TSTP Solution File: SYN178-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN178-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 23:54:04 EDT 2022
% Result : Unsatisfiable 1.40s 1.16s
% Output : Proof 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN178-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:18:07 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 1.40/1.16 % SZS status Unsatisfiable
% 1.40/1.16 % SZS output start Proof
% 1.40/1.16 tff(q2_type, type, (
% 1.40/1.16 q2: ( $i * $i * $i ) > $o)).
% 1.40/1.16 tff(d_type, type, (
% 1.40/1.16 d: $i)).
% 1.40/1.16 tff(b_type, type, (
% 1.40/1.16 b: $i)).
% 1.40/1.16 tff(q1_type, type, (
% 1.40/1.16 q1: ( $i * $i * $i ) > $o)).
% 1.40/1.16 tff(c_type, type, (
% 1.40/1.16 c: $i)).
% 1.40/1.16 tff(n0_type, type, (
% 1.40/1.16 n0: ( $i * $i ) > $o)).
% 1.40/1.16 tff(p0_type, type, (
% 1.40/1.16 p0: ( $i * $i ) > $o)).
% 1.40/1.16 tff(r1_type, type, (
% 1.40/1.16 r1: $i > $o)).
% 1.40/1.16 tff(q0_type, type, (
% 1.40/1.16 q0: ( $i * $i ) > $o)).
% 1.40/1.16 tff(s0_type, type, (
% 1.40/1.16 s0: $i > $o)).
% 1.40/1.16 tff(m0_type, type, (
% 1.40/1.16 m0: ( $i * $i * $i ) > $o)).
% 1.40/1.16 tff(k0_type, type, (
% 1.40/1.16 k0: $i > $o)).
% 1.40/1.16 tff(q3_type, type, (
% 1.40/1.16 q3: ( $i * $i ) > $o)).
% 1.40/1.16 tff(1,plain,
% 1.40/1.16 (^[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)))),
% 1.40/1.16 inference(bind,[status(th)],[])).
% 1.40/1.16 tff(2,plain,
% 1.40/1.16 (![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))),
% 1.40/1.16 inference(quant_intro,[status(thm)],[1])).
% 1.40/1.16 tff(3,plain,
% 1.40/1.16 (![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))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(4,plain,
% 1.40/1.16 (^[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))))),
% 1.40/1.16 inference(bind,[status(th)],[])).
% 1.40/1.16 tff(5,plain,
% 1.40/1.16 (![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))),
% 1.40/1.16 inference(quant_intro,[status(thm)],[4])).
% 1.40/1.16 tff(6,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')).
% 1.40/1.16 tff(7,plain,
% 1.40/1.16 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.40/1.16 tff(8,plain,
% 1.40/1.16 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.40/1.16 tff(9,plain,(
% 1.40/1.16 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.40/1.16 inference(skolemize,[status(sab)],[8])).
% 1.40/1.16 tff(10,plain,
% 1.40/1.16 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.40/1.16 tff(11,plain,
% 1.40/1.16 (n0(d, c) <=> n0(d, c)),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(12,axiom,(n0(d, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 1.40/1.16 tff(13,plain,
% 1.40/1.16 (n0(d, c)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.40/1.16 tff(14,plain,
% 1.40/1.16 (p0(c, b) <=> p0(c, b)),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(15,axiom,(p0(c, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.40/1.16 tff(16,plain,
% 1.40/1.16 (p0(c, b)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.40/1.16 tff(17,plain,
% 1.40/1.16 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(18,plain,
% 1.40/1.16 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 1.40/1.16 inference(quant_inst,[status(thm)],[])).
% 1.40/1.16 tff(19,plain,
% 1.40/1.16 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.40/1.16 tff(20,plain,
% 1.40/1.16 (q1(b, c, b)),
% 1.40/1.16 inference(unit_resolution,[status(thm)],[19, 16, 13, 10])).
% 1.40/1.16 tff(21,plain,
% 1.40/1.16 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.40/1.16 inference(bind,[status(th)],[])).
% 1.40/1.16 tff(22,plain,
% 1.40/1.16 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(quant_intro,[status(thm)],[21])).
% 1.40/1.16 tff(23,plain,
% 1.40/1.16 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(24,plain,
% 1.40/1.16 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.40/1.16 inference(bind,[status(th)],[])).
% 1.40/1.16 tff(25,plain,
% 1.40/1.16 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(quant_intro,[status(thm)],[24])).
% 1.40/1.16 tff(26,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 1.40/1.16 tff(27,plain,
% 1.40/1.16 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.40/1.16 tff(28,plain,
% 1.40/1.16 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.40/1.16 tff(29,plain,(
% 1.40/1.16 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(skolemize,[status(sab)],[28])).
% 1.40/1.16 tff(30,plain,
% 1.40/1.16 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.40/1.16 tff(31,plain,
% 1.40/1.16 (((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))) <=> ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(32,plain,
% 1.40/1.16 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 1.40/1.16 inference(quant_inst,[status(thm)],[])).
