%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 11:18:37 AM UTC 2026
% Result : Unsatisfiable 61.38s 61.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.34 % Computer : n019.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 03:32:08 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.23/0.51 start to proof:theBenchmark
% 61.38/61.50 %-------------------------------------------
% 61.38/61.50 % File :CSE---1.7
% 61.38/61.50 % Problem :theBenchmark
% 61.38/61.50 % Transform :cnf
% 61.38/61.50 % Format :tptp:raw
% 61.38/61.50 % Command :java -jar mcs_scs.jar %d %s
% 61.38/61.50
% 61.38/61.50 % Result :Theorem 61.006871s
% 61.38/61.50 % Output :CNFRefutation 61.006871s
% 61.38/61.50 %-------------------------------------------
% 61.38/61.50 %--------------------------------------------------------------------------
% 61.38/61.50 % File : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% 61.38/61.50 % Domain : Logic Calculi (Implicational propositional)
% 61.38/61.50 % Problem : IC-2 depends on the 4th Lukasiewicz axiom
% 61.38/61.50 % Version : [TPTP] axioms.
% 61.38/61.50 % English : Axiomatisations of the Implicational propositional calculus
% 61.38/61.50 % are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
% 61.38/61.50 % axioms. Show that IC-2 depends on the fourth Lukasiewicz
% 61.38/61.50 % axiom.
% 61.38/61.50
% 61.38/61.50 % Refs : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
% 61.38/61.50 % : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
% 61.38/61.50 % Source : [TPTP]
% 61.38/61.50 % Names :
% 61.38/61.50
% 61.38/61.50 % Status : Unsatisfiable
% 61.38/61.50 % Rating : 0.00 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.12 v5.4.0, 0.17 v5.3.0, 0.20 v5.2.0, 0.08 v5.1.0, 0.19 v5.0.0, 0.20 v4.0.1, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.22 v2.1.0, 0.25 v2.0.0
% 61.38/61.50 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 61.38/61.50 % Number of literals : 5 ( 0 equ; 3 neg)
% 61.38/61.50 % Maximal clause size : 3 ( 1 avg)
% 61.38/61.50 % Maximal term depth : 5 ( 2 avg)
% 61.38/61.50 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 61.38/61.50 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 61.38/61.50 % Number of variables : 7 ( 2 sgn)
% 61.38/61.50 % SPC : CNF_UNS_RFO_NEQ_HRN
% 61.38/61.50
% 61.38/61.50 % Comments :
% 61.38/61.50 %--------------------------------------------------------------------------
% 61.38/61.50 cnf(condensed_detachment,axiom,
% 61.38/61.50 ( ~ is_a_theorem(implies(X,Y))
% 61.38/61.50 | ~ is_a_theorem(X)
% 61.38/61.50 | is_a_theorem(Y) ) ).
% 61.38/61.50
% 61.38/61.50 cnf(ic_JLukasiewicz_4,axiom,
% 61.38/61.50 is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))) ).
% 61.38/61.50
% 61.38/61.50 cnf(prove_ic_2,negated_conjecture,
% 61.38/61.50 ~ is_a_theorem(implies(a,implies(b,a))) ).
% 61.38/61.50
% 61.38/61.50 %--------------------------------------------------------------------------
% 61.38/61.50 %-------------------------------------------
% 61.38/61.50 % Proof found
% 61.38/61.50 % SZS status Theorem for theBenchmark
% 61.38/61.50 % SZS output start Proof
% 61.38/61.50 %ClaNum:3(EqnAxiom:0)
% 61.38/61.50 %VarNum:13(SingletonVarNum:7)
% 61.38/61.50 %MaxLitNum:3
% 61.38/61.50 %MaxfuncDepth:4
% 61.38/61.50 %SharedTerms:5
% 61.38/61.50 %goalClause: 2
% 61.38/61.50 %singleGoalClaCount:1
% 61.38/61.50 [2]~P1(f1(a2,f1(a3,a2)))
% 61.38/61.50 [1]P1(f1(f1(f1(x11,x12),f1(x13,x14)),f1(x15,f1(f1(x14,x11),f1(x13,x11)))))
% 61.38/61.50 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 61.38/61.50 %EqnAxiom
% 61.38/61.50
% 61.38/61.50 %-------------------------------------------
% 61.38/61.51 cnf(4,plain,
% 61.38/61.51 (P1(f1(x41,f1(f1(x42,x43),f1(x44,x43))))+~P1(f1(f1(x43,x45),f1(x44,x42)))),
% 61.38/61.51 inference(scs_inference,[],[1,3])).
