%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 116.31s 116.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 22:49:15 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.23/0.52 start to proof:theBenchmark
% 116.31/116.43 %-------------------------------------------
% 116.31/116.43 % File :CSE---1.7
% 116.31/116.43 % Problem :theBenchmark
% 116.31/116.43 % Transform :cnf
% 116.31/116.43 % Format :tptp:raw
% 116.31/116.43 % Command :java -jar mcs_scs.jar %d %s
% 116.31/116.43
% 116.31/116.43 % Result :Theorem 115.924329s
% 116.31/116.43 % Output :CNFRefutation 115.924329s
% 116.31/116.43 %-------------------------------------------
% 116.31/116.43 %--------------------------------------------------------------------------
% 116.31/116.43 % File : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% 116.31/116.43 % Domain : Logic Calculi (Implicational propositional)
% 116.31/116.43 % Problem : IC-2 depends on the 5th Lukasiewicz axiom
% 116.31/116.43 % Version : [TPTP] axioms.
% 116.31/116.43 % English : Axiomatisations of the Implicational propositional calculus
% 116.31/116.43 % are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
% 116.31/116.43 % axioms.Show that IC-2 depends on the fifth Lukasiewicz axiom.
% 116.31/116.43
% 116.31/116.43 % Refs : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
% 116.31/116.43 % : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
% 116.31/116.43 % Source : [TPTP]
% 116.31/116.43 % Names :
% 116.31/116.43
% 116.31/116.43 % Status : Unsatisfiable
% 116.31/116.43 % 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, 0.56 v2.1.0, 0.63 v2.0.0
% 116.31/116.43 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 116.31/116.43 % Number of literals : 5 ( 0 equ; 3 neg)
% 116.31/116.43 % Maximal clause size : 3 ( 1 avg)
% 116.31/116.43 % Maximal term depth : 5 ( 2 avg)
% 116.31/116.43 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 116.31/116.43 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 116.31/116.43 % Number of variables : 7 ( 2 sgn)
% 116.31/116.43 % SPC : CNF_UNS_RFO_NEQ_HRN
% 116.31/116.43
% 116.31/116.43 % Comments :
% 116.31/116.43 %--------------------------------------------------------------------------
% 116.31/116.43 cnf(condensed_detachment,axiom,
% 116.31/116.43 ( ~ is_a_theorem(implies(X,Y))
% 116.31/116.43 | ~ is_a_theorem(X)
% 116.31/116.43 | is_a_theorem(Y) ) ).
% 116.31/116.43
% 116.31/116.43 cnf(ic_JLukasiewicz_5,axiom,
% 116.31/116.43 is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(implies(S,P),implies(T,implies(R,P))))) ).
% 116.31/116.43
% 116.31/116.43 cnf(prove_ic_2,negated_conjecture,
% 116.31/116.43 ~ is_a_theorem(implies(a,implies(b,a))) ).
% 116.31/116.43
% 116.31/116.43 %--------------------------------------------------------------------------
% 116.31/116.43 %-------------------------------------------
% 116.31/116.43 % Proof found
% 116.31/116.43 % SZS status Theorem for theBenchmark
% 116.31/116.43 % SZS output start Proof
% 116.31/116.43 %ClaNum:3(EqnAxiom:0)
% 116.31/116.43 %VarNum:13(SingletonVarNum:7)
% 116.31/116.43 %MaxLitNum:3
% 116.31/116.43 %MaxfuncDepth:4
% 116.31/116.43 %SharedTerms:5
% 116.31/116.43 %goalClause: 2
% 116.31/116.43 %singleGoalClaCount:1
% 116.31/116.43 [2]~P1(f1(a2,f1(a3,a2)))
% 116.31/116.43 [1]P1(f1(f1(f1(x11,x12),f1(x13,x14)),f1(f1(x14,x11),f1(x15,f1(x13,x11)))))
% 116.31/116.43 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 116.31/116.43 %EqnAxiom
% 116.31/116.43
% 116.31/116.43 %-------------------------------------------
% 116.31/116.44 cnf(4,plain,
% 116.31/116.44 (P1(f1(f1(x41,x42),f1(x43,f1(x44,x42))))+~P1(f1(f1(x42,x45),f1(x44,x41)))),
% 116.31/116.44 inference(scs_inference,[],[1,3])).
