TSTP Solution File: SYN250-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN250-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:54:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN250-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n018.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 02:20:46 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.
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(m1_type, type, (
% 0.20/0.51 m1: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(a_type, type, (
% 0.20/0.51 a: $i)).
% 0.20/0.51 tff(b_type, type, (
% 0.20/0.51 b: $i)).
% 0.20/0.51 tff(c_type, type, (
% 0.20/0.51 c: $i)).
% 0.20/0.51 tff(s0_type, type, (
% 0.20/0.51 s0: $i > $o)).
% 0.20/0.51 tff(p0_type, type, (
% 0.20/0.51 p0: ( $i * $i ) > $o)).
% 0.20/0.51 tff(m0_type, type, (
% 0.20/0.51 m0: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(d_type, type, (
% 0.20/0.51 d: $i)).
% 0.20/0.51 tff(q0_type, type, (
% 0.20/0.51 q0: ( $i * $i ) > $o)).
% 0.20/0.51 tff(l0_type, type, (
% 0.20/0.51 l0: $i > $o)).
% 0.20/0.51 tff(e_type, type, (
% 0.20/0.51 e: $i)).
% 0.20/0.51 tff(r0_type, type, (
% 0.20/0.51 r0: $i > $o)).
% 0.20/0.51 tff(1,plain,
% 0.20/0.51 (^[I: $i, H: $i] : refl((m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H))) <=> ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (^[I: $i, H: $i] : trans(monotonicity(rewrite((m1(H, I, H) | (~p0(H, I))) <=> (m1(H, I, H) | (~p0(H, I)))), (((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> ((m1(H, I, H) | (~p0(H, I))) | (~s0(H))))), rewrite(((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))), (((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 (![I: $i, H: $i] : ((m1(H, I, H) | (~p0(H, I))) | (~s0(H))) <=> ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.51 tff(6,axiom,(![I: $i, H: $i] : ((m1(H, I, H) | (~p0(H, I))) | (~s0(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_029')).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.51 tff(9,plain,(
% 0.20/0.51 ![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[8])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 (![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.51 tff(11,plain,
% 0.20/0.51 (p0(b, c) <=> p0(b, c)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(12,axiom,(p0(b, c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_22')).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (p0(b, c)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 (s0(b) <=> s0(b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(15,axiom,(s0(b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_5')).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (s0(b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | ((~s0(b)) | (~p0(b, c)) | m1(b, c, b))) <=> ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, c)) | m1(b, c, b))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 ((m1(b, c, b) | (~p0(b, c)) | (~s0(b))) <=> ((~s0(b)) | (~p0(b, c)) | m1(b, c, b))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, c, b) | (~p0(b, c)) | (~s0(b)))) <=> ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | ((~s0(b)) | (~p0(b, c)) | m1(b, c, b)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, c, b) | (~p0(b, c)) | (~s0(b)))) <=> ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, c)) | m1(b, c, b))),
% 0.20/0.51 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (m1(b, c, b) | (~p0(b, c)) | (~s0(b)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 ((~![I: $i, H: $i] : (m1(H, I, H) | (~p0(H, I)) | (~s0(H)))) | (~s0(b)) | (~p0(b, c)) | m1(b, c, b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (m1(b, c, b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[22, 16, 13, 10])).
