%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL197-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 11:18:47 AM UTC 2026
% Result : Unsatisfiable 1.71s 2.00s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL197-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 5 18:32:22 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.22/0.52 start to proof:theBenchmark
% 1.71/1.99 %-------------------------------------------
% 1.71/1.99 % File :CSE---1.7
% 1.71/1.99 % Problem :theBenchmark
% 1.71/1.99 % Transform :cnf
% 1.71/1.99 % Format :tptp:raw
% 1.71/1.99 % Command :java -jar mcs_scs.jar %d %s
% 1.71/1.99
% 1.71/1.99 % Result :Theorem 1.488917s
% 1.71/1.99 % Output :CNFRefutation 1.488917s
% 1.71/1.99 %-------------------------------------------
% 1.71/2.00 %--------------------------------------------------------------------------
% 1.71/2.00 % File : LCL197-1 : TPTP v9.3.1. Released v1.1.0.
% 1.71/2.00 % Domain : Logic Calculi (Propositional)
% 1.71/2.00 % Problem : Principia Mathematica 2.41
% 1.71/2.00 % Version : [WR27] axioms : Reduced & Augmented.
% 1.71/2.00 % English :
% 1.71/2.00
% 1.71/2.00 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 1.71/2.00 % : [NSS63] Newell et al. (1963), Empirical Explorations with the
% 1.71/2.00 % : [ORo89] O'Rourke (1989), LT Revisited: Explanation-Based Learn
% 1.71/2.00 % : [SE94] Segre & Elkan (1994), A High-Performance Explanation-B
% 1.71/2.00 % Source : [SE94]
% 1.71/2.00 % Names : Problem 2.41 [WR27]
% 1.71/2.00
% 1.71/2.00 % Status : Unsatisfiable
% 1.71/2.00 % Rating : 0.00 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.00 v2.1.0, 0.00 v2.0.0
% 1.71/2.00 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% 1.71/2.00 % Number of literals : 14 ( 0 equ; 6 neg)
% 1.71/2.00 % Maximal clause size : 3 ( 1 avg)
% 1.71/2.00 % Maximal term depth : 5 ( 2 avg)
% 1.71/2.00 % Number of predicates : 2 ( 2 usr; 0 prp; 1-1 aty)
% 1.71/2.00 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 1.71/2.00 % Number of variables : 17 ( 1 sgn)
% 1.71/2.00 % SPC : CNF_UNS_RFO_NEQ_HRN
% 1.71/2.00
% 1.71/2.00 % Comments : Reduced to use only or and not, and includes a redundant rule
% 1.71/2.00 % of transitivity of implication, and a reduced rule of
% 1.71/2.00 % detachment.
% 1.71/2.00 %--------------------------------------------------------------------------
% 1.71/2.00 %----Include axioms of propositional logic
% 1.71/2.00 include('Axioms/LCL003-0.ax').
% 1.71/2.00 %--------------------------------------------------------------------------
% 1.71/2.00 cnf(prove_this,negated_conjecture,
% 1.71/2.00 ~ theorem(or(not(or(q,or(p,q))),or(p,q))) ).
% 1.71/2.00
% 1.71/2.00 %--------------------------------------------------------------------------
% 1.71/2.00 %-------------------------------------------
% 1.71/2.00 % Proof found
% 1.71/2.00 % SZS status Theorem for theBenchmark
% 1.71/2.00 % SZS output start Proof
% 1.71/2.00 %ClaNum:9(EqnAxiom:0)
% 1.71/2.00 %VarNum:34(SingletonVarNum:17)
% 1.71/2.00 %MaxLitNum:3
% 1.71/2.00 %MaxfuncDepth:3
% 1.71/2.00 %SharedTerms:7
% 1.71/2.00 %goalClause: 6
% 1.71/2.00 %singleGoalClaCount:1
% 1.71/2.00 [6]~P2(f2(f1(f2(a3,f2(a4,a3))),f2(a4,a3)))
% 1.71/2.00 [2]P1(f2(f1(f2(x21,x21)),x21))
% 1.71/2.00 [1]P1(f2(f1(x11),f2(x12,x11)))
% 1.71/2.00 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 1.71/2.00 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 1.71/2.00 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 1.71/2.00 [7]~P1(x71)+P2(x71)
% 1.71/2.00 [8]P2(x81)+~P2(x82)+~P1(f2(f1(x82),x81))
% 1.71/2.00 [9]~P2(f2(f1(x93),x92))+P2(f2(f1(x91),x92))+~P1(f2(f1(x91),x93))
% 1.71/2.00 %EqnAxiom
% 1.71/2.00
% 1.71/2.00 %-------------------------------------------
% 1.71/2.00 cnf(22,plain,
% 1.71/2.00 (P2(f2(f1(f2(x221,x222)),f2(x221,x223)))+~P2(f2(f1(x222),x223))),
% 1.71/2.00 inference(scs_inference,[],[6,5,7,8])).
% 1.71/2.00 cnf(313,plain,
% 1.71/2.00 (P2(f2(f1(f2(x3131,x3132)),f2(x3131,f2(x3133,x3132))))),
% 1.71/2.00 inference(scs_inference,[],[1,22,7])).
% 1.71/2.01 cnf(828,plain,
% 1.71/2.01 (P2(f2(f1(f2(x8281,x8282)),f2(x8282,f2(x8283,x8281))))),
% 1.71/2.01 inference(scs_inference,[],[3,6,313,7,9])).
% 1.71/2.01 cnf(875,plain,
% 1.71/2.01 (P2(f2(x8751,f2(f1(f2(x8752,x8751)),f2(x8753,x8752))))),
% 1.71/2.01 inference(scs_inference,[],[6,828,4,7,8])).
% 1.71/2.01 cnf(932,plain,
% 1.71/2.01 (P2(f2(f2(f1(f2(x9321,x9322)),f2(x9323,x9321)),x9322))),
% 1.71/2.01 inference(scs_inference,[],[3,6,875,7,8])).
% 1.71/2.01 cnf(937,plain,
% 1.71/2.01 (P2(f2(x9371,f2(f2(f1(f2(x9372,x9373)),f2(x9374,x9372)),x9373)))),
% 1.71/2.01 inference(scs_inference,[],[6,932,1,7,8])).
% 1.71/2.01 cnf(957,plain,
% 1.71/2.01 (P2(f2(f2(f1(f2(x9571,x9572)),f2(x9573,x9571)),f2(x9574,x9572)))),
% 1.71/2.01 inference(scs_inference,[],[6,937,4,7,8])).
% 1.71/2.01 cnf(962,plain,
% 1.71/2.01 (P2(f2(f2(x9621,x9622),f2(f1(f2(x9623,x9622)),f2(x9624,x9623))))),
% 1.71/2.01 inference(scs_inference,[],[3,6,957,7,8])).
% 1.71/2.01 cnf(967,plain,
% 1.71/2.01 ($false),
% 1.71/2.01 inference(scs_inference,[],[6,962,2,7,8]),
% 1.71/2.01 ['proof']).
% 1.71/2.01 % SZS output end Proof
% 1.71/2.01 % Total time :1.488917s
%------------------------------------------------------------------------------