%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:18:40 AM UTC 2026
% Result : Unsatisfiable 119.84s 119.93s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 22:29:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.27/0.53 start to proof:theBenchmark
% 119.84/119.92 %-------------------------------------------
% 119.84/119.92 % File :CSE---1.7
% 119.84/119.92 % Problem :theBenchmark
% 119.84/119.92 % Transform :cnf
% 119.84/119.92 % Format :tptp:raw
% 119.84/119.92 % Command :java -jar mcs_scs.jar %d %s
% 119.84/119.92
% 119.84/119.92 % Result :Theorem 119.402666s
% 119.84/119.92 % Output :CNFRefutation 119.402666s
% 119.84/119.92 %-------------------------------------------
% 119.84/119.92 %--------------------------------------------------------------------------
% 119.84/119.92 % File : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 119.84/119.92 % Domain : Logic Calculi (Right group)
% 119.84/119.92 % Problem : LG-4 depends on LG-2
% 119.84/119.92 % Version : [McC92b] axioms.
% 119.84/119.92 % English : Kalman's axiomatisation of the right group calculus
% 119.84/119.92 % is {LG-1,LG-2,LG-3,LG-4,LG-5}. McCune has shown that LG-2
% 119.84/119.92 % is a single axiom. Other axiomatisations by McCune are
% 119.84/119.92 % {Q-2,Q-3}, {Q-3,Q-4}, S-2, S-3, S-4, P-4, S-6. Show that LG-4
% 119.84/119.92 % depends on LG-2.
% 119.84/119.92
% 119.84/119.92 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 119.84/119.92 % : [McC92a] McCune (1992), Automated Discovery of New Axiomatisat
% 119.84/119.92 % : [McC92b] McCune (1992), Email to G. Sutcliffe
% 119.84/119.92 % Source : [McC92b]
% 119.84/119.92 % Names : RG-104 [MW92]
% 119.84/119.92
% 119.84/119.92 % Status : Unsatisfiable
% 119.84/119.92 % Rating : 0.00 v9.3.0, 0.18 v9.1.0, 0.27 v9.0.0, 0.09 v8.2.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.21 v6.0.0, 0.22 v5.5.0, 0.25 v5.4.0, 0.39 v5.3.0, 0.45 v5.2.0, 0.38 v5.1.0, 0.31 v5.0.0, 0.33 v4.0.1, 0.14 v4.0.0, 0.00 v2.7.0, 0.25 v2.6.0, 0.14 v2.4.0, 0.25 v2.3.0
% 119.84/119.92 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 119.84/119.92 % Number of literals : 5 ( 0 equ; 3 neg)
% 119.84/119.92 % Maximal clause size : 3 ( 1 avg)
% 119.84/119.92 % Maximal term depth : 6 ( 2 avg)
% 119.84/119.92 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 119.84/119.92 % Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% 119.84/119.92 % Number of variables : 6 ( 0 sgn)
% 119.84/119.92 % SPC : CNF_UNS_RFO_NEQ_HRN
% 119.84/119.92
% 119.84/119.92 % Comments :
% 119.84/119.92 % Bugfixes : v2.3.0 - Clause prove_lg_4 fixed.
% 119.84/119.92 %--------------------------------------------------------------------------
% 119.84/119.92 cnf(condensed_detachment,axiom,
% 119.84/119.92 ( ~ is_a_theorem(equivalent(X,Y))
% 119.84/119.92 | ~ is_a_theorem(X)
% 119.84/119.92 | is_a_theorem(Y) ) ).
% 119.84/119.93
% 119.84/119.93 cnf(lg_2,axiom,
% 119.84/119.93 is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Y,U),equivalent(Z,U)))))) ).
% 119.84/119.93
% 119.84/119.93 cnf(prove_lg_4,negated_conjecture,
% 119.84/119.93 ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(e,equivalent(b,f))),equivalent(a,equivalent(e,equivalent(c,f))))) ).