% 0.20/0.51 tff(24,assumption,(~m0(a, d, a)), introduced(assumption)).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 (^[X: $i] : refl(m0(a, X, a) <=> m0(a, X, a))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (![X: $i] : m0(a, X, a) <=> ![X: $i] : m0(a, X, a)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(28,axiom,(![X: $i] : m0(a, X, a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_12')).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (![X: $i] : m0(a, X, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.51 tff(30,plain,(
% 0.20/0.51 ![X: $i] : m0(a, X, a)),
% 0.20/0.51 inference(skolemize,[status(sab)],[29])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (![X: $i] : m0(a, X, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 ((~![X: $i] : m0(a, X, a)) | m0(a, d, a)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.20/0.51 tff(34,plain,(m0(a, d, a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)) <=> ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1(F, a, G) | (~m0(a, H, a))) <=> ((~m0(a, H, a)) | m1(F, a, G))), (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) <=> (((~m0(a, H, a)) | m1(F, a, G)) | (~q0(F, G))))), rewrite((((~m0(a, H, a)) | m1(F, a, G)) | (~q0(F, G))) <=> ((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G))), (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) <=> ((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G)))), ((((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G))) <=> (((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G)) | (~m1(G, c, G))))), rewrite((((~q0(F, G)) | (~m0(a, H, a)) | m1(F, a, G)) | (~m1(G, c, G))) <=> ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))), ((((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G))) <=> ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.51 tff(40,axiom,(![H: $i, F: $i, G: $i] : (((m1(F, a, G) | (~m0(a, H, a))) | (~q0(F, G))) | (~m1(G, c, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_024')).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.51 tff(43,plain,(
% 0.20/0.51 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(skolemize,[status(sab)],[42])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (q0(a, b) <=> q0(a, b)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(46,axiom,(q0(a, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.20/0.52 tff(47,plain,
% 0.20/0.52 (q0(a, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.52 tff(48,plain,
% 0.20/0.52 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~m0(a, d, a)) | (~q0(a, b)) | (~m1(b, c, b)) | m1(a, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (~m0(a, d, a)) | (~q0(a, b)) | (~m1(b, c, b)) | m1(a, a, b))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(49,plain,
% 0.20/0.52 (((~q0(a, b)) | (~m1(b, c, b)) | (~m0(a, d, a)) | m1(a, a, b)) <=> ((~m0(a, d, a)) | (~q0(a, b)) | (~m1(b, c, b)) | m1(a, a, b))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(50,plain,
% 0.20/0.52 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(a, b)) | (~m1(b, c, b)) | (~m0(a, d, a)) | m1(a, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~m0(a, d, a)) | (~q0(a, b)) | (~m1(b, c, b)) | m1(a, a, b)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.52 tff(51,plain,
% 0.20/0.52 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(a, b)) | (~m1(b, c, b)) | (~m0(a, d, a)) | m1(a, a, b))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (~m0(a, d, a)) | (~q0(a, b)) | (~m1(b, c, b)) | m1(a, a, b))),
% 0.20/0.52 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.52 tff(52,plain,
% 0.20/0.52 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(a, b)) | (~m1(b, c, b)) | (~m0(a, d, a)) | m1(a, a, b))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(53,plain,
% 0.20/0.52 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (~m0(a, d, a)) | (~q0(a, b)) | (~m1(b, c, b)) | m1(a, a, b)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.52 tff(54,plain,
% 0.20/0.52 (m1(a, a, b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[53, 47, 44, 34, 23])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 (m1(a, a, a) <=> m1(a, a, a)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(56,plain,
% 0.20/0.52 ((m1(a, a, a) | $false | $false) <=> m1(a, a, a)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(57,plain,
% 0.20/0.52 ((~$true) <=> $false),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(58,axiom,(l0(a)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.20/0.52 tff(59,plain,
% 0.20/0.52 (l0(a) <=> $true),
% 0.20/0.52 inference(iff_true,[status(thm)],[58])).
% 0.20/0.52 tff(60,plain,
% 0.20/0.52 ((~l0(a)) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.52 tff(61,plain,
% 0.20/0.52 ((~l0(a)) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[60, 57])).
% 0.20/0.52 tff(62,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.20/0.52 tff(63,plain,
% 0.20/0.52 (s0(d) <=> $true),
% 0.20/0.52 inference(iff_true,[status(thm)],[62])).
% 0.20/0.52 tff(64,plain,
% 0.20/0.52 ((~s0(d)) <=> (~$true)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.52 tff(65,plain,
% 0.20/0.52 ((~s0(d)) <=> $false),
% 0.20/0.52 inference(transitivity,[status(thm)],[64, 57])).
% 0.20/0.52 tff(66,plain,
% 0.20/0.52 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | $false | $false)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[65, 61])).
% 0.20/0.52 tff(67,plain,
% 0.20/0.52 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> m1(a, a, a)),
% 0.20/0.52 inference(transitivity,[status(thm)],[66, 56])).
% 0.20/0.52 tff(68,plain,
% 0.20/0.52 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(69,plain,
% 0.20/0.52 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(70,plain,
% 0.20/0.52 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(71,plain,
% 0.20/0.52 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.52 tff(72,plain,
% 0.20/0.52 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.52 tff(73,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.20/0.52 tff(74,plain,
% 0.20/0.52 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.52 tff(75,plain,
% 0.20/0.52 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[74, 68])).
