%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 11:18:38 AM UTC 2026
% Result : Unsatisfiable 59.45s 59.67s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 01:50:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.22/0.52 start to proof:theBenchmark
% 59.45/59.66 %-------------------------------------------
% 59.45/59.66 % File :CSE---1.7
% 59.45/59.66 % Problem :theBenchmark
% 59.45/59.66 % Transform :cnf
% 59.45/59.66 % Format :tptp:raw
% 59.45/59.66 % Command :java -jar mcs_scs.jar %d %s
% 59.45/59.66
% 59.45/59.66 % Result :Theorem 59.123257s
% 59.45/59.66 % Output :CNFRefutation 59.123257s
% 59.45/59.66 %-------------------------------------------
% 59.45/59.66 %--------------------------------------------------------------------------
% 59.45/59.66 % File : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 59.45/59.66 % Domain : Logic Calculi (Left group)
% 59.45/59.66 % Problem : P-1 depends on the 6th McCune system
% 59.45/59.66 % Version : [McC92b] axioms.
% 59.45/59.66 % English : Axiomatisations of the left group calculus are {LG-1,
% 59.45/59.66 % LG-2,LG-3,LG-4,LG-5} by Kalman, {LG-2,LG-3}, {LG-2,P-1},
% 59.45/59.66 % {LG-2,P-4}, {LG-2,Q-1,Q-2}, {P-1,Q-3}, {P-4,Q-3}, {Q-1,
% 59.45/59.66 % Q-2,Q-3}, {Q-1,Q-3,Q-4}, {LG-27-1690} all by McCune. Show
% 59.45/59.66 % that P-1 depends on the sixth McCune system.
% 59.45/59.66
% 59.45/59.66 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 59.45/59.66 % : [McC92a] McCune (1992), Automated Discovery of New Axiomatisat
% 59.45/59.66 % : [McC92b] McCune (1992), Email to G. Sutcliffe
% 59.45/59.66 % Source : [McC92b]
% 59.45/59.66 % Names : LG-97 [MW92]
% 59.45/59.66
% 59.45/59.66 % Status : Unsatisfiable
% 59.45/59.66 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.00 v2.2.1, 0.11 v2.1.0, 0.13 v2.0.0
% 59.45/59.66 % Syntax : Number of clauses : 4 ( 3 unt; 0 nHn; 2 RR)
% 59.45/59.66 % Number of literals : 6 ( 0 equ; 3 neg)
% 59.45/59.66 % Maximal clause size : 3 ( 1 avg)
% 59.45/59.66 % Maximal term depth : 6 ( 2 avg)
% 59.45/59.66 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 59.45/59.66 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% 59.45/59.66 % Number of variables : 9 ( 0 sgn)
% 59.45/59.66 % SPC : CNF_UNS_RFO_NEQ_HRN
% 59.45/59.66
% 59.45/59.66 % Comments :
% 59.45/59.66 %--------------------------------------------------------------------------
% 59.45/59.67 cnf(condensed_detachment,axiom,
% 59.45/59.67 ( ~ is_a_theorem(equivalent(X,Y))
% 59.45/59.67 | ~ is_a_theorem(X)
% 59.45/59.67 | is_a_theorem(Y) ) ).
% 59.45/59.67
% 59.45/59.67 cnf(p_4,axiom,
% 59.45/59.67 is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))) ).
% 59.45/59.67
% 59.45/59.67 cnf(q_3,axiom,
% 59.45/59.67 is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)) ).
% 59.45/59.67
% 59.45/59.67 cnf(prove_p_1,negated_conjecture,
% 59.45/59.67 ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) ).
