TSTP Solution File: LCL087-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL087-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:47:55 EDT 2023
% Result : Unsatisfiable 120.84s 121.33s
% Output : CNFRefutation 120.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL087-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Thu Aug 24 23:39:13 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 120.75/121.26 %-------------------------------------------
% 120.75/121.26 % File :CSE---1.6
% 120.75/121.26 % Problem :theBenchmark
% 120.75/121.26 % Transform :cnf
% 120.75/121.26 % Format :tptp:raw
% 120.75/121.26 % Command :java -jar mcs_scs.jar %d %s
% 120.75/121.26
% 120.75/121.26 % Result :Theorem 120.220000s
% 120.75/121.26 % Output :CNFRefutation 120.220000s
% 120.75/121.26 %-------------------------------------------
% 120.84/121.33 %--------------------------------------------------------------------------
% 120.84/121.33 % File : LCL087-1 : TPTP v8.1.2. Released v1.0.0.
% 120.84/121.33 % Domain : Logic Calculi (Implicational propositional)
% 120.84/121.33 % Problem : IC-2 depends on the 4th Lukasiewicz axiom
% 120.84/121.33 % Version : [TPTP] axioms.
% 120.84/121.33 % English : Axiomatisations of the Implicational propositional calculus
% 120.84/121.33 % are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
% 120.84/121.33 % axioms. Show that IC-2 depends on the fourth Lukasiewicz
% 120.84/121.33 % axiom.
% 120.84/121.33
% 120.84/121.33 % Refs : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
% 120.84/121.33 % : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
% 120.84/121.33 % Source : [TPTP]
% 120.84/121.33 % Names :
% 120.84/121.33
% 120.84/121.33 % Status : Unsatisfiable
% 120.84/121.33 % 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
% 120.84/121.33 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 2 RR)
% 120.84/121.33 % Number of literals : 5 ( 0 equ; 3 neg)
% 120.84/121.33 % Maximal clause size : 3 ( 1 avg)
% 120.84/121.33 % Maximal term depth : 5 ( 2 avg)
% 120.84/121.33 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 120.84/121.33 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% 120.84/121.33 % Number of variables : 7 ( 2 sgn)
% 120.84/121.33 % SPC : CNF_UNS_RFO_NEQ_HRN
% 120.84/121.33
% 120.84/121.33 % Comments :
% 120.84/121.33 %--------------------------------------------------------------------------
% 120.84/121.33 cnf(condensed_detachment,axiom,
% 120.84/121.33 ( ~ is_a_theorem(implies(X,Y))
% 120.84/121.33 | ~ is_a_theorem(X)
% 120.84/121.33 | is_a_theorem(Y) ) ).
% 120.84/121.33
% 120.84/121.33 cnf(ic_JLukasiewicz_4,axiom,
% 120.84/121.33 is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))) ).
% 120.84/121.33
% 120.84/121.33 cnf(prove_ic_2,negated_conjecture,
% 120.84/121.33 ~ is_a_theorem(implies(a,implies(b,a))) ).
% 120.84/121.33
% 120.84/121.33 %--------------------------------------------------------------------------
% 120.84/121.33 %-------------------------------------------
% 120.84/121.33 % Proof found
% 120.84/121.33 % SZS status Theorem for theBenchmark
% 120.84/121.33 % SZS output start Proof
% 120.84/121.40 %ClaNum:3(EqnAxiom:0)
% 120.84/121.40 %VarNum:13(SingletonVarNum:7)
% 120.84/121.40 %MaxLitNum:3
% 120.84/121.40 %MaxfuncDepth:4
% 120.84/121.40 %SharedTerms:5
% 120.84/121.40 %goalClause: 2
% 120.84/121.40 %singleGoalClaCount:1
% 120.84/121.40 [2]~P1(f1(a2,f1(a3,a2)))
% 120.84/121.40 [1]P1(f1(f1(f1(x11,x12),f1(x13,x14)),f1(x15,f1(f1(x14,x11),f1(x13,x11)))))
% 120.84/121.40 [3]P1(x31)+~P1(x32)+~P1(f1(x32,x31))
% 120.84/121.40 %EqnAxiom
% 120.84/121.40
% 120.84/121.40 %-------------------------------------------
% 120.85/121.47 cnf(4,plain,
% 120.85/121.47 (P1(f1(x41,f1(f1(x42,x43),f1(x44,x43))))+~P1(f1(f1(x43,x45),f1(x44,x42)))),
% 120.85/121.47 inference(scs_inference,[],[1,3])).
