TSTP Solution File: SYN203-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN203-1 : 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 23:54:11 EDT 2022
% Result : Unsatisfiable 1.95s 1.46s
% Output : Proof 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN203-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13 % 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 02:23:07 EDT 2022
% 0.12/0.34 % 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.
% 1.95/1.46 % SZS status Unsatisfiable
% 1.95/1.46 % SZS output start Proof
% 1.95/1.46 tff(s3_type, type, (
% 1.95/1.46 s3: ( $i * $i ) > $o)).
% 1.95/1.46 tff(b_type, type, (
% 1.95/1.46 b: $i)).
% 1.95/1.46 tff(m0_type, type, (
% 1.95/1.46 m0: ( $i * $i * $i ) > $o)).
% 1.95/1.46 tff(d_type, type, (
% 1.95/1.46 d: $i)).
% 1.95/1.46 tff(q2_type, type, (
% 1.95/1.46 q2: ( $i * $i * $i ) > $o)).
% 1.95/1.46 tff(q1_type, type, (
% 1.95/1.46 q1: ( $i * $i * $i ) > $o)).
% 1.95/1.46 tff(c_type, type, (
% 1.95/1.46 c: $i)).
% 1.95/1.46 tff(n0_type, type, (
% 1.95/1.46 n0: ( $i * $i ) > $o)).
% 1.95/1.46 tff(p0_type, type, (
% 1.95/1.46 p0: ( $i * $i ) > $o)).
% 1.95/1.46 tff(r1_type, type, (
% 1.95/1.46 r1: $i > $o)).
% 1.95/1.46 tff(q0_type, type, (
% 1.95/1.46 q0: ( $i * $i ) > $o)).
% 1.95/1.46 tff(s0_type, type, (
% 1.95/1.46 s0: $i > $o)).
% 1.95/1.46 tff(k0_type, type, (
% 1.95/1.46 k0: $i > $o)).
% 1.95/1.46 tff(s2_type, type, (
% 1.95/1.46 s2: $i > $o)).
% 1.95/1.46 tff(s1_type, type, (
% 1.95/1.46 s1: $i > $o)).
% 1.95/1.46 tff(1,plain,
% 1.95/1.46 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.95/1.46 inference(bind,[status(th)],[])).
% 1.95/1.46 tff(2,plain,
% 1.95/1.46 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.95/1.46 inference(quant_intro,[status(thm)],[1])).
% 1.95/1.46 tff(3,plain,
% 1.95/1.46 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.95/1.46 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(4,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.95/1.47 tff(5,plain,
% 1.95/1.47 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.95/1.47 tff(6,plain,(
% 1.95/1.47 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.95/1.47 inference(skolemize,[status(sab)],[5])).
% 1.95/1.47 tff(7,plain,
% 1.95/1.47 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.95/1.47 tff(8,plain,
% 1.95/1.47 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, b)),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(9,plain,
% 1.95/1.47 (m0(d, d, b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.95/1.47 tff(10,assumption,(~m0(b, d, d)), introduced(assumption)).
% 1.95/1.47 tff(11,plain,
% 1.95/1.47 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, d)),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(12,plain,
% 1.95/1.47 ($false),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[11, 7, 10])).
% 1.95/1.47 tff(13,plain,(m0(b, d, d)), inference(lemma,lemma(discharge,[]))).
% 1.95/1.47 tff(14,plain,
% 1.95/1.47 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(15,plain,
% 1.95/1.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[14])).
% 1.95/1.47 tff(16,plain,
% 1.95/1.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(17,plain,
% 1.95/1.47 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(18,plain,
% 1.95/1.47 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[17])).
% 1.95/1.47 tff(19,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 1.95/1.47 tff(20,plain,
% 1.95/1.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.95/1.47 tff(21,plain,
% 1.95/1.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.95/1.47 tff(22,plain,(
% 1.95/1.47 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(skolemize,[status(sab)],[21])).
% 1.95/1.47 tff(23,plain,
% 1.95/1.47 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[22, 15])).
