TSTP Solution File: SYN202-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN202-1 : 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 23:54:11 EDT 2022
% Result : Unsatisfiable 1.37s 1.14s
% Output : Proof 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN202-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.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 02:04:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.37/1.14 % SZS status Unsatisfiable
% 1.37/1.14 % SZS output start Proof
% 1.37/1.14 tff(m0_type, type, (
% 1.37/1.14 m0: ( $i * $i * $i ) > $o)).
% 1.37/1.14 tff(b_type, type, (
% 1.37/1.14 b: $i)).
% 1.37/1.14 tff(d_type, type, (
% 1.37/1.14 d: $i)).
% 1.37/1.14 tff(e_type, type, (
% 1.37/1.14 e: $i)).
% 1.37/1.14 tff(q2_type, type, (
% 1.37/1.14 q2: ( $i * $i * $i ) > $o)).
% 1.37/1.14 tff(s1_type, type, (
% 1.37/1.14 s1: $i > $o)).
% 1.37/1.14 tff(p0_type, type, (
% 1.37/1.14 p0: ( $i * $i ) > $o)).
% 1.37/1.14 tff(s2_type, type, (
% 1.37/1.14 s2: $i > $o)).
% 1.37/1.14 tff(p1_type, type, (
% 1.37/1.14 p1: ( $i * $i * $i ) > $o)).
% 1.37/1.14 tff(k0_type, type, (
% 1.37/1.14 k0: $i > $o)).
% 1.37/1.14 tff(r0_type, type, (
% 1.37/1.14 r0: $i > $o)).
% 1.37/1.14 tff(r1_type, type, (
% 1.37/1.14 r1: $i > $o)).
% 1.37/1.14 tff(q1_type, type, (
% 1.37/1.14 q1: ( $i * $i * $i ) > $o)).
% 1.37/1.14 tff(q0_type, type, (
% 1.37/1.14 q0: ( $i * $i ) > $o)).
% 1.37/1.14 tff(s0_type, type, (
% 1.37/1.14 s0: $i > $o)).
% 1.37/1.14 tff(1,plain,
% 1.37/1.14 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 1.37/1.14 inference(bind,[status(th)],[])).
% 1.37/1.14 tff(2,plain,
% 1.37/1.14 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.37/1.14 inference(quant_intro,[status(thm)],[1])).
% 1.37/1.14 tff(3,plain,
% 1.37/1.14 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(4,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 1.37/1.14 tff(5,plain,
% 1.37/1.14 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.37/1.14 tff(6,plain,(
% 1.37/1.14 ![Y: $i, X: $i] : m0(X, d, Y)),
% 1.37/1.14 inference(skolemize,[status(sab)],[5])).
% 1.37/1.14 tff(7,plain,
% 1.37/1.14 (![Y: $i, X: $i] : m0(X, d, Y)),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.37/1.14 tff(8,plain,
% 1.37/1.14 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(e, d, b)),
% 1.37/1.14 inference(quant_inst,[status(thm)],[])).
% 1.37/1.14 tff(9,plain,
% 1.37/1.14 (m0(e, d, b)),
% 1.37/1.14 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.37/1.14 tff(10,assumption,(~p0(b, b)), introduced(assumption)).
% 1.37/1.14 tff(11,plain,
% 1.37/1.14 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 1.37/1.14 inference(bind,[status(th)],[])).
% 1.37/1.14 tff(12,plain,
% 1.37/1.14 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.37/1.14 inference(quant_intro,[status(thm)],[11])).
% 1.37/1.14 tff(13,plain,
% 1.37/1.14 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(14,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 1.37/1.14 tff(15,plain,
% 1.37/1.14 (![X: $i] : p0(b, X)),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.37/1.14 tff(16,plain,(
% 1.37/1.14 ![X: $i] : p0(b, X)),
% 1.37/1.14 inference(skolemize,[status(sab)],[15])).
% 1.37/1.14 tff(17,plain,
% 1.37/1.14 (![X: $i] : p0(b, X)),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.37/1.14 tff(18,plain,
% 1.37/1.14 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 1.37/1.14 inference(quant_inst,[status(thm)],[])).
