TSTP Solution File: SYN111-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN111-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Thu Sep 29 23:53:47 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN111-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 : Mon Sep 5 01:46:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.50 % SZS status Unsatisfiable
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 tff(k2_type, type, (
% 0.18/0.50 k2: ( $i * $i ) > $o)).
% 0.18/0.50 tff(b_type, type, (
% 0.18/0.50 b: $i)).
% 0.18/0.50 tff(q1_type, type, (
% 0.18/0.50 q1: ( $i * $i * $i ) > $o)).
% 0.18/0.50 tff(r0_type, type, (
% 0.18/0.50 r0: $i > $o)).
% 0.18/0.50 tff(m1_type, type, (
% 0.18/0.50 m1: ( $i * $i * $i ) > $o)).
% 0.18/0.50 tff(c_type, type, (
% 0.18/0.50 c: $i)).
% 0.18/0.50 tff(k0_type, type, (
% 0.18/0.50 k0: $i > $o)).
% 0.18/0.50 tff(l0_type, type, (
% 0.18/0.50 l0: $i > $o)).
% 0.18/0.50 tff(k1_type, type, (
% 0.18/0.50 k1: $i > $o)).
% 0.18/0.50 tff(n0_type, type, (
% 0.18/0.50 n0: ( $i * $i ) > $o)).
% 0.18/0.50 tff(d_type, type, (
% 0.18/0.50 d: $i)).
% 0.18/0.50 tff(1,plain,
% 0.18/0.50 (^[A: $i, J: $i] : refl(((~q1(A, J, J)) | k2(J, J)) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(2,plain,
% 0.18/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.50 tff(3,plain,
% 0.18/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J)) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(4,plain,
% 0.18/0.50 (^[A: $i, J: $i] : rewrite((k2(J, J) | (~q1(A, J, J))) <=> ((~q1(A, J, J)) | k2(J, J)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(5,plain,
% 0.18/0.50 (![A: $i, J: $i] : (k2(J, J) | (~q1(A, J, J))) <=> ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.50 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')).
% 0.18/0.50 tff(7,plain,
% 0.18/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.50 tff(8,plain,
% 0.18/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.50 tff(9,plain,(
% 0.18/0.50 ![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(skolemize,[status(sab)],[8])).
% 0.18/0.50 tff(10,plain,
% 0.18/0.50 (![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.50 tff(11,plain,
% 0.18/0.50 (q1(b, b, b) <=> q1(b, b, b)),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(12,plain,
% 0.18/0.50 (($false | q1(b, b, b)) <=> q1(b, b, b)),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(13,plain,
% 0.18/0.50 ((~$true) <=> $false),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(14,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.18/0.50 tff(15,plain,
% 0.18/0.50 (r0(b) <=> $true),
% 0.18/0.50 inference(iff_true,[status(thm)],[14])).
% 0.18/0.50 tff(16,plain,
% 0.18/0.50 ((~r0(b)) <=> (~$true)),
% 0.18/0.50 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.50 tff(17,plain,
% 0.18/0.50 ((~r0(b)) <=> $false),
% 0.18/0.50 inference(transitivity,[status(thm)],[16, 13])).
% 0.18/0.50 tff(18,plain,
% 0.18/0.50 (((~r0(b)) | q1(b, b, b)) <=> ($false | q1(b, b, b))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[17])).
% 0.18/0.50 tff(19,plain,
% 0.18/0.50 (((~r0(b)) | q1(b, b, b)) <=> q1(b, b, b)),
% 0.18/0.50 inference(transitivity,[status(thm)],[18, 12])).
% 0.18/0.50 tff(20,plain,
% 0.18/0.50 ((q1(b, b, b) | (~r0(b))) <=> ((~r0(b)) | q1(b, b, b))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(21,axiom,(q1(b, b, b) | (~r0(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_120')).
% 0.18/0.50 tff(22,plain,
% 0.18/0.50 ((~r0(b)) | q1(b, b, b)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.50 tff(23,plain,
% 0.18/0.50 (q1(b, b, b)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.18/0.50 tff(24,plain,
% 0.18/0.50 (q1(b, b, b)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.18/0.50 tff(25,plain,
% 0.18/0.50 (((~![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))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(26,plain,
% 0.18/0.50 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | ((~q1(b, b, b)) | k2(b, b))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(27,plain,
% 0.18/0.50 ((~![A: $i, J: $i] : ((~q1(A, J, J)) | k2(J, J))) | (~q1(b, b, b)) | k2(b, b)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.50 tff(28,plain,
% 0.18/0.50 (k2(b, b)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[27, 24, 10])).
