b, b, b)) | (~q2(b, b, d)) | (~k3(d, d, d)) | q4(d, b))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (q4(d, b) | (~k3(d, d, d)) | (~m3(b, b, b)) | (~q2(b, b, d))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[148])).
% 0.41/0.60 tff(150,plain,
% 0.41/0.60 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(b, b, b)) | (~q2(b, b, d)) | (~k3(d, d, d)) | q4(d, b))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(d, b) | (~k3(d, d, d)) | (~m3(b, b, b)) | (~q2(b, b, d)))),
% 0.41/0.60 inference(transitivity,[status(thm)],[149, 147])).
% 0.41/0.60 tff(151,plain,
% 0.41/0.60 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(b, b, b)) | (~q2(b, b, d)) | (~k3(d, d, d)) | q4(d, b))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(152,plain,
% 0.41/0.60 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | q4(d, b) | (~k3(d, d, d)) | (~m3(b, b, b)) | (~q2(b, b, d))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.41/0.60 tff(153,plain,
% 0.41/0.60 ($false),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[152, 146, 90, 62, 52, 49])).
% 0.41/0.60 % SZS output end Proof
% 0.41/0.61 % E exiting
%------------------------------------------------------------------------------