% 120.85/121.47 cnf(5,plain,
% 120.85/121.47 (P1(f1(x51,f1(f1(f1(f1(x52,x53),f1(x54,x53)),f1(x53,x55)),f1(x56,f1(x53,x55)))))),
% 120.85/121.47 inference(scs_inference,[],[1,4])).
% 120.85/121.47 cnf(6,plain,
% 120.85/121.47 (P1(f1(f1(f1(f1(x61,x62),f1(x63,x62)),f1(x62,x64)),f1(x65,f1(x62,x64))))),
% 120.85/121.47 inference(scs_inference,[],[1,4,3])).
% 120.85/121.47 cnf(10,plain,
% 120.85/121.47 (P1(f1(x101,f1(f1(f1(x102,f1(x103,x104)),x105),f1(f1(f1(f1(x106,x103),f1(x107,x103)),f1(x103,x104)),x105))))),
% 120.85/121.47 inference(scs_inference,[],[1,5,3])).
% 120.85/121.47 cnf(14,plain,
% 120.85/121.47 (P1(f1(f1(f1(x141,f1(x142,x143)),x144),f1(f1(f1(f1(x145,x142),f1(x146,x142)),f1(x142,x143)),x144)))),
% 120.85/121.47 inference(scs_inference,[],[1,10,3])).
% 120.85/121.47 cnf(20,plain,
% 120.85/121.47 (P1(f1(f1(f1(f1(x201,x202),f1(x203,x202)),f1(x202,x204)),f1(x205,f1(f1(x204,x206),f1(x202,x206)))))),
% 120.85/121.47 inference(scs_inference,[],[1,14,3])).
% 120.85/121.47 cnf(23,plain,
% 120.85/121.47 (P1(f1(x231,f1(f1(f1(f1(x232,x233),f1(x234,x233)),f1(f1(x235,x234),f1(x236,x234))),f1(x237,f1(f1(x235,x234),f1(x236,x234))))))),
% 120.85/121.47 inference(scs_inference,[],[1,20,3])).
% 120.85/121.47 cnf(26,plain,
% 120.85/121.47 (P1(f1(f1(f1(f1(x261,x262),f1(x263,x262)),f1(f1(x264,x263),f1(x265,x263))),f1(x266,f1(f1(x264,x263),f1(x265,x263)))))),
% 120.85/121.47 inference(scs_inference,[],[1,23,3])).
% 120.85/121.47 cnf(29,plain,
% 120.85/121.47 (P1(f1(x291,f1(f1(f1(f1(x292,x293),f1(x294,x293)),f1(f1(x295,x296),f1(x293,x296))),f1(x297,f1(f1(x295,x296),f1(x293,x296))))))),
% 120.85/121.47 inference(scs_inference,[],[1,26,3])).
% 120.85/121.47 cnf(32,plain,
% 120.85/121.47 (P1(f1(f1(f1(f1(x321,x322),f1(x323,x322)),f1(f1(x324,x325),f1(x322,x325))),f1(x326,f1(f1(x324,x325),f1(x322,x325)))))),
% 120.85/121.47 inference(scs_inference,[],[1,29,3])).
% 120.85/121.47 cnf(35,plain,
% 120.85/121.47 (P1(f1(x351,f1(f1(x352,f1(x353,x353)),f1(f1(x353,x353),f1(x353,x353)))))),
% 120.85/121.47 inference(scs_inference,[],[32,26,3])).