% 1.95/1.47 tff(24,plain,
% 1.95/1.47 (n0(d, c) <=> n0(d, c)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(25,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 1.95/1.47 tff(26,plain,
% 1.95/1.47 (n0(d, c)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.95/1.47 tff(27,plain,
% 1.95/1.47 (p0(c, b) <=> p0(c, b)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(28,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 1.95/1.47 tff(29,plain,
% 1.95/1.47 (p0(c, b)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.95/1.47 tff(30,plain,
% 1.95/1.47 (((~![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))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(31,plain,
% 1.95/1.47 ((~![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))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(32,plain,
% 1.95/1.47 ((~![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)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.95/1.47 tff(33,plain,
% 1.95/1.47 (q1(b, c, b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[32, 29, 26, 23])).
% 1.95/1.47 tff(34,plain,
% 1.95/1.47 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(35,plain,
% 1.95/1.47 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[34])).
% 1.95/1.47 tff(36,plain,
% 1.95/1.47 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(37,plain,
% 1.95/1.47 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(38,plain,
% 1.95/1.47 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[37])).
% 1.95/1.47 tff(39,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 1.95/1.47 tff(40,plain,
% 1.95/1.47 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.95/1.47 tff(41,plain,
% 1.95/1.47 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.95/1.47 tff(42,plain,(
% 1.95/1.47 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(skolemize,[status(sab)],[41])).
% 1.95/1.47 tff(43,plain,
% 1.95/1.47 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.95/1.47 tff(44,plain,
% 1.95/1.47 (((~![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))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(45,plain,
% 1.95/1.47 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(46,plain,
% 1.95/1.47 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.95/1.47 tff(47,plain,
% 1.95/1.47 (q2(b, b, b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 1.95/1.47 tff(48,plain,
% 1.95/1.47 (p0(b, d) <=> p0(b, d)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(49,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 1.95/1.47 tff(50,plain,
% 1.95/1.47 (p0(b, d)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.95/1.47 tff(51,plain,
% 1.95/1.47 (n0(d, b) <=> n0(d, b)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(52,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 1.95/1.47 tff(53,plain,
% 1.95/1.47 (n0(d, b)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.95/1.47 tff(54,plain,
% 1.95/1.47 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(55,plain,
% 1.95/1.47 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(56,plain,
% 1.95/1.47 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.95/1.47 tff(57,plain,
% 1.95/1.47 (q1(d, b, d)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[56, 53, 50, 23])).
% 1.95/1.47 tff(58,plain,
% 1.95/1.47 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(59,plain,
% 1.95/1.47 (![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))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[58])).
% 1.95/1.47 tff(60,plain,
% 1.95/1.47 (![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))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(61,plain,
% 1.95/1.47 (^[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))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(62,plain,
% 1.95/1.47 (![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))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[61])).
% 1.95/1.47 tff(63,plain,
% 1.95/1.47 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(64,plain,
% 1.95/1.47 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[63])).
% 1.95/1.47 tff(65,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 1.95/1.47 tff(66,plain,
% 1.95/1.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.95/1.47 tff(67,plain,
% 1.95/1.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.95/1.47 tff(68,plain,
% 1.95/1.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.95/1.47 tff(69,plain,(
% 1.95/1.47 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.95/1.47 inference(skolemize,[status(sab)],[68])).
% 1.95/1.47 tff(70,plain,
% 1.95/1.47 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[69, 59])).
% 1.95/1.47 tff(71,plain,
% 1.95/1.47 (q0(b, b) <=> q0(b, b)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(72,axiom,(q0(b, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_6')).
% 1.95/1.47 tff(73,plain,
% 1.95/1.47 (q0(b, b)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.95/1.47 tff(74,plain,
% 1.95/1.47 (((~![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)))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(75,plain,
% 1.95/1.47 (((~q0(b, b)) | (~q1(d, b, d)) | r1(b)) <=> ((~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(76,plain,
% 1.95/1.47 (((~![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))))),
% 1.95/1.47 inference(monotonicity,[status(thm)],[75])).
% 1.95/1.47 tff(77,plain,
% 1.95/1.47 (((~![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)))),
% 1.95/1.47 inference(transitivity,[status(thm)],[76, 74])).
% 1.95/1.47 tff(78,plain,
% 1.95/1.47 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~q1(d, b, d)) | r1(b))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(79,plain,
% 1.95/1.47 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.95/1.47 tff(80,plain,
% 1.95/1.47 (r1(b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[79, 73, 70, 57])).
% 1.95/1.47 tff(81,plain,
% 1.95/1.47 (^[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)))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(82,plain,
% 1.95/1.47 (![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))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[81])).