% 61.38/61.51 cnf(6,plain,
% 61.38/61.51 (P1(f1(x61,f1(f1(f1(f1(x62,x63),f1(x64,x63)),f1(x63,x65)),f1(x66,f1(x63,x65)))))),
% 61.38/61.51 inference(scs_inference,[],[1,4])).
% 61.38/61.51 cnf(10,plain,
% 61.38/61.51 (P1(f1(f1(f1(f1(x101,x102),f1(x103,x102)),f1(x102,x104)),f1(x105,f1(x102,x104))))),
% 61.38/61.51 inference(scs_inference,[],[6,1,3])).
% 61.38/61.51 cnf(18,plain,
% 61.38/61.51 (P1(f1(x181,f1(x182,f1(f1(x182,x183),f1(x184,x183)))))),
% 61.38/61.51 inference(scs_inference,[],[10,1,3])).
% 61.38/61.51 cnf(22,plain,
% 61.38/61.51 (P1(f1(x221,f1(f1(x221,x222),f1(x223,x222))))),
% 61.38/61.51 inference(scs_inference,[],[10,18,3])).
% 61.38/61.51 cnf(27,plain,
% 61.38/61.51 (P1(f1(x271,f1(f1(f1(f1(x272,x273),f1(x274,x273)),x275),f1(x272,x275))))),
% 61.38/61.51 inference(scs_inference,[],[18,1,3])).
% 61.38/61.51 cnf(31,plain,
% 61.38/61.51 (~P1(f1(f1(x311,f1(f1(x311,x312),f1(x313,x312))),f1(a2,f1(a3,a2))))),
% 61.38/61.51 inference(scs_inference,[],[22,2,3])).
% 61.38/61.51 cnf(33,plain,
% 61.38/61.51 (P1(f1(f1(f1(f1(x331,x332),f1(x333,x332)),x334),f1(x331,x334)))),
% 61.38/61.51 inference(scs_inference,[],[22,27,3])).
% 61.38/61.51 cnf(36,plain,
% 61.38/61.51 (P1(f1(f1(f1(f1(f1(f1(x361,x362),f1(x363,x362)),x364),f1(x361,x364)),x365),f1(x366,x365)))),
% 61.38/61.51 inference(scs_inference,[],[22,33,3])).
% 61.38/61.51 cnf(45,plain,
% 61.38/61.51 (~P1(f1(f1(f1(f1(f1(x451,x452),f1(x453,x452)),x454),f1(x451,x454)),f1(a2,f1(a3,a2))))),
% 61.38/61.51 inference(scs_inference,[],[31,36,3])).
% 61.38/61.51 cnf(48,plain,
% 61.38/61.51 (P1(f1(f1(x481,x482),f1(x483,f1(x482,f1(x484,x482)))))),
% 61.38/61.51 inference(scs_inference,[],[33,10,3])).
% 61.38/61.51 cnf(66,plain,
% 61.38/61.51 (~P1(f1(f1(f1(x661,a2),f1(x662,a2)),f1(a2,f1(a3,a2))))),
% 61.38/61.51 inference(scs_inference,[],[45,10,3])).
% 61.38/61.51 cnf(71,plain,
% 61.38/61.51 (P1(f1(x711,f1(f1(x712,x713),f1(x714,f1(x712,x713)))))),
% 61.38/61.51 inference(scs_inference,[],[48,36,3])).
% 61.38/61.51 cnf(74,plain,
% 61.38/61.51 (P1(f1(f1(x741,x742),f1(x743,f1(x741,x742))))),
% 61.38/61.51 inference(scs_inference,[],[48,71,3])).
% 61.38/61.51 cnf(79,plain,
% 61.38/61.51 (P1(f1(x791,f1(f1(f1(x792,x793),x792),f1(x794,x792))))),
% 61.38/61.51 inference(scs_inference,[],[74,1,3])).
% 61.38/61.51 cnf(84,plain,
% 61.38/61.51 ($false),
% 61.38/61.51 inference(scs_inference,[],[66,74,79,3]),
% 61.38/61.51 ['proof']).
% 61.38/61.51 % SZS output end Proof
% 61.38/61.51 % Total time :61.006871s
%------------------------------------------------------------------------------