% 59.45/59.67
% 59.45/59.67 %--------------------------------------------------------------------------
% 59.45/59.67 %-------------------------------------------
% 59.45/59.67 % Proof found
% 59.45/59.67 % SZS status Theorem for theBenchmark
% 59.45/59.67 % SZS output start Proof
% 59.45/59.67 %ClaNum:4(EqnAxiom:0)
% 59.45/59.67 %VarNum:18(SingletonVarNum:9)
% 59.45/59.67 %MaxLitNum:3
% 59.45/59.67 %MaxfuncDepth:4
% 59.45/59.67 %SharedTerms:12
% 59.45/59.67 %goalClause: 3
% 59.45/59.67 %singleGoalClaCount:1
% 59.45/59.67 [3]~P1(f1(f1(f1(a2,a3),a4),f1(f1(a5,a3),f1(f1(a2,a5),a4))))
% 59.45/59.67 [1]P1(f1(f1(f1(x11,x12),f1(f1(x12,x11),x13)),x13))
% 59.45/59.67 [2]P1(f1(x21,f1(f1(f1(f1(x22,x23),f1(x22,x24)),f1(x23,x24)),x21)))
% 59.45/59.67 [4]P1(x41)+~P1(x42)+~P1(f1(x42,x41))
% 59.45/59.67 %EqnAxiom
% 59.45/59.67
% 59.45/59.67 %-------------------------------------------
% 59.45/59.67 cnf(5,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(x51,x52),f1(x51,x53)),f1(x52,x53)),f1(f1(f1(x54,x55),f1(f1(x55,x54),x56)),x56)))),
% 59.45/59.67 inference(scs_inference,[],[2,1,4])).
% 59.45/59.67 cnf(8,plain,
% 59.45/59.67 (P1(f1(x81,x81))),
% 59.45/59.67 inference(scs_inference,[],[1,5,4])).
% 59.45/59.67 cnf(12,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(x121,x122),f1(x121,x123)),f1(x122,x123)),f1(x124,x124)))),
% 59.45/59.67 inference(scs_inference,[],[2,8,4])).
% 59.45/59.67 cnf(15,plain,
% 59.45/59.67 (~P1(f1(f1(x151,x151),f1(f1(f1(a2,a3),a4),f1(f1(a5,a3),f1(f1(a2,a5),a4)))))),
% 59.45/59.67 inference(scs_inference,[],[8,3,4])).
% 59.45/59.67 cnf(17,plain,
% 59.45/59.67 (P1(f1(f1(x171,x172),f1(f1(x173,x171),f1(x173,x172))))),
% 59.45/59.67 inference(scs_inference,[],[12,1,4])).
% 59.45/59.67 cnf(21,plain,
% 59.45/59.67 (P1(f1(f1(x211,f1(f1(x212,x213),f1(f1(x213,x212),x214))),f1(x211,x214)))),
% 59.45/59.67 inference(scs_inference,[],[1,17,4])).
% 59.45/59.67 cnf(28,plain,
% 59.45/59.67 (P1(f1(f1(x281,f1(x282,f1(f1(x283,x284),f1(f1(x284,x283),x285)))),f1(x281,f1(x282,x285))))),
% 59.45/59.67 inference(scs_inference,[],[17,21,4])).
% 59.45/59.67 cnf(31,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(x311,x312),f1(x311,x313)),f1(x312,x313)),f1(f1(x314,x315),f1(f1(x316,x314),f1(x316,x315)))))),
% 59.45/59.67 inference(scs_inference,[],[17,2,4])).
% 59.45/59.67 cnf(34,plain,
% 59.45/59.67 (P1(f1(f1(x341,f1(f1(x342,x343),x344)),f1(f1(f1(x343,x342),x341),x344)))),
% 59.45/59.67 inference(scs_inference,[],[28,17,4])).
% 59.45/59.67 cnf(41,plain,
% 59.45/59.67 (P1(f1(f1(f1(x411,x412),f1(f1(f1(x413,x414),f1(x413,x415)),f1(x414,x415))),f1(f1(x416,x412),f1(x416,x411))))),
% 59.45/59.67 inference(scs_inference,[],[31,34,4])).
% 59.45/59.67 cnf(44,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(f1(x441,x442),x443),x444),f1(f1(f1(x445,x446),f1(x445,x447)),f1(x446,x447))),f1(f1(f1(x442,x441),x444),x443)))),
% 59.45/59.67 inference(scs_inference,[],[41,28,4])).