% 1.95/1.47 tff(83,plain,
% 1.95/1.47 (![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))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(84,plain,
% 1.95/1.47 (^[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))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(85,plain,
% 1.95/1.47 (![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))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[84])).
% 1.95/1.47 tff(86,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/sandbox/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 1.95/1.47 tff(87,plain,
% 1.95/1.47 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.95/1.47 tff(88,plain,
% 1.95/1.47 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.95/1.47 tff(89,plain,(
% 1.95/1.47 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.95/1.47 inference(skolemize,[status(sab)],[88])).
% 1.95/1.47 tff(90,plain,
% 1.95/1.47 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[89, 82])).
% 1.95/1.47 tff(91,plain,
% 1.95/1.47 (k0(b) <=> k0(b)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(92,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 1.95/1.47 tff(93,plain,
% 1.95/1.47 (k0(b)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.95/1.47 tff(94,plain,
% 1.95/1.47 (((~![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)) | (~q2(b, b, b)) | (~m0(b, d, d)) | 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)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(95,plain,
% 1.95/1.47 (((~m0(b, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d)) <=> ((~k0(b)) | (~r1(b)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(96,plain,
% 1.95/1.47 (((~![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(b, 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)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d)))),
% 1.95/1.47 inference(monotonicity,[status(thm)],[95])).
% 1.95/1.47 tff(97,plain,
% 1.95/1.47 (((~![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(b, 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)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d))),
% 1.95/1.47 inference(transitivity,[status(thm)],[96, 94])).
% 1.95/1.47 tff(98,plain,
% 1.95/1.47 ((~![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(b, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(99,plain,
% 1.95/1.47 ((~![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)) | (~q2(b, b, b)) | (~m0(b, d, d)) | q2(d, b, d)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.95/1.47 tff(100,plain,
% 1.95/1.47 (q2(d, b, d)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[99, 93, 90, 80, 47, 13])).
% 1.95/1.47 tff(101,assumption,(~p0(b, b)), introduced(assumption)).
% 1.95/1.47 tff(102,plain,
% 1.95/1.47 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(103,plain,
% 1.95/1.47 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.95/1.47 inference(quant_intro,[status(thm)],[102])).
% 1.95/1.47 tff(104,plain,
% 1.95/1.47 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(105,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.95/1.47 tff(106,plain,
% 1.95/1.47 (![X: $i] : p0(b, X)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.95/1.47 tff(107,plain,(
% 1.95/1.47 ![X: $i] : p0(b, X)),
% 1.95/1.47 inference(skolemize,[status(sab)],[106])).
% 1.95/1.47 tff(108,plain,
% 1.95/1.47 (![X: $i] : p0(b, X)),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.95/1.47 tff(109,plain,
% 1.95/1.47 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(110,plain,
% 1.95/1.47 ($false),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[109, 108, 101])).
% 1.95/1.47 tff(111,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.95/1.47 tff(112,plain,
% 1.95/1.47 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(113,plain,
% 1.95/1.47 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[112])).
% 1.95/1.47 tff(114,plain,
% 1.95/1.47 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(115,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.95/1.47 tff(116,plain,
% 1.95/1.47 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.95/1.47 tff(117,plain,(
% 1.95/1.47 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.95/1.47 inference(skolemize,[status(sab)],[116])).
% 1.95/1.47 tff(118,plain,
% 1.95/1.47 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[117, 113])).
% 1.95/1.47 tff(119,plain,
% 1.95/1.47 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(120,plain,
% 1.95/1.47 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(121,plain,
% 1.95/1.47 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.95/1.47 tff(122,plain,
% 1.95/1.47 (s1(b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[121, 118, 111])).
% 1.95/1.47 tff(123,plain,
% 1.95/1.47 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(124,plain,
% 1.95/1.47 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[123])).
% 1.95/1.47 tff(125,plain,
% 1.95/1.47 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(126,plain,
% 1.95/1.47 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(127,plain,
% 1.95/1.47 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[126])).
% 1.95/1.47 tff(128,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.95/1.47 tff(129,plain,
% 1.95/1.47 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.95/1.47 tff(130,plain,
% 1.95/1.47 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[129, 125])).
% 1.95/1.47 tff(131,plain,(
% 1.95/1.47 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(skolemize,[status(sab)],[130])).
% 1.95/1.47 tff(132,plain,
% 1.95/1.47 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[131, 124])).