% 1.37/1.14 tff(19,plain,
% 1.37/1.14 ($false),
% 1.37/1.14 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 1.37/1.14 tff(20,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.14 tff(21,plain,
% 1.37/1.14 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 1.37/1.14 inference(bind,[status(th)],[])).
% 1.37/1.14 tff(22,plain,
% 1.37/1.14 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.37/1.14 inference(quant_intro,[status(thm)],[21])).
% 1.37/1.14 tff(23,plain,
% 1.37/1.14 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(24,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 1.37/1.14 tff(25,plain,
% 1.37/1.14 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.37/1.14 tff(26,plain,(
% 1.37/1.14 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.37/1.14 inference(skolemize,[status(sab)],[25])).
% 1.37/1.14 tff(27,plain,
% 1.37/1.14 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[26, 22])).
% 1.37/1.14 tff(28,plain,
% 1.37/1.14 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(29,plain,
% 1.37/1.14 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 1.37/1.14 inference(quant_inst,[status(thm)],[])).
% 1.37/1.14 tff(30,plain,
% 1.37/1.14 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.37/1.14 tff(31,plain,
% 1.37/1.14 (s1(b)),
% 1.37/1.14 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 1.37/1.14 tff(32,plain,
% 1.37/1.14 ((~s2(e)) <=> (~s2(e))),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(33,axiom,(~s2(e)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 1.37/1.14 tff(34,plain,
% 1.37/1.14 (~s2(e)),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.37/1.14 tff(35,plain,
% 1.37/1.14 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.37/1.14 inference(bind,[status(th)],[])).
% 1.37/1.14 tff(36,plain,
% 1.37/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(quant_intro,[status(thm)],[35])).
% 1.37/1.14 tff(37,plain,
% 1.37/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(38,plain,
% 1.37/1.14 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 1.37/1.14 inference(bind,[status(th)],[])).
% 1.37/1.14 tff(39,plain,
% 1.37/1.14 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(quant_intro,[status(thm)],[38])).
% 1.37/1.14 tff(40,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 1.37/1.14 tff(41,plain,
% 1.37/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.37/1.14 tff(42,plain,
% 1.37/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.37/1.14 tff(43,plain,(
% 1.37/1.14 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(skolemize,[status(sab)],[42])).
% 1.37/1.14 tff(44,plain,
% 1.37/1.14 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[43, 36])).
% 1.37/1.14 tff(45,plain,
% 1.37/1.14 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(e) | (~q2(b, e, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(e) | (~q2(b, e, b)))),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(46,plain,
% 1.37/1.14 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(e) | (~q2(b, e, b)))),
% 1.37/1.14 inference(quant_inst,[status(thm)],[])).
% 1.37/1.14 tff(47,plain,
% 1.37/1.14 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(e) | (~q2(b, e, b))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.37/1.14 tff(48,plain,
% 1.37/1.14 ((~s1(b)) | (~q2(b, e, b))),
% 1.37/1.14 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 1.37/1.14 tff(49,plain,
% 1.37/1.14 (~q2(b, e, b)),
% 1.37/1.14 inference(unit_resolution,[status(thm)],[48, 31])).
% 1.37/1.14 tff(50,plain,
% 1.37/1.14 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 1.37/1.14 inference(bind,[status(th)],[])).
% 1.37/1.14 tff(51,plain,
% 1.37/1.14 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.37/1.14 inference(quant_intro,[status(thm)],[50])).
% 1.37/1.14 tff(52,plain,
% 1.37/1.14 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(53,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 1.37/1.14 tff(54,plain,
% 1.37/1.14 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.37/1.14 tff(55,plain,(
% 1.37/1.14 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.37/1.14 inference(skolemize,[status(sab)],[54])).
% 1.37/1.14 tff(56,plain,
% 1.37/1.14 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 1.37/1.14 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.37/1.14 tff(57,plain,
% 1.37/1.14 (p1(e, e, e) <=> p1(e, e, e)),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(58,plain,
% 1.37/1.14 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(59,plain,
% 1.37/1.14 ((~$true) <=> $false),
% 1.37/1.14 inference(rewrite,[status(thm)],[])).