% 116.31/116.44 cnf(6,plain,
% 116.31/116.44 (P1(f1(f1(f1(x61,f1(x62,x63)),f1(x63,x64)),f1(x65,f1(f1(x66,x63),f1(x63,x64)))))),
% 116.31/116.44 inference(scs_inference,[],[1,4])).
% 116.31/116.44 cnf(8,plain,
% 116.31/116.44 (~P1(f1(f1(f1(f1(x81,x82),f1(x83,x84)),f1(f1(x84,x81),f1(x85,f1(x83,x81)))),f1(a2,f1(a3,a2))))),
% 116.31/116.44 inference(scs_inference,[],[2,1,4,3])).
% 116.31/116.44 cnf(10,plain,
% 116.31/116.44 (P1(f1(x101,f1(f1(x102,x103),f1(x103,x104))))+~P1(f1(f1(x105,f1(x106,x103)),f1(x103,x104)))),
% 116.31/116.44 inference(scs_inference,[],[6,3])).
% 116.31/116.44 cnf(12,plain,
% 116.31/116.44 (P1(f1(f1(f1(x121,f1(f1(x122,x123),f1(x123,x121))),x124),f1(x125,f1(f1(x126,x121),x124))))),
% 116.31/116.44 inference(scs_inference,[],[6,10,4])).
% 116.31/116.44 cnf(13,plain,
% 116.31/116.44 (P1(f1(x131,f1(f1(x132,f1(x133,x134)),f1(f1(x133,x134),f1(x135,f1(x136,f1(x133,x134)))))))),
% 116.31/116.44 inference(scs_inference,[],[6,10,4])).
% 116.31/116.44 cnf(19,plain,
% 116.31/116.44 (P1(f1(x191,f1(f1(x192,x193),f1(x193,f1(f1(x194,x195),f1(x196,x193))))))),
% 116.31/116.44 inference(scs_inference,[],[6,12,3])).
% 116.31/116.44 cnf(27,plain,
% 116.31/116.44 (P1(f1(f1(x271,f1(x272,x273)),f1(f1(x272,x273),f1(x274,f1(x275,f1(x272,x273))))))),
% 116.31/116.44 inference(scs_inference,[],[6,13,3])).
% 116.31/116.44 cnf(30,plain,
% 116.31/116.44 (P1(f1(f1(x301,x302),f1(x302,f1(f1(x303,x304),f1(x305,x302)))))),
% 116.31/116.44 inference(scs_inference,[],[6,19,3])).
% 116.31/116.44 cnf(33,plain,
% 116.31/116.44 (P1(f1(f1(f1(f1(x331,x332),f1(x332,x333)),f1(x334,f1(x335,x332))),f1(x336,f1(x337,f1(x334,f1(x335,x332))))))),
% 116.31/116.44 inference(scs_inference,[],[6,1,3])).
% 116.31/116.44 cnf(36,plain,
% 116.31/116.44 (P1(f1(x361,f1(f1(x362,x363),f1(x363,f1(x364,f1(x365,x363))))))),
% 116.31/116.44 inference(scs_inference,[],[30,4,10])).
% 116.31/116.44 cnf(37,plain,
% 116.31/116.44 (P1(f1(f1(x371,x372),f1(x372,f1(x373,f1(x374,x372)))))),
% 116.31/116.44 inference(scs_inference,[],[36,27,3])).
% 116.31/116.44 cnf(41,plain,
% 116.31/116.44 (P1(f1(f1(f1(x411,f1(x412,x413)),x414),f1(x415,f1(x413,x414))))),
% 116.31/116.44 inference(scs_inference,[],[37,1,3])).
% 116.31/116.44 cnf(51,plain,
% 116.31/116.44 (P1(f1(f1(f1(x511,f1(x512,f1(x513,x514))),f1(f1(x515,x514),f1(x514,x516))),f1(x517,f1(x518,f1(f1(x515,x514),f1(x514,x516))))))),
% 116.31/116.44 inference(scs_inference,[],[33,1,3])).