% 0.20/0.52 tff(76,plain,
% 0.20/0.52 (m1(a, a, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[75, 67])).
% 0.20/0.52 tff(77,plain,
% 0.20/0.52 (m1(a, a, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[76, 55])).
% 0.20/0.52 tff(78,plain,
% 0.20/0.52 (^[I: $i, A: $i, J: $i, H: $i] : refl(((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I)) <=> ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(79,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.52 tff(80,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I)) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(81,plain,
% 0.20/0.52 (^[I: $i, A: $i, J: $i, H: $i] : trans(monotonicity(rewrite((m1(H, I, I) | (~m1(J, I, H))) <=> ((~m1(J, I, H)) | m1(H, I, I))), (((m1(H, I, I) | (~m1(J, I, H))) | (~m1(J, A, I))) <=> (((~m1(J, I, H)) | m1(H, I, I)) | (~m1(J, A, I))))), rewrite((((~m1(J, I, H)) | m1(H, I, I)) | (~m1(J, A, I))) <=> ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))), (((m1(H, I, I) | (~m1(J, I, H))) | (~m1(J, A, I))) <=> ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(82,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((m1(H, I, I) | (~m1(J, I, H))) | (~m1(J, A, I))) <=> ![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.52 tff(83,axiom,(![I: $i, A: $i, J: $i, H: $i] : ((m1(H, I, I) | (~m1(J, I, H))) | (~m1(J, A, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_016')).
% 0.20/0.52 tff(84,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.52 tff(85,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.52 tff(86,plain,(
% 0.20/0.52 ![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(skolemize,[status(sab)],[85])).
% 0.20/0.52 tff(87,plain,
% 0.20/0.52 (![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.52 tff(88,plain,
% 0.20/0.52 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | ((~m1(a, a, a)) | (~m1(a, a, b)) | m1(b, a, a))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | (~m1(a, a, a)) | (~m1(a, a, b)) | m1(b, a, a))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | ((~m1(a, a, a)) | (~m1(a, a, b)) | m1(b, a, a))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | (~m1(a, a, a)) | (~m1(a, a, b)) | m1(b, a, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 (m1(b, a, a)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[90, 87, 77, 54])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 ((~m1(e, a, a)) <=> (~m1(e, a, a))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(93,axiom,(~m1(e, a, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 (~m1(e, a, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.52 tff(95,assumption,(~m1(e, c, e)), introduced(assumption)).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 (^[I: $i, J: $i] : refl((m1(I, J, I) | (~r0(I)) | (~l0(J))) <=> (m1(I, J, I) | (~r0(I)) | (~l0(J))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 (![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.52 tff(98,plain,
% 0.20/0.52 (![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 (^[I: $i, J: $i] : trans(monotonicity(rewrite((m1(I, J, I) | (~r0(I))) <=> (m1(I, J, I) | (~r0(I)))), (((m1(I, J, I) | (~r0(I))) | (~l0(J))) <=> ((m1(I, J, I) | (~r0(I))) | (~l0(J))))), rewrite(((m1(I, J, I) | (~r0(I))) | (~l0(J))) <=> (m1(I, J, I) | (~r0(I)) | (~l0(J)))), (((m1(I, J, I) | (~r0(I))) | (~l0(J))) <=> (m1(I, J, I) | (~r0(I)) | (~l0(J)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 (![I: $i, J: $i] : ((m1(I, J, I) | (~r0(I))) | (~l0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.52 tff(101,axiom,(![I: $i, J: $i] : ((m1(I, J, I) | (~r0(I))) | (~l0(J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_035')).
% 0.20/0.52 tff(102,plain,
% 0.20/0.52 (![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 (![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.52 tff(104,plain,(
% 0.20/0.52 ![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[103])).