% 1.37/1.14 tff(60,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 1.37/1.14 tff(61,plain,
% 1.37/1.14 (k0(e) <=> $true),
% 1.37/1.14 inference(iff_true,[status(thm)],[60])).
% 1.37/1.14 tff(62,plain,
% 1.37/1.14 ((~k0(e)) <=> (~$true)),
% 1.37/1.14 inference(monotonicity,[status(thm)],[61])).
% 1.37/1.14 tff(63,plain,
% 1.37/1.14 ((~k0(e)) <=> $false),
% 1.37/1.14 inference(transitivity,[status(thm)],[62, 59])).
% 1.37/1.14 tff(64,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 1.37/1.14 tff(65,plain,
% 1.37/1.14 (r0(e) <=> $true),
% 1.37/1.15 inference(iff_true,[status(thm)],[64])).
% 1.37/1.15 tff(66,plain,
% 1.37/1.15 ((~r0(e)) <=> (~$true)),
% 1.37/1.15 inference(monotonicity,[status(thm)],[65])).
% 1.37/1.15 tff(67,plain,
% 1.37/1.15 ((~r0(e)) <=> $false),
% 1.37/1.15 inference(transitivity,[status(thm)],[66, 59])).
% 1.37/1.15 tff(68,plain,
% 1.37/1.15 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 1.37/1.15 inference(monotonicity,[status(thm)],[67, 63])).
% 1.37/1.15 tff(69,plain,
% 1.37/1.15 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 1.37/1.15 inference(transitivity,[status(thm)],[68, 58])).
% 1.37/1.15 tff(70,plain,
% 1.37/1.15 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.37/1.15 inference(rewrite,[status(thm)],[])).
% 1.37/1.15 tff(71,plain,
% 1.37/1.15 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.37/1.15 inference(rewrite,[status(thm)],[])).
% 1.37/1.15 tff(72,plain,
% 1.37/1.15 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 1.37/1.15 inference(rewrite,[status(thm)],[])).
% 1.37/1.15 tff(73,plain,
% 1.37/1.15 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 1.37/1.15 inference(monotonicity,[status(thm)],[72])).
% 1.37/1.15 tff(74,plain,
% 1.37/1.15 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 1.37/1.15 inference(transitivity,[status(thm)],[73, 71])).
% 1.37/1.15 tff(75,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 1.37/1.15 tff(76,plain,
% 1.37/1.15 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.37/1.15 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.37/1.15 tff(77,plain,
% 1.37/1.15 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 1.37/1.15 inference(modus_ponens,[status(thm)],[76, 70])).
% 1.37/1.15 tff(78,plain,
% 1.37/1.15 (p1(e, e, e)),
% 1.37/1.15 inference(modus_ponens,[status(thm)],[77, 69])).
% 1.37/1.15 tff(79,plain,
% 1.37/1.15 (p1(e, e, e)),
% 1.37/1.15 inference(modus_ponens,[status(thm)],[78, 57])).
% 1.37/1.15 tff(80,plain,
% 1.37/1.15 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 1.37/1.15 inference(rewrite,[status(thm)],[])).
% 1.37/1.15 tff(81,plain,
% 1.37/1.15 ((q2(e, e, e) | (~p1(e, e, e))) <=> ((~p1(e, e, e)) | q2(e, e, e))),
% 1.37/1.15 inference(rewrite,[status(thm)],[])).
% 1.37/1.15 tff(82,plain,
% 1.37/1.15 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e)))),
% 1.37/1.15 inference(monotonicity,[status(thm)],[81])).
% 1.37/1.15 tff(83,plain,
% 1.37/1.15 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 1.37/1.15 inference(transitivity,[status(thm)],[82, 80])).
% 1.37/1.15 tff(84,plain,
% 1.37/1.15 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))),
% 1.37/1.15 inference(quant_inst,[status(thm)],[])).