% 1.95/1.47 tff(133,plain,
% 1.95/1.47 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(134,plain,
% 1.95/1.47 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 1.95/1.47 inference(quant_inst,[status(thm)],[])).
% 1.95/1.47 tff(135,plain,
% 1.95/1.47 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b))),
% 1.95/1.47 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.95/1.47 tff(136,plain,
% 1.95/1.47 ((~s1(b)) | s2(b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[135, 132, 47])).
% 1.95/1.47 tff(137,plain,
% 1.95/1.47 (s2(b)),
% 1.95/1.47 inference(unit_resolution,[status(thm)],[136, 122])).
% 1.95/1.47 tff(138,plain,
% 1.95/1.47 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 1.95/1.47 inference(bind,[status(th)],[])).
% 1.95/1.47 tff(139,plain,
% 1.95/1.47 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.47 inference(quant_intro,[status(thm)],[138])).
% 1.95/1.47 tff(140,plain,
% 1.95/1.47 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.47 inference(rewrite,[status(thm)],[])).
% 1.95/1.47 tff(141,plain,
% 1.95/1.47 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 1.95/1.48 inference(bind,[status(th)],[])).
% 1.95/1.48 tff(142,plain,
% 1.95/1.48 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.48 inference(quant_intro,[status(thm)],[141])).
% 1.95/1.48 tff(143,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 1.95/1.48 tff(144,plain,
% 1.95/1.48 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.95/1.48 tff(145,plain,
% 1.95/1.48 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[144, 140])).
% 1.95/1.48 tff(146,plain,(
% 1.95/1.48 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.48 inference(skolemize,[status(sab)],[145])).
% 1.95/1.48 tff(147,plain,
% 1.95/1.48 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[146, 139])).
% 1.95/1.48 tff(148,plain,
% 1.95/1.48 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(d, d, b)) | (~q2(d, b, d)) | s3(b, b))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(d, d, b)) | (~q2(d, b, d)) | s3(b, b))),
% 1.95/1.48 inference(rewrite,[status(thm)],[])).
% 1.95/1.48 tff(149,plain,
% 1.95/1.48 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(d, d, b)) | (~q2(d, b, d)) | s3(b, b))),
% 1.95/1.48 inference(quant_inst,[status(thm)],[])).
% 1.95/1.48 tff(150,plain,
% 1.95/1.48 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(d, d, b)) | (~q2(d, b, d)) | s3(b, b)),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.95/1.48 tff(151,plain,
% 1.95/1.48 (s3(b, b)),
% 1.95/1.48 inference(unit_resolution,[status(thm)],[150, 147, 137, 100, 9])).
% 1.95/1.48 tff(152,plain,
% 1.95/1.48 (^[X: $i] : refl((~s3(X, b)) <=> (~s3(X, b)))),
% 1.95/1.48 inference(bind,[status(th)],[])).
% 1.95/1.48 tff(153,plain,
% 1.95/1.48 (![X: $i] : (~s3(X, b)) <=> ![X: $i] : (~s3(X, b))),
% 1.95/1.48 inference(quant_intro,[status(thm)],[152])).
% 1.95/1.48 tff(154,plain,
% 1.95/1.48 (![X: $i] : (~s3(X, b)) <=> ![X: $i] : (~s3(X, b))),
% 1.95/1.48 inference(rewrite,[status(thm)],[])).
% 1.95/1.48 tff(155,axiom,(![X: $i] : (~s3(X, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.95/1.48 tff(156,plain,
% 1.95/1.48 (![X: $i] : (~s3(X, b))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.95/1.48 tff(157,plain,(
% 1.95/1.48 ![X: $i] : (~s3(X, b))),
% 1.95/1.48 inference(skolemize,[status(sab)],[156])).
% 1.95/1.48 tff(158,plain,
% 1.95/1.48 (![X: $i] : (~s3(X, b))),
% 1.95/1.48 inference(modus_ponens,[status(thm)],[157, 153])).
% 1.95/1.48 tff(159,plain,
% 1.95/1.48 ((~![X: $i] : (~s3(X, b))) | (~s3(b, b))),
% 1.95/1.48 inference(quant_inst,[status(thm)],[])).
% 1.95/1.48 tff(160,plain,
% 1.95/1.48 ($false),
% 1.95/1.48 inference(unit_resolution,[status(thm)],[159, 158, 151])).
% 1.95/1.48 % SZS output end Proof
%------------------------------------------------------------------------------