% 120.85/121.47 cnf(39,plain,
% 120.85/121.47 (P1(f1(f1(x391,f1(x392,x392)),f1(f1(x392,x392),f1(x392,x392))))),
% 120.85/121.47 inference(scs_inference,[],[5,35,3])).
% 120.85/121.47 cnf(42,plain,
% 120.85/121.47 (P1(f1(f1(f1(x421,x422),f1(x421,x422)),f1(f1(x421,x422),f1(x421,x422))))),
% 120.85/121.47 inference(scs_inference,[],[6,39,3])).
% 120.85/121.47 cnf(46,plain,
% 120.85/121.47 (P1(f1(x461,f1(f1(x462,x462),f1(x462,x462))))),
% 120.85/121.47 inference(scs_inference,[],[42,32,3])).
% 120.85/121.47 cnf(53,plain,
% 120.85/121.47 (P1(f1(x531,f1(f1(f1(x532,f1(x533,x532)),x534),f1(f1(x533,x532),x534))))),
% 120.85/121.47 inference(scs_inference,[],[6,20,3])).
% 120.85/121.47 cnf(57,plain,
% 120.85/121.47 (P1(f1(f1(f1(x571,f1(x572,x571)),x573),f1(f1(x572,x571),x573)))),
% 120.85/121.47 inference(scs_inference,[],[6,53,3])).
% 120.85/121.47 cnf(66,plain,
% 120.85/121.47 (P1(f1(x661,f1(f1(f1(x662,x663),f1(f1(x664,x662),f1(x665,x662))),f1(x666,f1(f1(x664,x662),f1(x665,x662))))))),
% 120.85/121.47 inference(scs_inference,[],[6,1,3])).
% 120.85/121.47 cnf(69,plain,
% 120.85/121.47 (P1(f1(f1(f1(x691,x692),f1(f1(x693,x691),f1(x694,x691))),f1(x695,f1(f1(x693,x691),f1(x694,x691)))))),
% 120.85/121.47 inference(scs_inference,[],[6,66,3])).
% 120.85/121.47 cnf(85,plain,
% 120.85/121.47 (P1(f1(x851,f1(f1(f1(f1(x852,x852),f1(x852,x852)),x853),f1(f1(x854,f1(x852,x852)),x853))))),
% 120.85/121.47 inference(scs_inference,[],[35,20,3])).
% 120.85/121.47 cnf(89,plain,
% 120.85/121.47 (P1(f1(f1(f1(f1(x891,x891),f1(x891,x891)),x892),f1(f1(x893,f1(x891,x891)),x892)))),
% 120.85/121.47 inference(scs_inference,[],[35,85,3])).
% 120.85/121.47 cnf(92,plain,
% 120.85/121.47 (P1(f1(x921,f1(f1(f1(x922,x922),x923),f1(f1(x922,x922),x923))))),
% 120.85/121.47 inference(scs_inference,[],[46,20,3])).
% 120.85/121.47 cnf(96,plain,
% 120.85/121.47 (P1(f1(f1(f1(x961,x961),x962),f1(f1(x961,x961),x962)))),
% 120.85/121.47 inference(scs_inference,[],[46,92,3])).
% 120.85/121.47 cnf(99,plain,
% 120.85/121.47 (P1(f1(x991,f1(f1(f1(x992,f1(x993,x994)),x995),f1(f1(x993,x994),x995))))),
% 120.85/121.47 inference(scs_inference,[],[57,20,3])).
% 120.85/121.47 cnf(103,plain,
% 120.85/121.47 (P1(f1(f1(f1(x1031,f1(x1032,x1033)),x1034),f1(f1(x1032,x1033),x1034)))),
% 120.85/121.47 inference(scs_inference,[],[96,99,3])).
% 120.85/121.47 cnf(109,plain,
% 120.85/121.47 (P1(f1(x1091,f1(f1(x1092,f1(f1(x1093,x1093),f1(x1093,x1093))),f1(f1(x1094,f1(x1093,x1093)),f1(f1(x1093,x1093),f1(x1093,x1093))))))),
% 120.85/121.47 inference(scs_inference,[],[89,1,3])).