% 116.31/116.44 cnf(67,plain,
% 116.31/116.44 (P1(f1(f1(f1(x671,x672),f1(x673,f1(x674,x671))),f1(x675,f1(x676,f1(x673,f1(x674,x671))))))),
% 116.31/116.44 inference(scs_inference,[],[41,1,3])).
% 116.31/116.44 cnf(168,plain,
% 116.31/116.44 (P1(f1(x1681,f1(x1682,f1(f1(f1(x1683,x1684),x1684),f1(x1684,f1(x1685,x1684))))))),
% 116.31/116.44 inference(scs_inference,[],[1,51,3])).
% 116.31/116.44 cnf(173,plain,
% 116.31/116.44 (P1(f1(x1731,f1(f1(f1(x1732,x1733),x1733),f1(x1733,f1(x1734,x1733)))))),
% 116.31/116.44 inference(scs_inference,[],[1,168,3])).
% 116.31/116.44 cnf(177,plain,
% 116.31/116.44 (P1(f1(f1(f1(x1771,x1772),x1772),f1(x1772,f1(x1773,x1772))))),
% 116.31/116.44 inference(scs_inference,[],[1,173,3])).
% 116.31/116.44 cnf(180,plain,
% 116.31/116.44 (P1(f1(f1(f1(x1801,x1802),f1(x1803,x1802)),f1(x1804,f1(x1802,f1(x1803,x1802)))))),
% 116.31/116.44 inference(scs_inference,[],[1,177,3])).
% 116.31/116.44 cnf(183,plain,
% 116.31/116.44 (P1(f1(f1(f1(x1831,f1(x1832,x1831)),f1(x1833,x1831)),f1(x1834,f1(x1835,f1(x1833,x1831)))))),
% 116.31/116.44 inference(scs_inference,[],[1,180,3])).
% 116.31/116.44 cnf(186,plain,
% 116.31/116.44 (P1(f1(f1(f1(x1861,f1(x1862,x1863)),f1(x1863,f1(x1864,x1863))),f1(x1865,f1(x1866,f1(x1863,f1(x1864,x1863))))))),
% 116.31/116.44 inference(scs_inference,[],[1,183,3])).
% 116.31/116.44 cnf(198,plain,
% 116.31/116.44 (P1(f1(x1981,f1(x1982,f1(f1(x1983,x1984),f1(x1985,f1(x1984,x1984))))))),
% 116.31/116.44 inference(scs_inference,[],[1,67,3])).
% 116.31/116.44 cnf(209,plain,
% 116.31/116.44 (P1(f1(x2091,f1(f1(x2092,x2093),f1(x2094,f1(x2093,x2093)))))),
% 116.31/116.44 inference(scs_inference,[],[6,198,3])).
% 116.31/116.44 cnf(212,plain,
% 116.31/116.44 (P1(f1(f1(x2121,x2122),f1(x2123,f1(x2122,x2122))))),
% 116.31/116.44 inference(scs_inference,[],[6,209,3])).
% 116.31/116.44 cnf(325,plain,
% 116.31/116.44 (P1(f1(x3251,f1(f1(x3252,f1(x3253,x3254)),f1(x3252,f1(x3253,x3254)))))),
% 116.31/116.44 inference(scs_inference,[],[41,212,3])).
% 116.31/116.44 cnf(328,plain,
% 116.31/116.44 (P1(f1(f1(x3281,f1(x3282,x3283)),f1(x3281,f1(x3282,x3283))))),
% 116.31/116.44 inference(scs_inference,[],[41,325,3])).
% 116.31/116.44 cnf(331,plain,
% 116.31/116.44 (P1(f1(x3311,f1(x3312,f1(x3313,f1(x3314,x3313)))))),
% 116.31/116.44 inference(scs_inference,[],[328,186,3])).
% 116.31/116.44 cnf(335,plain,
% 116.31/116.44 ($false),
% 116.31/116.44 inference(scs_inference,[],[41,331,8,3]),
% 116.31/116.44 ['proof']).
% 116.31/116.44 % SZS output end Proof
% 116.31/116.44 % Total time :115.924329s
%------------------------------------------------------------------------------