%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL226-1 : 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 : n028.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 11:18:50 AM UTC 2026
% Result : Unsatisfiable 3.33s 3.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL226-1 : 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
% 0.07/0.34 % Computer : n028.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 18:34:58 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.24/0.51 start to proof:theBenchmark
% 3.33/3.58 %-------------------------------------------
% 3.33/3.58 % File :CSE---1.7
% 3.33/3.58 % Problem :theBenchmark
% 3.33/3.58 % Transform :cnf
% 3.33/3.58 % Format :tptp:raw
% 3.33/3.58 % Command :java -jar mcs_scs.jar %d %s
% 3.33/3.58
% 3.33/3.58 % Result :Theorem 3.088619s
% 3.33/3.58 % Output :CNFRefutation 3.088619s
% 3.33/3.58 %-------------------------------------------
% 3.33/3.58 %--------------------------------------------------------------------------
% 3.33/3.58 % File : LCL226-1 : TPTP v9.3.1. Released v1.1.0.
% 3.33/3.58 % Domain : Logic Calculi (Propositional)
% 3.33/3.58 % Problem : Principia Mathematica 2.8
% 3.33/3.58 % Version : [WR27] axioms : Reduced & Augmented.
% 3.33/3.58 % English :
% 3.33/3.58
% 3.33/3.58 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 3.33/3.58 % : [NSS63] Newell et al. (1963), Empirical Explorations with the
% 3.33/3.58 % : [ORo89] O'Rourke (1989), LT Revisited: Explanation-Based Learn
% 3.33/3.58 % : [SE94] Segre & Elkan (1994), A High-Performance Explanation-B
% 3.33/3.58 % Source : [SE94]
% 3.33/3.58 % Names : Problem 2.8 [WR27]
% 3.33/3.58
% 3.33/3.58 % Status : Unsatisfiable
% 3.33/3.58 % 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 v2.4.0, 0.14 v2.3.0, 0.00 v2.1.0, 0.00 v2.0.0
% 3.33/3.58 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% 3.33/3.58 % Number of literals : 14 ( 0 equ; 6 neg)
% 3.33/3.58 % Maximal clause size : 3 ( 1 avg)
% 3.33/3.58 % Maximal term depth : 6 ( 2 avg)
% 3.33/3.59 % Number of predicates : 2 ( 2 usr; 0 prp; 1-1 aty)
% 3.33/3.59 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% 3.33/3.59 % Number of variables : 17 ( 1 sgn)
% 3.33/3.59 % SPC : CNF_UNS_RFO_NEQ_HRN
% 3.33/3.59
% 3.33/3.59 % Comments : Reduced to use only or and not, and includes a redundant rule
% 3.33/3.59 % of transitivity of implication, and a reduced rule of
% 3.33/3.59 % detachment.
% 3.33/3.59 %--------------------------------------------------------------------------
% 3.33/3.59 %----Include axioms of propositional logic
% 3.33/3.59 include('Axioms/LCL003-0.ax').
% 3.33/3.59 %--------------------------------------------------------------------------
% 3.33/3.59 cnf(prove_this,negated_conjecture,
% 3.33/3.59 ~ theorem(or(not(or(q,r)),or(not(or(not(r),s)),or(q,s)))) ).
% 3.33/3.59
% 3.33/3.59 %--------------------------------------------------------------------------
% 3.33/3.59 %-------------------------------------------
% 3.33/3.59 % Proof found
% 3.33/3.59 % SZS status Theorem for theBenchmark
% 3.33/3.59 % SZS output start Proof
% 3.33/3.59 %ClaNum:9(EqnAxiom:0)
% 3.33/3.59 %VarNum:34(SingletonVarNum:17)
% 3.33/3.59 %MaxLitNum:3
% 3.33/3.59 %MaxfuncDepth:3
% 3.33/3.59 %SharedTerms:12
% 3.33/3.59 %goalClause: 6
% 3.33/3.59 %singleGoalClaCount:1
% 3.33/3.59 [6]~P2(f2(f1(f2(a3,a4)),f2(f1(f2(f1(a4),a5)),f2(a3,a5))))
% 3.33/3.59 [2]P1(f2(f1(f2(x21,x21)),x21))
% 3.33/3.59 [1]P1(f2(f1(x11),f2(x12,x11)))
% 3.33/3.59 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 3.33/3.59 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 3.33/3.59 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 3.33/3.59 [7]~P1(x71)+P2(x71)
% 3.33/3.59 [8]P2(x81)+~P2(x82)+~P1(f2(f1(x82),x81))
% 3.33/3.59 [9]~P2(f2(f1(x93),x92))+P2(f2(f1(x91),x92))+~P1(f2(f1(x91),x93))
% 3.33/3.59 %EqnAxiom
% 3.33/3.59
% 3.33/3.59 %-------------------------------------------
% 3.33/3.59 cnf(22,plain,
% 3.33/3.59 (~P2(f2(f1(f2(f1(a4),a5)),f2(f1(f2(a3,a4)),f2(a3,a5))))),
% 3.33/3.59 inference(scs_inference,[],[6,4,7,8])).
% 3.33/3.59 cnf(4229,plain,
% 3.33/3.59 ($false),
% 3.33/3.59 inference(scs_inference,[],[22,5,7]),
% 3.33/3.59 ['proof']).
% 3.33/3.60 % SZS output end Proof
% 3.33/3.60 % Total time :3.088619s
%------------------------------------------------------------------------------