%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL178-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 11:18:44 AM UTC 2026
% Result : Unsatisfiable 22.16s 22.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL178-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 15:24:36 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.25/0.51 start to proof:theBenchmark
% 22.16/22.35 %-------------------------------------------
% 22.16/22.35 % File :CSE---1.7
% 22.16/22.35 % Problem :theBenchmark
% 22.16/22.35 % Transform :cnf
% 22.16/22.35 % Format :tptp:raw
% 22.16/22.35 % Command :java -jar mcs_scs.jar %d %s
% 22.16/22.35
% 22.16/22.35 % Result :Theorem 21.861472s
% 22.16/22.35 % Output :CNFRefutation 21.861472s
% 22.16/22.35 %-------------------------------------------
% 22.16/22.36 %--------------------------------------------------------------------------
% 22.16/22.36 % File : LCL178-1 : TPTP v9.3.1. Released v1.1.0.
% 22.16/22.36 % Domain : Logic Calculi (Propositional)
% 22.16/22.36 % Problem : Principia Mathematica 2.12
% 22.16/22.36 % Version : [WR27] axioms : Reduced & Augmented.
% 22.16/22.36 % English :
% 22.16/22.36
% 22.16/22.36 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 22.16/22.36 % : [NSS63] Newell et al. (1963), Empirical Explorations with the
% 22.16/22.36 % : [ORo89] O'Rourke (1989), LT Revisited: Explanation-Based Learn
% 22.16/22.36 % : [SE94] Segre & Elkan (1994), A High-Performance Explanation-B
% 22.16/22.36 % Source : [SE94]
% 22.16/22.36 % Names : Problem 2.12 [WR27]
% 22.16/22.36
% 22.16/22.36 % Status : Unsatisfiable
% 22.16/22.36 % 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 v2.0.0
% 22.16/22.36 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% 22.16/22.36 % Number of literals : 14 ( 0 equ; 6 neg)
% 22.16/22.36 % Maximal clause size : 3 ( 1 avg)
% 22.16/22.36 % Maximal term depth : 5 ( 2 avg)
% 22.16/22.36 % Number of predicates : 2 ( 2 usr; 0 prp; 1-1 aty)
% 22.16/22.36 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 22.16/22.36 % Number of variables : 17 ( 1 sgn)
% 22.16/22.36 % SPC : CNF_UNS_RFO_NEQ_HRN
% 22.16/22.36
% 22.16/22.36 % Comments : Reduced to use only or and not, and includes a redundant rule
% 22.16/22.36 % of transitivity of implication, and a reduced rule of
% 22.16/22.36 % detachment.
% 22.16/22.36 %--------------------------------------------------------------------------
% 22.16/22.36 %----Include axioms of propositional logic
% 22.16/22.36 include('Axioms/LCL003-0.ax').
% 22.16/22.36 %--------------------------------------------------------------------------
% 22.16/22.36 cnf(prove_this,negated_conjecture,
% 22.16/22.36 ~ theorem(or(not(p),not(not(p)))) ).
% 22.16/22.36
% 22.16/22.36 %--------------------------------------------------------------------------
% 22.16/22.36 %-------------------------------------------
% 22.16/22.36 % Proof found
% 22.16/22.36 % SZS status Theorem for theBenchmark
% 22.16/22.36 % SZS output start Proof
% 22.16/22.36 %ClaNum:9(EqnAxiom:0)
% 22.16/22.36 %VarNum:34(SingletonVarNum:17)
% 22.16/22.36 %MaxLitNum:3
% 22.16/22.36 %MaxfuncDepth:3
% 22.16/22.36 %SharedTerms:5
% 22.16/22.36 %goalClause: 6
% 22.16/22.36 %singleGoalClaCount:1
% 22.16/22.36 [6]~P2(f2(f1(a3),f1(f1(a3))))
% 22.16/22.36 [2]P1(f2(f1(f2(x21,x21)),x21))
% 22.16/22.36 [1]P1(f2(f1(x11),f2(x12,x11)))
% 22.16/22.36 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 22.16/22.36 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 22.16/22.36 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 22.16/22.36 [7]~P1(x71)+P2(x71)
% 22.16/22.36 [8]P2(x81)+~P2(x82)+~P1(f2(f1(x82),x81))
% 22.16/22.36 [9]~P2(f2(f1(x93),x92))+P2(f2(f1(x91),x92))+~P1(f2(f1(x91),x93))
% 22.16/22.36 %EqnAxiom
% 22.16/22.36
% 22.16/22.36 %-------------------------------------------
% 22.16/22.37 cnf(12,plain,
% 22.16/22.37 (~P2(f2(f1(f1(a3)),f1(a3)))),
% 22.16/22.37 inference(scs_inference,[],[6,3,7,8])).
% 22.16/22.37 cnf(22,plain,
% 22.16/22.37 (P2(f2(x221,f2(x222,x223)))+~P2(f2(x222,f2(x221,x223)))),
% 22.16/22.37 inference(scs_inference,[],[6,4,7,8])).
% 22.16/22.37 cnf(339,plain,
% 22.16/22.37 (P2(f2(x3391,f2(f1(x3392),x3392)))),
% 22.16/22.37 inference(scs_inference,[],[1,7,22])).
% 22.16/22.37 cnf(1730,plain,
% 22.16/22.37 ($false),
% 22.16/22.37 inference(scs_inference,[],[12,339,2,7,8]),
% 22.16/22.37 ['proof']).
% 22.16/22.37 % SZS output end Proof
% 22.16/22.37 % Total time :21.861472s
%------------------------------------------------------------------------------