%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL360-1 : 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 : 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 11:19:01 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL360-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.36 % Computer : n028.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 13:58:29 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.25/0.52 start to proof:theBenchmark
% 0.25/0.52 %-------------------------------------------
% 0.25/0.52 % File :CSE---1.7
% 0.25/0.52 % Problem :theBenchmark
% 0.25/0.52 % Transform :cnf
% 0.25/0.52 % Format :tptp:raw
% 0.25/0.52 % Command :java -jar mcs_scs.jar %d %s
% 0.25/0.52
% 0.25/0.52 % Result :Theorem 0.003312s
% 0.25/0.52 % Output :CNFRefutation 0.003312s
% 0.25/0.52 %-------------------------------------------
% 0.25/0.52 %--------------------------------------------------------------------------
% 0.25/0.52 % File : LCL360-1 : TPTP v9.3.1. Released v2.3.0.
% 0.25/0.52 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 0.25/0.52 % Problem : CN-09 depends on the Lukasiewicz system
% 0.25/0.52 % Version : [McC92] axioms.
% 0.25/0.52 % English : An axiomatisation of the Implication/Negation 2 valued
% 0.25/0.52 % sentential calculus is {CN-1,CN-2,CN-3} by Lukasiewicz.
% 0.25/0.52 % Show that CN-09 depends on the Lukasiewicz system.
% 0.25/0.52
% 0.25/0.52 % Refs : [Wos96] Wos (1996), Combining Resonance with Heat
% 0.25/0.52 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 0.25/0.52 % Source : [Wos96]
% 0.25/0.52 % Names : thesis_09 [Wos96]
% 0.25/0.52
% 0.25/0.52 % Status : Unsatisfiable
% 0.25/0.52 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.3.0
% 0.25/0.52 % Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 2 RR)
% 0.25/0.52 % Number of literals : 7 ( 0 equ; 3 neg)
% 0.25/0.52 % Maximal clause size : 3 ( 1 avg)
% 0.25/0.52 % Maximal term depth : 5 ( 2 avg)
% 0.25/0.52 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 0.25/0.52 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.25/0.52 % Number of variables : 8 ( 1 sgn)
% 0.25/0.52 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.25/0.52
% 0.25/0.52 % Comments :
% 0.25/0.52 %--------------------------------------------------------------------------
% 0.25/0.52 cnf(condensed_detachment,axiom,
% 0.25/0.52 ( ~ is_a_theorem(implies(X,Y))
% 0.25/0.52 | ~ is_a_theorem(X)
% 0.25/0.52 | is_a_theorem(Y) ) ).
% 0.25/0.52
% 0.25/0.52 cnf(cn_1,axiom,
% 0.25/0.52 is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
% 0.25/0.52
% 0.25/0.52 cnf(cn_2,axiom,
% 0.25/0.52 is_a_theorem(implies(implies(not(X),X),X)) ).
% 0.25/0.52
% 0.25/0.52 cnf(cn_3,axiom,
% 0.25/0.52 is_a_theorem(implies(X,implies(not(X),Y))) ).
% 0.25/0.52
% 0.25/0.52 cnf(prove_cn_09,negated_conjecture,
% 0.25/0.52 ~ is_a_theorem(implies(implies(implies(not(x),y),z),implies(x,z))) ).
% 0.25/0.52
% 0.25/0.52 %--------------------------------------------------------------------------
% 0.25/0.52 %-------------------------------------------
% 0.25/0.52 % Proof found
% 0.25/0.52 % SZS status Theorem for theBenchmark
% 0.25/0.52 % SZS output start Proof
% 0.25/0.52 %ClaNum:5(EqnAxiom:0)
% 0.25/0.52 %VarNum:16(SingletonVarNum:8)
% 0.25/0.52 %MaxLitNum:3
% 0.25/0.52 %MaxfuncDepth:3
% 0.25/0.52 %SharedTerms:9
% 0.25/0.52 %goalClause: 4
% 0.25/0.52 %singleGoalClaCount:1
% 0.25/0.52 [4]~P1(f2(f2(f2(f1(a3),a4),a5),f2(a3,a5)))
% 0.25/0.52 [2]P1(f2(f2(f1(x21),x21),x21))
% 0.25/0.52 [1]P1(f2(x11,f2(f1(x11),x12)))
% 0.25/0.52 [3]P1(f2(f2(x31,x32),f2(f2(x32,x33),f2(x31,x33))))
% 0.25/0.52 [5]P1(x51)+~P1(x52)+~P1(f2(x52,x51))
% 0.25/0.52 %EqnAxiom
% 0.25/0.52
% 0.25/0.52 %-------------------------------------------
% 0.25/0.52 cnf(6,plain,
% 0.25/0.52 ($false),
% 0.25/0.52 inference(scs_inference,[],[4,3,1,5]),
% 0.25/0.52 ['proof']).
% 0.25/0.52 % SZS output end Proof
% 0.25/0.52 % Total time :0.003312s
%------------------------------------------------------------------------------