% 120.85/121.47 cnf(115,plain,
% 120.85/121.47 (P1(f1(x1151,f1(f1(x1152,f1(x1153,x1154)),f1(f1(x1153,x1154),f1(x1153,x1154)))))),
% 120.85/121.47 inference(scs_inference,[],[69,26,3])).
% 120.85/121.47 cnf(119,plain,
% 120.85/121.47 (P1(f1(f1(x1191,f1(x1192,x1193)),f1(f1(x1192,x1193),f1(x1192,x1193))))),
% 120.85/121.47 inference(scs_inference,[],[115,109,3])).
% 120.85/121.47 cnf(125,plain,
% 120.85/121.47 (P1(f1(x1251,f1(f1(x1252,x1253),f1(x1252,x1253))))),
% 120.85/121.47 inference(scs_inference,[],[119,69,3])).
% 120.85/121.47 cnf(129,plain,
% 120.85/121.47 (P1(f1(f1(x1291,x1292),f1(x1291,x1292)))),
% 120.85/121.47 inference(scs_inference,[],[85,125,3])).
% 120.85/121.47 cnf(139,plain,
% 120.85/121.47 (P1(f1(x1391,f1(f1(x1392,f1(x1393,f1(x1394,x1395))),f1(f1(x1394,x1395),f1(x1393,f1(x1394,x1395))))))),
% 120.85/121.47 inference(scs_inference,[],[103,1,3])).
% 120.85/121.47 cnf(142,plain,
% 120.85/121.47 (P1(f1(f1(x1421,f1(x1422,f1(x1423,x1424))),f1(f1(x1423,x1424),f1(x1422,f1(x1423,x1424)))))),
% 120.85/121.47 inference(scs_inference,[],[103,139,3])).
% 120.85/121.47 cnf(158,plain,
% 120.85/121.47 (P1(f1(f1(x1581,x1582),f1(x1583,f1(x1581,x1582))))),
% 120.85/121.47 inference(scs_inference,[],[129,142,3])).
% 120.85/121.47 cnf(195,plain,
% 120.85/121.47 (P1(f1(x1951,f1(f1(f1(x1952,x1953),x1952),f1(x1954,x1952))))),
% 120.85/121.47 inference(scs_inference,[],[158,1,3])).
% 120.85/121.47 cnf(198,plain,
% 120.85/121.47 (P1(f1(f1(f1(x1981,x1982),x1981),f1(x1983,x1981)))),
% 120.85/121.47 inference(scs_inference,[],[158,195,3])).
% 120.85/121.47 cnf(269,plain,
% 120.85/121.47 (P1(f1(x2691,f1(f1(f1(x2692,x2693),x2694),f1(f1(f1(x2693,x2695),x2693),x2694))))),
% 120.85/121.47 inference(scs_inference,[],[195,20,3])).
% 120.85/121.47 cnf(273,plain,
% 120.85/121.47 (P1(f1(f1(f1(x2731,x2732),x2733),f1(f1(f1(x2732,x2734),x2732),x2733)))),
% 120.85/121.47 inference(scs_inference,[],[195,269,3])).
% 120.85/121.47 cnf(276,plain,
% 120.85/121.47 (P1(f1(x2761,f1(f1(f1(x2762,x2763),x2764),f1(x2763,x2764))))),
% 120.85/121.47 inference(scs_inference,[],[198,20,3])).
% 120.85/121.47 cnf(280,plain,
% 120.85/121.47 (P1(f1(f1(f1(x2801,x2802),x2803),f1(x2802,x2803)))),
% 120.85/121.47 inference(scs_inference,[],[276,273,3])).
% 120.85/121.47 cnf(297,plain,
% 120.85/121.47 ($false),
% 120.85/121.47 inference(scs_inference,[],[280,129,2,3]),
% 120.85/121.47 ['proof']).
% 120.85/121.47 % SZS output end Proof
% 120.85/121.47 % Total time :120.220000s
%------------------------------------------------------------------------------