% 1.37/1.15 tff(85,plain,
% 1.37/1.15 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e)),
% 1.37/1.15 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.37/1.15 tff(86,plain,
% 1.37/1.15 (q2(e, e, e)),
% 1.37/1.15 inference(unit_resolution,[status(thm)],[85, 79, 56])).
% 1.37/1.15 tff(87,plain,
% 1.37/1.15 (^[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)))),
% 1.37/1.15 inference(bind,[status(th)],[])).
% 1.37/1.15 tff(88,plain,
% 1.37/1.15 (![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))),
% 1.37/1.15 inference(quant_intro,[status(thm)],[87])).
% 1.37/1.15 tff(89,plain,
% 1.37/1.15 (![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))),
% 1.37/1.15 inference(rewrite,[status(thm)],[])).
% 1.37/1.15 tff(90,plain,
% 1.37/1.15 (^[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))))),
% 1.42/1.15 inference(bind,[status(th)],[])).
% 1.42/1.15 tff(91,plain,
% 1.42/1.15 (![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))),
% 1.42/1.15 inference(quant_intro,[status(thm)],[90])).
% 1.42/1.15 tff(92,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')).
% 1.42/1.15 tff(93,plain,
% 1.42/1.15 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.42/1.15 tff(94,plain,
% 1.42/1.15 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[93, 89])).
% 1.42/1.15 tff(95,plain,(
% 1.42/1.15 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.42/1.15 inference(skolemize,[status(sab)],[94])).
% 1.42/1.15 tff(96,plain,
% 1.42/1.15 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[95, 88])).
% 1.42/1.15 tff(97,plain,
% 1.42/1.15 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 1.42/1.15 inference(bind,[status(th)],[])).
% 1.42/1.15 tff(98,plain,
% 1.42/1.15 (![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))),
% 1.42/1.15 inference(quant_intro,[status(thm)],[97])).
% 1.42/1.15 tff(99,plain,
% 1.42/1.15 (![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))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(100,plain,
% 1.42/1.15 (^[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))))),
% 1.42/1.15 inference(bind,[status(th)],[])).
% 1.42/1.15 tff(101,plain,
% 1.42/1.15 (![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))),
% 1.42/1.15 inference(quant_intro,[status(thm)],[100])).
% 1.42/1.15 tff(102,plain,
% 1.42/1.15 (^[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))))),
% 1.42/1.15 inference(bind,[status(th)],[])).
% 1.42/1.15 tff(103,plain,
% 1.42/1.15 (![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))),
% 1.42/1.15 inference(quant_intro,[status(thm)],[102])).
% 1.42/1.15 tff(104,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')).
% 1.42/1.15 tff(105,plain,
% 1.42/1.15 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.42/1.15 tff(106,plain,
% 1.42/1.15 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.42/1.15 tff(107,plain,
% 1.42/1.15 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[106, 99])).
% 1.42/1.15 tff(108,plain,(
% 1.42/1.15 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.42/1.15 inference(skolemize,[status(sab)],[107])).
% 1.42/1.15 tff(109,plain,
% 1.42/1.15 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[108, 98])).
% 1.42/1.15 tff(110,plain,
% 1.42/1.15 (q1(d, d, d) <=> q1(d, d, d)),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(111,plain,
% 1.42/1.15 (($false | $false | q1(d, d, d)) <=> q1(d, d, d)),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(112,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 1.42/1.15 tff(113,plain,
% 1.42/1.15 (s0(d) <=> $true),
% 1.42/1.15 inference(iff_true,[status(thm)],[112])).
% 1.42/1.15 tff(114,plain,
% 1.42/1.15 ((~s0(d)) <=> (~$true)),
% 1.42/1.15 inference(monotonicity,[status(thm)],[113])).
% 1.42/1.15 tff(115,plain,
% 1.42/1.15 ((~s0(d)) <=> $false),
% 1.42/1.15 inference(transitivity,[status(thm)],[114, 59])).
% 1.42/1.15 tff(116,plain,
% 1.42/1.15 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ($false | $false | q1(d, d, d))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[115, 63])).