% 0.20/0.52 tff(105,plain,
% 0.20/0.52 (![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 (l0(c) <=> l0(c)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(107,axiom,(l0(c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.20/0.52 tff(108,plain,
% 0.20/0.52 (l0(c)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.52 tff(109,plain,
% 0.20/0.52 (r0(e) <=> r0(e)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(110,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.20/0.52 tff(111,plain,
% 0.20/0.52 (r0(e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.52 tff(112,plain,
% 0.20/0.52 (((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | ((~r0(e)) | (~l0(c)) | m1(e, c, e))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | (~r0(e)) | (~l0(c)) | m1(e, c, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(113,plain,
% 0.20/0.52 ((m1(e, c, e) | (~r0(e)) | (~l0(c))) <=> ((~r0(e)) | (~l0(c)) | m1(e, c, e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(114,plain,
% 0.20/0.52 (((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | (m1(e, c, e) | (~r0(e)) | (~l0(c)))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | ((~r0(e)) | (~l0(c)) | m1(e, c, e)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.52 tff(115,plain,
% 0.20/0.52 (((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | (m1(e, c, e) | (~r0(e)) | (~l0(c)))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | (~r0(e)) | (~l0(c)) | m1(e, c, e))),
% 0.20/0.52 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.52 tff(116,plain,
% 0.20/0.52 ((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | (m1(e, c, e) | (~r0(e)) | (~l0(c)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(117,plain,
% 0.20/0.52 ((~![I: $i, J: $i] : (m1(I, J, I) | (~r0(I)) | (~l0(J)))) | (~r0(e)) | (~l0(c)) | m1(e, c, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.52 tff(118,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[117, 111, 108, 105, 95])).
% 0.20/0.52 tff(119,plain,(m1(e, c, e)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(120,plain,
% 0.20/0.52 (q0(b, e) <=> q0(b, e)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(121,axiom,(q0(b, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_21')).
% 0.20/0.52 tff(122,plain,
% 0.20/0.52 (q0(b, e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.52 tff(123,plain,
% 0.20/0.52 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(b, e)) | m1(b, a, e) | (~m0(a, d, a)) | (~m1(e, c, e)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (~q0(b, e)) | m1(b, a, e) | (~m0(a, d, a)) | (~m1(e, c, e)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(124,plain,
% 0.20/0.52 (((~q0(b, e)) | (~m1(e, c, e)) | (~m0(a, d, a)) | m1(b, a, e)) <=> ((~q0(b, e)) | m1(b, a, e) | (~m0(a, d, a)) | (~m1(e, c, e)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(125,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(b, e)) | (~m1(e, c, e)) | (~m0(a, d, a)) | m1(b, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(b, e)) | m1(b, a, e) | (~m0(a, d, a)) | (~m1(e, c, e))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.53 tff(126,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(b, e)) | (~m1(e, c, e)) | (~m0(a, d, a)) | m1(b, a, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (~q0(b, e)) | m1(b, a, e) | (~m0(a, d, a)) | (~m1(e, c, e)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.53 tff(127,plain,
% 0.20/0.53 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | ((~q0(b, e)) | (~m1(e, c, e)) | (~m0(a, d, a)) | m1(b, a, e))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(128,plain,
% 0.20/0.53 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~m1(G, c, G)) | (~m0(a, H, a)) | m1(F, a, G))) | (~q0(b, e)) | m1(b, a, e) | (~m0(a, d, a)) | (~m1(e, c, e))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.53 tff(129,plain,
% 0.20/0.53 (m1(b, a, e) | (~m1(e, c, e))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[128, 122, 44, 34])).
% 0.20/0.53 tff(130,plain,
% 0.20/0.53 (m1(b, a, e)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[129, 119])).
% 0.20/0.53 tff(131,plain,
% 0.20/0.53 (((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | ((~m1(b, a, a)) | (~m1(b, a, e)) | m1(e, a, a))) <=> ((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | (~m1(b, a, a)) | (~m1(b, a, e)) | m1(e, a, a))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(132,plain,
% 0.20/0.53 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | ((~m1(b, a, a)) | (~m1(b, a, e)) | m1(e, a, a))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(133,plain,
% 0.20/0.53 ((~![I: $i, A: $i, J: $i, H: $i] : ((~m1(J, A, I)) | (~m1(J, I, H)) | m1(H, I, I))) | (~m1(b, a, a)) | (~m1(b, a, e)) | m1(e, a, a)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.53 tff(134,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[133, 87, 130, 94, 91])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------