%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN111-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:16 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN111-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 12:32:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(k2_type, type, (
% 0.20/0.49 k2: ( $i * $i ) > $o)).
% 0.20/0.49 tff(b_type, type, (
% 0.20/0.49 b: $i)).
% 0.20/0.49 tff(q1_type, type, (
% 0.20/0.49 q1: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(r0_type, type, (
% 0.20/0.49 r0: $i > $o)).
% 0.20/0.49 tff(m1_type, type, (
% 0.20/0.49 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(c_type, type, (
% 0.20/0.49 c: $i)).
% 0.20/0.49 tff(k0_type, type, (
% 0.20/0.49 k0: $i > $o)).
% 0.20/0.49 tff(l0_type, type, (
% 0.20/0.49 l0: $i > $o)).
% 0.20/0.49 tff(k1_type, type, (
% 0.20/0.49 k1: $i > $o)).
% 0.20/0.49 tff(n0_type, type, (
% 0.20/0.49 n0: ( $i * $i ) > $o)).
% 0.20/0.49 tff(d_type, type, (
% 0.20/0.49 d: $i)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 (^[A: $i, J: $i] : refl(((~q1(A, J, J)) | k2(J, J)) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[A: $i, J: $i] : rewrite((k2(J, J) | (~q1(A, J, J))) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J))) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,axiom,(![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_129')).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.49 tff(9,plain,(
% 0.20/0.49 ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(skolemize,[status(sab)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (r0(b) <=> r0(b)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(12,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (r0(b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (((~r0(b)) | q1(b, b, b)) <=> ((~r0(b)) | q1(b, b, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 ((q1(b, b, b) | (~r0(b))) <=> ((~r0(b)) | q1(b, b, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(16,axiom,(q1(b, b, b) | (~r0(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_120')).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 ((~r0(b)) | q1(b, b, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 ((~r0(b)) | q1(b, b, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (q1(b, b, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[18, 13])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(b, b, b)) | k2(b, b))) <=> ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(b, b, b)) | k2(b, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(b, b, b)) | k2(b, b))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(b, b, b)) | k2(b, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (k2(b, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[22, 19, 10])).
% 0.20/0.49 tff(24,assumption,(~m1(c, b, c)), introduced(assumption)).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (^[I: $i, J: $i] : refl((m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (^[I: $i, J: $i] : trans(monotonicity(rewrite((m1(I, J, I) | (~l0(I))) <=> (m1(I, J, I) | (~l0(I)))), (((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> ((m1(I, J, I) | (~l0(I))) | (~k0(J))))), rewrite(((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J)))), (((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (![I: $i, J: $i] : ((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.49 tff(30,axiom,(![I: $i, J: $i] : ((m1(I, J, I) | (~l0(I))) | (~k0(J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_021')).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.49 tff(33,plain,(
% 0.20/0.49 ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[32])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (k0(b) <=> k0(b)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(36,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (k0(b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (l0(c) <=> l0(c)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(39,axiom,(l0(c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (l0(c)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | ((~l0(c)) | (~k0(b)) | m1(c, b, c))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(b)) | m1(c, b, c))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 ((m1(c, b, c) | (~l0(c)) | (~k0(b))) <=> ((~l0(c)) | (~k0(b)) | m1(c, b, c))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, b, c) | (~l0(c)) | (~k0(b)))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | ((~l0(c)) | (~k0(b)) | m1(c, b, c)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, b, c) | (~l0(c)) | (~k0(b)))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(b)) | m1(c, b, c))),
% 0.20/0.49 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, b, c) | (~l0(c)) | (~k0(b)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(b)) | m1(c, b, c)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[46, 40, 37, 34, 24])).
% 0.20/0.49 tff(48,plain,(m1(c, b, c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 ((~k2(c, b)) <=> (~k2(c, b))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(50,axiom,(~k2(c, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (~k2(c, b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(55,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.49 tff(57,plain,(
% 0.20/0.49 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[56])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (n0(d, b) <=> n0(d, b)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(60,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (n0(d, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 (k1(b)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[64, 61, 58])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k2(C, D) | (~m1(E, D, C))) <=> ((~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> (((~m1(E, D, C)) | k2(C, D)) | (~k1(F))))), rewrite((((~m1(E, D, C)) | k2(C, D)) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D)))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> (((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))))), rewrite((((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.50 tff(71,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_127')).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.50 tff(74,plain,(
% 0.20/0.50 ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(skolemize,[status(sab)],[73])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(b)) | (~k2(b, b)) | (~m1(c, b, c)) | k2(c, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(b)) | (~k2(b, b)) | (~m1(c, b, c)) | k2(c, b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(b)) | (~k2(b, b)) | (~m1(c, b, c)) | k2(c, b))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(b)) | (~k2(b, b)) | (~m1(c, b, c)) | k2(c, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[78, 75, 65, 51, 48, 23])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------