%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 58.17s 58.33s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n027.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 11:02:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 58.17/58.32 %-------------------------------------------
% 58.17/58.32 % File :CSE---1.7
% 58.17/58.32 % Problem :theBenchmark
% 58.17/58.32 % Transform :cnf
% 58.17/58.32 % Format :tptp:raw
% 58.17/58.32 % Command :java -jar mcs_scs.jar %d %s
% 58.17/58.32
% 58.17/58.32 % Result :Theorem 57.819585s
% 58.17/58.32 % Output :CNFRefutation 57.819585s
% 58.17/58.32 %-------------------------------------------
% 58.17/58.32 %--------------------------------------------------------------------------
% 58.17/58.32 % File : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% 58.17/58.32 % Domain : Logic Calculi (Right group)
% 58.17/58.32 % Problem : Q-2 depends on the 2nd McCune system
% 58.17/58.32 % Version : [McC92b] axioms.
% 58.17/58.32 % English : Kalman's axiomatisation of the right group calculus
% 58.17/58.32 % is {LG-1,LG-2,LG-3,LG-4,LG-5}. McCune has shown that LG-2
% 58.17/58.32 % is a single axiom. Other axiomatisations by McCune are
% 58.17/58.32 % {Q-2,Q-3}, {Q-3,Q-4}, S-2, S-3, S-4, P-4, S-6. Show that Q-2
% 58.17/58.32 % depends on the second McCune system.
% 58.17/58.32
% 58.17/58.32 % Refs : [MW92] McCune & Wos (1992), Experiments in Automated Deductio
% 58.17/58.32 % : [McC92a] McCune (1992), Automated Discovery of New Axiomatisat
% 58.17/58.32 % : [McC92b] McCune (1992), Email to G. Sutcliffe
% 58.17/58.32 % Source : [McC92b]
% 58.17/58.32 % Names : RG-107 [MW92]
% 58.17/58.33
% 58.17/58.33 % Status : Unsatisfiable
% 58.17/58.33 % 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 v2.1.0, 0.00 v2.0.0
% 58.17/58.33 % Syntax : Number of clauses : 4 ( 3 unt; 0 nHn; 2 RR)
% 58.17/58.33 % Number of literals : 6 ( 0 equ; 3 neg)
% 58.17/58.33 % Maximal clause size : 3 ( 1 avg)
% 58.17/58.33 % Maximal term depth : 5 ( 2 avg)
% 58.17/58.33 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 58.17/58.33 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 58.17/58.33 % Number of variables : 8 ( 0 sgn)
% 58.17/58.33 % SPC : CNF_UNS_RFO_NEQ_HRN
% 58.17/58.33
% 58.17/58.33 % Comments :
% 58.17/58.33 %--------------------------------------------------------------------------
% 58.17/58.33 cnf(condensed_detachment,axiom,
% 58.17/58.33 ( ~ is_a_theorem(equivalent(X,Y))
% 58.17/58.33 | ~ is_a_theorem(X)
% 58.17/58.33 | is_a_theorem(Y) ) ).
% 58.17/58.33
% 58.17/58.33 cnf(q_3,axiom,
% 58.17/58.33 is_a_theorem(equivalent(X,equivalent(equivalent(X,equivalent(Y,Z)),equivalent(Z,Y)))) ).
% 58.17/58.33
% 58.17/58.33 cnf(q_4,axiom,
% 58.17/58.33 is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Y,Z)))) ).
% 58.17/58.33
% 58.17/58.33 cnf(prove_q_2,negated_conjecture,
% 58.17/58.33 ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))) ).
% 58.17/58.33
% 58.17/58.33 %--------------------------------------------------------------------------
% 58.17/58.33 %-------------------------------------------
% 58.17/58.33 % Proof found
% 58.17/58.33 % SZS status Theorem for theBenchmark
% 58.17/58.33 % SZS output start Proof
% 58.17/58.33 %ClaNum:4(EqnAxiom:0)
% 58.17/58.33 %VarNum:16(SingletonVarNum:8)
% 58.17/58.33 %MaxLitNum:3
% 58.17/58.33 %MaxfuncDepth:3
% 58.17/58.33 %SharedTerms:9
% 58.17/58.33 %goalClause: 3
% 58.17/58.33 %singleGoalClaCount:1
% 58.17/58.33 [3]~P1(f1(f1(f1(a2,a3),f1(a4,a3)),f1(a2,a4)))
% 58.17/58.33 [1]P1(f1(f1(x11,x12),f1(f1(x11,x13),f1(x12,x13))))
% 58.17/58.33 [2]P1(f1(x21,f1(f1(x21,f1(x22,x23)),f1(x23,x22))))
% 58.17/58.33 [4]P1(x41)+~P1(x42)+~P1(f1(x42,x41))
% 58.17/58.33 %EqnAxiom
% 58.17/58.33
% 58.17/58.33 %-------------------------------------------
% 58.17/58.33 cnf(5,plain,
% 58.17/58.33 (P1(f1(f1(f1(f1(x51,x52),f1(f1(x51,x53),f1(x52,x53))),f1(x54,x55)),f1(x55,x54)))),
% 58.17/58.33 inference(scs_inference,[],[1,2,4])).
% 58.17/58.33 cnf(11,plain,
% 58.17/58.33 (P1(f1(f1(x111,x112),f1(f1(f1(x111,f1(x113,x114)),f1(x114,x113)),x112)))),
% 58.17/58.33 inference(scs_inference,[],[2,1,4])).
% 58.17/58.33 cnf(20,plain,
% 58.17/58.33 (P1(f1(f1(f1(f1(x201,x202),f1(x203,x204)),f1(x204,x203)),f1(f1(x201,x205),f1(x202,x205))))),
% 58.17/58.33 inference(scs_inference,[],[1,11,4])).
% 58.17/58.33 cnf(23,plain,
% 58.17/58.33 (P1(f1(f1(f1(x231,x232),x233),f1(f1(f1(x231,x234),f1(x232,x234)),x233)))),
% 58.17/58.33 inference(scs_inference,[],[5,20,4])).
% 58.17/58.33 cnf(26,plain,
% 58.17/58.33 (~P1(f1(f1(a2,a4),f1(a2,a4)))),
% 58.17/58.33 inference(scs_inference,[],[23,3,4])).
% 58.17/58.33 cnf(35,plain,
% 58.17/58.33 (P1(f1(f1(f1(f1(f1(f1(x351,x352),f1(x353,x354)),f1(x354,x353)),f1(x355,x356)),f1(x356,x355)),f1(f1(x351,x357),f1(x352,x357))))),
% 58.17/58.33 inference(scs_inference,[],[20,11,4])).
% 58.17/58.33 cnf(38,plain,
% 58.17/58.33 (~P1(f1(f1(f1(f1(f1(a2,a2),f1(x381,x382)),f1(x382,x381)),f1(x383,x384)),f1(x384,x383)))),
% 58.17/58.33 inference(scs_inference,[],[35,26,4])).
% 58.17/58.33 cnf(57,plain,
% 58.17/58.33 ($false),
% 58.17/58.33 inference(scs_inference,[],[38,23,20,4]),
% 58.17/58.33 ['proof']).
% 58.17/58.33 % SZS output end Proof
% 58.17/58.33 % Total time :57.819585s
%------------------------------------------------------------------------------