% 59.45/59.67 cnf(52,plain,
% 59.45/59.67 (P1(f1(f1(x521,f1(f1(f1(x522,x523),f1(x522,x524)),f1(x523,x524))),f1(x521,f1(f1(f1(x525,x526),f1(x525,x527)),f1(x526,x527)))))),
% 59.45/59.67 inference(scs_inference,[],[41,44,4])).
% 59.45/59.67 cnf(59,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(f1(x591,x592),f1(x591,x593)),x594),f1(f1(f1(x595,x596),f1(x595,x597)),f1(x596,x597))),f1(x594,f1(x592,x593))))),
% 59.45/59.67 inference(scs_inference,[],[52,44,4])).
% 59.45/59.67 cnf(63,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(x631,x632),f1(x631,x633)),f1(x632,x633)),f1(f1(f1(x634,x635),f1(x634,x636)),f1(x635,x636))))),
% 59.45/59.67 inference(scs_inference,[],[59,52,4])).
% 59.45/59.67 cnf(67,plain,
% 59.45/59.67 (P1(f1(f1(f1(x671,x672),f1(x671,x673)),f1(x672,x673)))),
% 59.45/59.67 inference(scs_inference,[],[63,59,4])).
% 59.45/59.67 cnf(73,plain,
% 59.45/59.67 (P1(f1(f1(x731,x732),f1(f1(x733,f1(x734,x731)),f1(x733,f1(x734,x732)))))),
% 59.45/59.67 inference(scs_inference,[],[67,31,4])).
% 59.45/59.67 cnf(77,plain,
% 59.45/59.67 (P1(f1(f1(x771,f1(x772,f1(x773,x774))),f1(x771,f1(x772,f1(f1(x775,x773),f1(x775,x774))))))),
% 59.45/59.67 inference(scs_inference,[],[17,73,4])).
% 59.45/59.67 cnf(80,plain,
% 59.45/59.67 (P1(f1(f1(f1(f1(x801,x802),f1(x801,x803)),f1(x802,x803)),f1(f1(f1(x804,x805),f1(x804,x806)),f1(f1(x807,x805),f1(x807,x806)))))),
% 59.45/59.67 inference(scs_inference,[],[77,63,4])).
% 59.45/59.67 cnf(84,plain,
% 59.45/59.67 (P1(f1(f1(f1(x841,x842),f1(x841,x843)),f1(f1(x844,x842),f1(x844,x843))))),
% 59.45/59.67 inference(scs_inference,[],[80,67,4])).
% 59.45/59.67 cnf(91,plain,
% 59.45/59.67 (~P1(f1(f1(x911,f1(f1(a2,a3),a4)),f1(x911,f1(f1(a5,a3),f1(f1(a2,a5),a4)))))),
% 59.45/59.67 inference(scs_inference,[],[84,15,4])).
% 59.45/59.67 cnf(150,plain,
% 59.45/59.67 (P1(f1(f1(x1501,f1(x1502,x1503)),f1(x1501,f1(f1(x1504,x1502),f1(x1504,x1503)))))),
% 59.45/59.67 inference(scs_inference,[],[41,63,4])).
% 59.45/59.67 cnf(154,plain,
% 59.45/59.67 (~P1(f1(f1(f1(f1(a5,a3),x1541),f1(f1(a2,a3),a4)),f1(x1541,f1(f1(a2,a5),a4))))),
% 59.45/59.67 inference(scs_inference,[],[150,91,4])).
% 59.45/59.67 cnf(170,plain,
% 59.45/59.67 (~P1(f1(f1(f1(f1(a5,a3),f1(f1(a2,a5),x1701)),f1(f1(a2,a3),a4)),f1(x1701,a4)))),
% 59.45/59.67 inference(scs_inference,[],[154,150,4])).
% 59.45/59.67 cnf(174,plain,
% 59.45/59.67 ($false),
% 59.45/59.67 inference(scs_inference,[],[170,21,2,4]),
% 59.45/59.67 ['proof']).
% 59.45/59.67 % SZS output end Proof
% 59.45/59.67 % Total time :59.123257s
%------------------------------------------------------------------------------