%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL176-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 58.18s 58.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL176-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.01 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 5 09:22:12 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.09/0.38 start to proof:theBenchmark
% 58.18/58.42 %-------------------------------------------
% 58.18/58.42 % File :CSE---1.7
% 58.18/58.42 % Problem :theBenchmark
% 58.18/58.42 % Transform :cnf
% 58.18/58.42 % Format :tptp:raw
% 58.18/58.42 % Command :java -jar mcs_scs.jar %d %s
% 58.18/58.42
% 58.18/58.42 % Result :Theorem 58.002905s
% 58.18/58.42 % Output :CNFRefutation 58.002905s
% 58.18/58.42 %-------------------------------------------
% 58.18/58.42 %--------------------------------------------------------------------------
% 58.18/58.42 % File : LCL176-3 : TPTP v9.3.1. Released v2.3.0.
% 58.18/58.42 % Domain : Logic Calculi (Propositional)
% 58.18/58.42 % Problem : Principia Mathematica 2.1 and 2.08
% 58.18/58.42 % Version : [WR27] axioms.
% 58.18/58.42 % English :
% 58.18/58.42
% 58.18/58.42 % Refs : [WR27] Whitehead & Russell (1927), Principia Mathematica
% 58.18/58.42 % Source : [WR27]
% 58.18/58.42 % Names : Problem 2.1 [WR27]
% 58.18/58.42 % : Problem 2.08 [WR27]
% 58.18/58.42
% 58.18/58.42 % Status : Unsatisfiable
% 58.18/58.42 % Rating : 0.00 v9.3.0, 0.33 v9.1.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.00 v2.3.0
% 58.18/58.42 % Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 3 RR)
% 58.18/58.42 % Number of literals : 12 ( 1 equ; 4 neg)
% 58.18/58.42 % Maximal clause size : 3 ( 1 avg)
% 58.18/58.42 % Maximal term depth : 4 ( 2 avg)
% 58.18/58.42 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 58.18/58.42 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 58.18/58.42 % Number of variables : 16 ( 1 sgn)
% 58.18/58.42 % SPC : CNF_UNS_RFO_SEQ_HRN
% 58.18/58.42
% 58.18/58.42 % Comments :
% 58.18/58.42 %--------------------------------------------------------------------------
% 58.18/58.42 %----Include axioms of propositional logic
% 58.18/58.42 include('Axioms/LCL004-0.ax').
% 58.18/58.42 %--------------------------------------------------------------------------
% 58.18/58.42 cnf(prove_this,negated_conjecture,
% 58.18/58.42 ~ theorem(implies(p,p)) ).
% 58.18/58.42
% 58.18/58.42 %--------------------------------------------------------------------------
% 58.18/58.42 %-------------------------------------------
% 58.18/58.42 % Proof found
% 58.18/58.42 % SZS status Theorem for theBenchmark
% 58.18/58.42 % SZS output start Proof
% 58.18/58.42 %ClaNum:8(EqnAxiom:0)
% 58.18/58.42 %VarNum:28(SingletonVarNum:14)
% 58.18/58.42 %MaxLitNum:3
% 58.18/58.42 %MaxfuncDepth:3
% 58.18/58.42 %SharedTerms:4
% 58.18/58.42 %goalClause: 6
% 58.18/58.43 %singleGoalClaCount:1
% 58.18/58.43 [6]~P2(f2(f1(a3),a3))
% 58.18/58.43 [2]P1(f2(f1(f2(x21,x21)),x21))
% 58.18/58.43 [1]P1(f2(f1(x11),f2(x12,x11)))
% 58.18/58.43 [3]P1(f2(f1(f2(x31,x32)),f2(x32,x31)))
% 58.18/58.43 [4]P1(f2(f1(f2(x41,f2(x42,x43))),f2(x42,f2(x41,x43))))
% 58.18/58.43 [5]P1(f2(f1(f2(f1(x51),x52)),f2(f1(f2(x53,x51)),f2(x53,x52))))
% 58.18/58.43 [7]~P1(x71)+P2(x71)
% 58.18/58.43 [8]P2(x81)+~P2(x82)+~P2(f2(f1(x82),x81))
% 58.18/58.43 %EqnAxiom
% 58.18/58.43
% 58.18/58.43 %-------------------------------------------
% 58.49/58.78 cnf(938797,plain,
% 58.49/58.78 (P2(f2(f1(x9387971),f2(x9387972,x9387971)))),
% 58.49/58.78 inference(scs_inference,[],[1,7])).
% 58.49/58.78 cnf(938799,plain,
% 58.49/58.78 (~P2(f2(f1(f2(f1(x9387991),f2(x9387992,x9387991))),f2(f1(a3),a3)))),
% 58.49/58.78 inference(scs_inference,[],[6,1,7,8])).
% 58.49/58.78 cnf(938807,plain,
% 58.49/58.78 (~P2(f2(f1(f2(f1(x9388071),f2(x9388072,x9388071))),f2(f1(f2(f1(x9388073),f2(x9388074,x9388073))),f2(f1(a3),a3))))),
% 58.49/58.78 inference(scs_inference,[],[938797,2,938799,7,8])).
% 58.49/58.78 cnf(938809,plain,
% 58.49/58.78 ($false),
% 58.49/58.78 inference(scs_inference,[],[4,938807,7]),
% 58.49/58.78 ['proof']).
% 58.69/59.00 % SZS output end Proof
% 58.69/59.00 % Total time :58.002905s
%------------------------------------------------------------------------------