% 1.40/1.16 tff(33,plain,
% 1.40/1.16 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.40/1.16 tff(34,plain,
% 1.40/1.16 (q2(b, b, b)),
% 1.40/1.16 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 1.40/1.16 tff(35,plain,
% 1.40/1.16 (p0(b, d) <=> p0(b, d)),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(36,axiom,(p0(b, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 1.40/1.16 tff(37,plain,
% 1.40/1.16 (p0(b, d)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.40/1.16 tff(38,plain,
% 1.40/1.16 (n0(d, b) <=> n0(d, b)),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(39,axiom,(n0(d, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 1.40/1.16 tff(40,plain,
% 1.40/1.16 (n0(d, b)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.40/1.16 tff(41,plain,
% 1.40/1.16 (((~![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))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(42,plain,
% 1.40/1.16 ((~![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))),
% 1.40/1.16 inference(quant_inst,[status(thm)],[])).
% 1.40/1.16 tff(43,plain,
% 1.40/1.16 ((~![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)),
% 1.40/1.16 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.40/1.16 tff(44,plain,
% 1.40/1.16 (q1(d, b, d)),
% 1.40/1.16 inference(unit_resolution,[status(thm)],[43, 40, 37, 10])).
% 1.40/1.16 tff(45,plain,
% 1.40/1.16 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 1.40/1.16 inference(bind,[status(th)],[])).
% 1.40/1.16 tff(46,plain,
% 1.40/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.40/1.16 inference(quant_intro,[status(thm)],[45])).
% 1.40/1.16 tff(47,plain,
% 1.40/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.40/1.16 inference(rewrite,[status(thm)],[])).
% 1.40/1.16 tff(48,plain,
% 1.40/1.16 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(49,plain,
% 1.45/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[48])).
% 1.45/1.16 tff(50,plain,
% 1.45/1.16 (^[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))))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(51,plain,
% 1.45/1.16 (![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))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[50])).
% 1.45/1.16 tff(52,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')).
% 1.45/1.16 tff(53,plain,
% 1.45/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.45/1.16 tff(54,plain,
% 1.45/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.45/1.16 tff(55,plain,
% 1.45/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.45/1.16 tff(56,plain,(
% 1.45/1.16 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.45/1.16 inference(skolemize,[status(sab)],[55])).
% 1.45/1.16 tff(57,plain,
% 1.45/1.16 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[56, 46])).
% 1.45/1.16 tff(58,plain,
% 1.45/1.16 (q0(b, b) <=> q0(b, b)),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(59,axiom,(q0(b, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_6')).
% 1.45/1.16 tff(60,plain,
% 1.45/1.16 (q0(b, b)),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.45/1.16 tff(61,plain,
% 1.45/1.16 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | r1(b) | (~q1(d, b, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(62,plain,
% 1.45/1.16 (((~q0(b, b)) | (~q1(d, b, d)) | r1(b)) <=> ((~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(63,plain,
% 1.45/1.16 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | r1(b) | (~q1(d, b, d))))),
% 1.45/1.16 inference(monotonicity,[status(thm)],[62])).
% 1.45/1.16 tff(64,plain,
% 1.45/1.16 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.45/1.16 inference(transitivity,[status(thm)],[63, 61])).
% 1.45/1.16 tff(65,plain,
% 1.45/1.16 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))),
% 1.45/1.16 inference(quant_inst,[status(thm)],[])).
% 1.45/1.16 tff(66,plain,
% 1.45/1.16 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.45/1.16 tff(67,plain,
% 1.45/1.16 (r1(b)),
% 1.45/1.16 inference(unit_resolution,[status(thm)],[66, 60, 57, 44])).
% 1.45/1.16 tff(68,assumption,(~m0(d, d, d)), introduced(assumption)).
% 1.45/1.16 tff(69,plain,
% 1.45/1.16 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(70,plain,
% 1.45/1.16 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.45/1.16 inference(quant_intro,[status(thm)],[69])).
% 1.45/1.16 tff(71,plain,
% 1.45/1.16 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(72,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.45/1.16 tff(73,plain,
% 1.45/1.16 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.45/1.16 tff(74,plain,(
% 1.45/1.16 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.45/1.16 inference(skolemize,[status(sab)],[73])).
% 1.45/1.16 tff(75,plain,
% 1.45/1.16 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.45/1.16 tff(76,plain,
% 1.45/1.16 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, d)),
% 1.45/1.16 inference(quant_inst,[status(thm)],[])).
% 1.45/1.16 tff(77,plain,
% 1.45/1.16 ($false),
% 1.45/1.16 inference(unit_resolution,[status(thm)],[76, 75, 68])).
% 1.45/1.16 tff(78,plain,(m0(d, d, d)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.16 tff(79,plain,
% 1.45/1.16 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(80,plain,
% 1.45/1.16 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[79])).