% 0.18/0.50 tff(29,assumption,(~m1(c, b, c)), introduced(assumption)).
% 0.18/0.50 tff(30,plain,
% 0.18/0.50 (^[I: $i, J: $i] : refl((m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(31,plain,
% 0.18/0.51 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.51 tff(32,plain,
% 0.18/0.51 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(33,plain,
% 0.18/0.51 (^[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)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(34,plain,
% 0.18/0.51 (![I: $i, J: $i] : ((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.51 tff(35,axiom,(![I: $i, J: $i] : ((m1(I, J, I) | (~l0(I))) | (~k0(J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_021')).
% 0.18/0.51 tff(36,plain,
% 0.18/0.51 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.51 tff(37,plain,
% 0.18/0.51 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.51 tff(38,plain,(
% 0.18/0.51 ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[37])).
% 0.18/0.51 tff(39,plain,
% 0.18/0.51 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.51 tff(40,plain,
% 0.18/0.51 (k0(b) <=> k0(b)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(41,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.18/0.51 tff(42,plain,
% 0.18/0.51 (k0(b)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.51 tff(43,plain,
% 0.18/0.51 (l0(c) <=> l0(c)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(44,axiom,(l0(c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.18/0.51 tff(45,plain,
% 0.18/0.51 (l0(c)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.51 tff(46,plain,
% 0.18/0.51 (((~![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))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(47,plain,
% 0.18/0.51 ((m1(c, b, c) | (~l0(c)) | (~k0(b))) <=> ((~l0(c)) | (~k0(b)) | m1(c, b, c))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(48,plain,
% 0.18/0.51 (((~![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)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.51 tff(49,plain,
% 0.18/0.51 (((~![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))),
% 0.18/0.51 inference(transitivity,[status(thm)],[48, 46])).
% 0.18/0.51 tff(50,plain,
% 0.18/0.51 ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, b, c) | (~l0(c)) | (~k0(b)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(51,plain,
% 0.18/0.51 ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(b)) | m1(c, b, c)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.51 tff(52,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[51, 45, 42, 39, 29])).
% 0.18/0.51 tff(53,plain,(m1(c, b, c)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(54,plain,
% 0.18/0.51 ((~k2(c, b)) <=> (~k2(c, b))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(55,axiom,(~k2(c, b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.18/0.51 tff(56,plain,
% 0.18/0.51 (~k2(c, b)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.51 tff(57,plain,
% 0.18/0.51 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(58,plain,
% 0.18/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.51 tff(59,plain,
% 0.18/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(60,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.18/0.51 tff(61,plain,
% 0.18/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.51 tff(62,plain,(
% 0.18/0.51 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[61])).
% 0.18/0.51 tff(63,plain,
% 0.18/0.51 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 (n0(d, b) <=> n0(d, b)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(65,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 (n0(d, b)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (((~![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)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.51 tff(70,plain,
% 0.18/0.51 (k1(b)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[69, 66, 63])).
% 0.18/0.51 tff(71,plain,
% 0.18/0.51 (^[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)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(72,plain,
% 0.18/0.51 (![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))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.51 tff(73,plain,
% 0.18/0.51 (![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))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(74,plain,
% 0.18/0.51 (^[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))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(75,plain,
% 0.18/0.51 (![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))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.51 tff(76,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')).
% 0.18/0.51 tff(77,plain,
% 0.18/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.51 tff(78,plain,
% 0.18/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.18/0.51 tff(79,plain,(
% 0.18/0.51 ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.18/0.51 inference(skolemize,[status(sab)],[78])).
% 0.18/0.51 tff(80,plain,
% 0.18/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.18/0.51 tff(81,plain,
% 0.18/0.51 (((~![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))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(82,plain,
% 0.18/0.52 ((~![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))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(83,plain,
% 0.18/0.52 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(b)) | (~k2(b, b)) | (~m1(c, b, c)) | k2(c, b)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.52 tff(84,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[83, 80, 70, 56, 53, 28])).
% 0.18/0.52 % SZS output end Proof
%------------------------------------------------------------------------------