% 119.84/119.93
% 119.84/119.93 %--------------------------------------------------------------------------
% 119.84/119.93 %-------------------------------------------
% 119.84/119.93 % Proof found
% 119.84/119.93 % SZS status Theorem for theBenchmark
% 119.84/119.93 % SZS output start Proof
% 119.84/119.93 %ClaNum:3(EqnAxiom:0)
% 119.84/119.93 %VarNum:12(SingletonVarNum:6)
% 119.84/119.93 %MaxLitNum:3
% 119.84/119.93 %MaxfuncDepth:5
% 119.84/119.93 %SharedTerms:15
% 119.84/119.93 %goalClause: 2
% 119.84/119.93 %singleGoalClaCount:1
% 119.84/119.93 [2]~P1(f1(f1(f1(a2,f1(a3,a4)),f1(a5,f1(a3,a6))),f1(a2,f1(a5,f1(a4,a6)))))
% 119.84/119.93 [1]P1(f1(x11,f1(x11,f1(f1(x12,x13),f1(f1(x12,x14),f1(x13,x14))))))
% 119.84/119.93 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 119.84/119.93 %EqnAxiom
% 119.84/119.93
% 119.84/119.93 %-------------------------------------------
% 119.84/119.93 cnf(4,plain,
% 119.84/119.93 (P1(f1(x41,f1(f1(x42,x43),f1(f1(x42,x44),f1(x43,x44)))))+~P1(x41)),
% 119.84/119.93 inference(scs_inference,[],[1,3])).
% 119.84/119.93 cnf(6,plain,
% 119.84/119.93 (P1(f1(f1(x61,f1(x61,f1(f1(x62,x63),f1(f1(x62,x64),f1(x63,x64))))),f1(f1(x65,x66),f1(f1(x65,x67),f1(x66,x67)))))),
% 119.84/119.93 inference(scs_inference,[],[1,4])).
% 119.84/119.93 cnf(8,plain,
% 119.84/119.93 (P1(f1(f1(x81,x82),f1(f1(x81,x83),f1(x82,x83))))),
% 119.84/119.93 inference(scs_inference,[],[1,4,3])).
% 119.84/119.93 cnf(10,plain,
% 119.84/119.93 (P1(f1(f1(f1(x101,x102),f1(f1(x101,x103),f1(x102,x103))),f1(f1(x104,x105),f1(f1(x104,x106),f1(x105,x106)))))),
% 119.84/119.93 inference(scs_inference,[],[8,4])).
% 119.84/119.93 cnf(14,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x141,x142),f1(f1(x141,x143),f1(x142,x143))),x144),f1(f1(f1(x145,x146),f1(f1(x145,x147),f1(x146,x147))),x144)))),
% 119.84/119.93 inference(scs_inference,[],[10,8,4,3])).
% 119.84/119.93 cnf(17,plain,
% 119.84/119.93 (P1(f1(f1(f1(x171,x172),f1(f1(x171,x173),f1(x172,x173))),f1(f1(f1(x174,x175),x176),f1(f1(f1(x174,x177),f1(x175,x177)),x176))))),
% 119.84/119.93 inference(scs_inference,[],[14,8,3])).
% 119.84/119.93 cnf(21,plain,
% 119.84/119.93 (P1(f1(f1(f1(x211,x212),x213),f1(f1(f1(x211,x214),f1(x212,x214)),x213)))),
% 119.84/119.93 inference(scs_inference,[],[17,8,3])).
% 119.84/119.93 cnf(31,plain,
% 119.84/119.93 (P1(f1(f1(f1(x311,x312),f1(f1(x311,x313),f1(x312,x313))),f1(f1(f1(x314,x315),f1(x316,x315)),f1(f1(x314,x317),f1(x316,x317)))))),
% 119.84/119.93 inference(scs_inference,[],[21,14,3])).
% 119.84/119.93 cnf(35,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x351,x352),f1(f1(x351,x353),f1(x352,x353))),f1(f1(f1(x354,x355),f1(x356,x355)),f1(f1(x354,x357),f1(x356,x357)))),f1(f1(x358,x359),f1(f1(x358,x3510),f1(x359,x3510)))))),
% 119.84/119.93 inference(scs_inference,[],[21,14,3,4])).
% 119.84/119.93 cnf(37,plain,
% 119.84/119.93 (P1(f1(f1(f1(x371,x372),f1(x373,x372)),f1(f1(x371,x374),f1(x373,x374))))),
% 119.84/119.93 inference(scs_inference,[],[31,17,3])).
% 119.84/119.93 cnf(41,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x411,x412),f1(x413,x412)),f1(f1(x411,x414),f1(x413,x414))),f1(f1(x415,x416),f1(f1(x415,x417),f1(x416,x417)))))),
% 119.84/119.93 inference(scs_inference,[],[31,17,3,4])).
% 119.84/119.93 cnf(45,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x451,x452),f1(x453,x452)),x454),f1(f1(x451,x453),x454)))),
% 119.84/119.93 inference(scs_inference,[],[37,41,4,3])).
% 119.84/119.93 cnf(49,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(f1(x491,x492),f1(x493,x492)),x494),f1(f1(x491,x493),x494)),f1(f1(x495,x496),f1(f1(x495,x497),f1(x496,x497)))))),
% 119.84/119.93 inference(scs_inference,[],[45,4])).