% 1.42/1.15 tff(117,plain,
% 1.42/1.15 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> q1(d, d, d)),
% 1.42/1.15 inference(transitivity,[status(thm)],[116, 111])).
% 1.42/1.15 tff(118,plain,
% 1.42/1.15 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(119,plain,
% 1.42/1.15 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(120,plain,
% 1.42/1.15 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(121,plain,
% 1.42/1.15 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[120])).
% 1.42/1.15 tff(122,plain,
% 1.42/1.15 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 1.42/1.15 inference(transitivity,[status(thm)],[121, 119])).
% 1.42/1.15 tff(123,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 1.42/1.15 tff(124,plain,
% 1.42/1.15 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.42/1.15 tff(125,plain,
% 1.42/1.15 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[124, 118])).
% 1.42/1.15 tff(126,plain,
% 1.42/1.15 (q1(d, d, d)),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[125, 117])).
% 1.42/1.15 tff(127,plain,
% 1.42/1.15 (q1(d, d, d)),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[126, 110])).
% 1.42/1.15 tff(128,plain,
% 1.42/1.15 (q0(e, d) <=> q0(e, d)),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(129,axiom,(q0(e, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 1.42/1.15 tff(130,plain,
% 1.42/1.15 (q0(e, d)),
% 1.42/1.15 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.42/1.15 tff(131,plain,
% 1.42/1.15 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(e) | (~q1(d, d, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(132,plain,
% 1.42/1.15 (((~q0(e, d)) | (~q1(d, d, d)) | r1(e)) <=> (r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 1.42/1.15 inference(rewrite,[status(thm)],[])).
% 1.42/1.15 tff(133,plain,
% 1.42/1.15 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(e) | (~q1(d, d, d)) | (~q0(e, d))))),
% 1.42/1.15 inference(monotonicity,[status(thm)],[132])).
% 1.42/1.15 tff(134,plain,
% 1.42/1.15 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 1.42/1.16 inference(transitivity,[status(thm)],[133, 131])).
% 1.42/1.16 tff(135,plain,
% 1.42/1.16 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(136,plain,
% 1.42/1.16 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))),
% 1.42/1.16 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.42/1.16 tff(137,plain,
% 1.42/1.16 (r1(e)),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[136, 130, 127, 109])).
% 1.42/1.16 tff(138,plain,
% 1.42/1.16 (k0(e) <=> k0(e)),
% 1.42/1.16 inference(rewrite,[status(thm)],[])).
% 1.42/1.16 tff(139,plain,
% 1.42/1.16 (k0(e)),
% 1.42/1.16 inference(modus_ponens,[status(thm)],[60, 138])).
% 1.42/1.16 tff(140,plain,
% 1.42/1.16 (((~![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(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(e, d, b)))) <=> ((~![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(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(e, d, b)))),
% 1.42/1.16 inference(rewrite,[status(thm)],[])).
% 1.42/1.16 tff(141,plain,
% 1.42/1.16 (((~m0(e, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b)) <=> ((~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(e, d, b)))),
% 1.42/1.16 inference(rewrite,[status(thm)],[])).
% 1.42/1.16 tff(142,plain,
% 1.42/1.16 (((~![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(e, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))) <=> ((~![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(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(e, d, b))))),
% 1.42/1.16 inference(monotonicity,[status(thm)],[141])).
% 1.42/1.16 tff(143,plain,
% 1.42/1.16 (((~![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(e, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))) <=> ((~![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(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(e, d, b)))),
% 1.42/1.16 inference(transitivity,[status(thm)],[142, 140])).
% 1.42/1.16 tff(144,plain,
% 1.42/1.16 ((~![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(e, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))),
% 1.42/1.16 inference(quant_inst,[status(thm)],[])).
% 1.42/1.16 tff(145,plain,
% 1.42/1.16 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(e, d, b))),
% 1.42/1.16 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.42/1.16 tff(146,plain,
% 1.42/1.16 ($false),
% 1.42/1.16 inference(unit_resolution,[status(thm)],[145, 139, 137, 96, 86, 49, 9])).
% 1.42/1.16 % SZS output end Proof
%------------------------------------------------------------------------------