% 1.45/1.16 tff(81,plain,
% 1.45/1.16 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(82,plain,
% 1.45/1.16 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((q2(C, D, C) | (~r1(D))) <=> ((~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> (((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))))), rewrite((((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> (((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))))), rewrite((((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> (((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))))), rewrite((((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(83,plain,
% 1.45/1.16 (![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[82])).
% 1.45/1.16 tff(84,axiom,(![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 1.45/1.16 tff(85,plain,
% 1.45/1.16 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.45/1.16 tff(86,plain,
% 1.45/1.16 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.45/1.16 tff(87,plain,(
% 1.45/1.16 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(skolemize,[status(sab)],[86])).
% 1.45/1.16 tff(88,plain,
% 1.45/1.16 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[87, 80])).
% 1.45/1.16 tff(89,plain,
% 1.45/1.16 (k0(b) <=> k0(b)),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(90,axiom,(k0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.45/1.16 tff(91,plain,
% 1.45/1.16 (k0(b)),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.45/1.16 tff(92,plain,
% 1.45/1.16 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(93,plain,
% 1.45/1.16 (((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d)) <=> ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(94,plain,
% 1.45/1.16 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d)))),
% 1.45/1.16 inference(monotonicity,[status(thm)],[93])).
% 1.45/1.16 tff(95,plain,
% 1.45/1.16 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 1.45/1.16 inference(transitivity,[status(thm)],[94, 92])).
% 1.45/1.16 tff(96,plain,
% 1.45/1.16 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))),
% 1.45/1.16 inference(quant_inst,[status(thm)],[])).
% 1.45/1.16 tff(97,plain,
% 1.45/1.16 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d)),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.45/1.16 tff(98,plain,
% 1.45/1.16 (q2(d, b, d)),
% 1.45/1.16 inference(unit_resolution,[status(thm)],[97, 91, 88, 78, 67, 34])).
% 1.45/1.16 tff(99,plain,
% 1.45/1.16 ((~q3(b, d)) <=> (~q3(b, d))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(100,axiom,(~q3(b, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 1.45/1.16 tff(101,plain,
% 1.45/1.16 (~q3(b, d)),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.45/1.16 tff(102,plain,
% 1.45/1.16 (^[I: $i, H: $i, G: $i] : refl(((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(103,plain,
% 1.45/1.16 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[102])).
% 1.45/1.16 tff(104,plain,
% 1.45/1.16 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.16 inference(rewrite,[status(thm)],[])).
% 1.45/1.16 tff(105,plain,
% 1.45/1.16 (^[I: $i, H: $i, G: $i] : trans(monotonicity(rewrite((q3(G, H) | (~q2(I, G, H))) <=> ((~q2(I, G, H)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> (((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))))), rewrite((((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))))),
% 1.45/1.16 inference(bind,[status(th)],[])).
% 1.45/1.16 tff(106,plain,
% 1.45/1.16 (![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.16 inference(quant_intro,[status(thm)],[105])).
% 1.45/1.16 tff(107,axiom,(![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_255')).
% 1.45/1.16 tff(108,plain,
% 1.45/1.16 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.16 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.45/1.17 tff(109,plain,
% 1.45/1.17 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.17 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.45/1.17 tff(110,plain,(
% 1.45/1.17 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.17 inference(skolemize,[status(sab)],[109])).
% 1.45/1.17 tff(111,plain,
% 1.45/1.17 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 1.45/1.17 inference(modus_ponens,[status(thm)],[110, 103])).
% 1.45/1.17 tff(112,plain,
% 1.45/1.17 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))),
% 1.45/1.17 inference(rewrite,[status(thm)],[])).
% 1.45/1.17 tff(113,plain,
% 1.45/1.17 (((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d)) <=> (q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))),
% 1.45/1.17 inference(rewrite,[status(thm)],[])).
% 1.45/1.17 tff(114,plain,
% 1.45/1.17 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(b, d) | (~n0(d, b)) | (~q2(d, b, d))))),
% 1.45/1.17 inference(monotonicity,[status(thm)],[113])).
% 1.45/1.17 tff(115,plain,
% 1.45/1.17 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(b, d) | (~n0(d, b)) | (~q2(d, b, d)))),
% 1.45/1.17 inference(transitivity,[status(thm)],[114, 112])).
% 1.45/1.17 tff(116,plain,
% 1.45/1.17 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))),
% 1.45/1.17 inference(quant_inst,[status(thm)],[])).
% 1.45/1.17 tff(117,plain,
% 1.45/1.17 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(b, d) | (~n0(d, b)) | (~q2(d, b, d))),
% 1.45/1.17 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.45/1.17 tff(118,plain,
% 1.45/1.17 ($false),
% 1.45/1.17 inference(unit_resolution,[status(thm)],[117, 40, 111, 101, 98])).
% 1.45/1.17 % SZS output end Proof
%------------------------------------------------------------------------------