% 119.84/119.93 cnf(51,plain,
% 119.84/119.93 (~P1(f1(f1(f1(f1(a2,f1(a3,a4)),x511),f1(f1(a5,f1(a3,a6)),x511)),f1(a2,f1(a5,f1(a4,a6)))))),
% 119.84/119.93 inference(scs_inference,[],[2,45,4,3])).
% 119.84/119.93 cnf(56,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(f1(x561,x562),f1(x563,x562)),f1(x564,x563)),x565),f1(f1(x561,x564),x565)))),
% 119.84/119.93 inference(scs_inference,[],[49,37,4,3])).
% 119.84/119.93 cnf(60,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(f1(f1(x601,x602),f1(x603,x602)),f1(x604,x603)),x605),f1(f1(x601,x604),x605)),f1(f1(x606,x607),f1(f1(x606,x608),f1(x607,x608)))))),
% 119.84/119.93 inference(scs_inference,[],[56,4])).
% 119.84/119.93 cnf(62,plain,
% 119.84/119.93 (P1(f1(f1(x621,x622),f1(f1(x621,f1(f1(x623,x624),f1(f1(x623,x625),f1(x624,x625)))),x622)))),
% 119.84/119.93 inference(scs_inference,[],[1,56,37,4,3])).
% 119.84/119.93 cnf(68,plain,
% 119.84/119.93 (~P1(f1(f1(f1(a2,f1(a3,a4)),f1(f1(a5,x681),f1(f1(a3,a6),x681))),f1(a2,f1(a5,f1(a4,a6)))))),
% 119.84/119.93 inference(scs_inference,[],[60,51,62,4,3])).
% 119.84/119.93 cnf(81,plain,
% 119.84/119.93 (P1(f1(f1(f1(x811,f1(f1(x812,x813),f1(x814,x813))),x815),f1(f1(x811,f1(x812,x814)),x815)))),
% 119.84/119.93 inference(scs_inference,[],[6,17,37,4,3])).
% 119.84/119.93 cnf(98,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x981,x982),f1(f1(x981,x983),f1(x982,x983))),x984),f1(f1(f1(x985,x986),f1(x985,x986)),x984)))),
% 119.84/119.93 inference(scs_inference,[],[35,37,3])).
% 119.84/119.93 cnf(109,plain,
% 119.84/119.93 (P1(f1(f1(f1(x1091,x1092),f1(x1091,x1092)),f1(f1(f1(x1093,x1094),x1095),f1(f1(f1(x1093,x1096),f1(x1094,x1096)),x1095))))),
% 119.84/119.93 inference(scs_inference,[],[8,98,3])).
% 119.84/119.93 cnf(113,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x1131,x1132),f1(x1131,x1132)),x1133),f1(f1(f1(f1(x1134,x1135),x1136),f1(f1(f1(x1134,x1137),f1(x1135,x1137)),x1136)),x1133)))),
% 119.84/119.93 inference(scs_inference,[],[8,109,3])).
% 119.84/119.93 cnf(173,plain,
% 119.84/119.93 (P1(f1(f1(f1(f1(x1731,x1732),x1733),f1(f1(f1(x1731,x1734),f1(x1732,x1734)),x1733)),f1(f1(f1(x1735,x1736),f1(x1737,x1736)),f1(x1735,x1737))))),
% 119.84/119.93 inference(scs_inference,[],[21,113,3])).
% 119.84/119.93 cnf(179,plain,
% 119.84/119.93 (P1(f1(f1(f1(x1791,x1792),f1(x1793,x1792)),f1(x1791,x1793)))),
% 119.84/119.93 inference(scs_inference,[],[21,173,3])).
% 119.84/119.93 cnf(218,plain,
% 119.84/119.93 (~P1(f1(f1(f1(f1(x2181,x2182),f1(x2183,x2182)),f1(x2181,x2183)),f1(f1(f1(a2,f1(a3,a4)),f1(f1(a5,x2184),f1(f1(a3,a6),x2184))),f1(a2,f1(a5,f1(a4,a6))))))),
% 119.84/119.93 inference(scs_inference,[],[179,68,3])).
% 119.84/119.93 cnf(220,plain,
% 119.84/119.93 ($false),
% 119.84/119.93 inference(scs_inference,[],[81,8,218,3]),
% 119.84/119.93 ['proof']).
% 119.84/119.93 % SZS output end Proof
% 119.84/119.93 % Total time :119.402666s
%------------------------------------------------------------------------------