%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 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 11:18:43 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 5 03:36:20 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.20/0.54 start to proof:theBenchmark
% 0.20/0.54 %-------------------------------------------
% 0.20/0.54 % File :CSE---1.7
% 0.20/0.54 % Problem :theBenchmark
% 0.20/0.54 % Transform :cnf
% 0.20/0.54 % Format :tptp:raw
% 0.20/0.55 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.55
% 0.20/0.55 % Result :Theorem 0.003930s
% 0.20/0.55 % Output :CNFRefutation 0.003930s
% 0.20/0.55 %-------------------------------------------
% 0.20/0.55 %--------------------------------------------------------------------------
% 0.20/0.55 % File : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 0.20/0.55 % Domain : Logic Calculi (Propositional)
% 0.20/0.55 % Problem : Principia Mathematica 2.05
% 0.20/0.55 % Version : [WR27] axioms.
% 0.20/0.55 % English :
% 0.20/0.55
% 0.20/0.55 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 0.20/0.55 % Source : [Wr27]
% 0.20/0.55 % Names : Problem 2.05 [WR27]
% 0.20/0.55
% 0.20/0.55 % Status : Unsatisfiable
% 0.20/0.55 % Rating : 0.00 v9.1.0, 0.08 v9.0.0, 0.00 v6.0.0, 0.22 v5.5.0, 0.25 v5.4.0, 0.27 v5.3.0, 0.33 v5.2.0, 0.12 v5.1.0, 0.00 v3.4.0, 0.17 v3.3.0, 0.29 v3.2.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.00 v2.3.0
% 0.20/0.55 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 0.20/0.55 % Number of literals : 12 ( 1 equ; 4 neg)
% 0.20/0.55 % Maximal clause size : 3 ( 1 avg)
% 0.20/0.55 % Maximal term depth : 4 ( 2 avg)
% 0.20/0.55 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.55 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.20/0.55 % Number of variables : 16 ( 1 sgn)
% 0.20/0.55 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.20/0.55
% 0.20/0.55 % Comments :
% 0.20/0.55 %--------------------------------------------------------------------------
% 0.20/0.55 %----Include axioms of propositional logic
% 0.20/0.55 include('Axioms/LCL004-0.ax').
% 0.20/0.55 %--------------------------------------------------------------------------
% 0.20/0.55 cnf(prove_this,negated_conjecture,
% 0.20/0.55 ~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ).
% 0.20/0.55
% 0.20/0.55 %--------------------------------------------------------------------------
% 0.20/0.55 %-------------------------------------------
% 0.20/0.55 % Proof found
% 0.20/0.55 % SZS status Theorem for theBenchmark
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 %ClaNum:8(EqnAxiom:0)
% 0.20/0.55 %VarNum:28(SingletonVarNum:14)
% 0.20/0.55 %MaxLitNum:3
% 0.20/0.55 %MaxfuncDepth:4
% 0.20/0.55 %SharedTerms:13
% 0.20/0.55 %goalClause: 6
% 0.20/0.55 %singleGoalClaCount:1
% 0.20/0.55 [6]~P2(f2(f1(f2(f1(a3),a5)),f2(f1(f2(f1(a4),a3)),f2(f1(a4),a5))))
% 0.20/0.55 [2]P1(f2(f1(f2(x21,x21)),x21))
% 0.20/0.55 [1]P1(f2(f1(x11),f2(x12,x11)))
% 0.20/0.55 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 0.20/0.55 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 0.20/0.55 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 0.20/0.55 [7]~P1(x71)+P2(x71)
% 0.20/0.55 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 0.20/0.55 %EqnAxiom
% 0.20/0.55
% 0.20/0.55 %-------------------------------------------
% 0.20/0.55 cnf(9,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(scs_inference,[],[6,5,7]),
% 0.20/0.55 ['proof']).
% 0.20/0.55 % SZS output end Proof
% 0.20/0.55 % Total time :0.003930s
%------------------------------------------------------------------------------