TSTP Solution File: LCL077-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL077-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n001.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 06:47:52 EDT 2023
% Result : Unsatisfiable 2.02s 2.12s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL077-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 06:02:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 2.02/2.11 %-------------------------------------------
% 2.02/2.11 % File :CSE---1.6
% 2.02/2.11 % Problem :theBenchmark
% 2.02/2.11 % Transform :cnf
% 2.02/2.11 % Format :tptp:raw
% 2.02/2.11 % Command :java -jar mcs_scs.jar %d %s
% 2.02/2.11
% 2.02/2.11 % Result :Theorem 1.480000s
% 2.02/2.11 % Output :CNFRefutation 1.480000s
% 2.02/2.11 %-------------------------------------------
% 2.02/2.11 %--------------------------------------------------------------------------
% 2.02/2.11 % File : LCL077-2 : TPTP v8.1.2. Released v1.0.0.
% 2.02/2.11 % Domain : Logic Calculi (Implication/Negation 2 valued sentential)
% 2.02/2.11 % Problem : CN-39 depends on the Church system
% 2.02/2.11 % Version : [ANL] axioms : Augmented.
% 2.02/2.11 % English : Axiomatisations of the Implication/Negation 2 valued
% 2.02/2.11 % sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz,
% 2.02/2.11 % {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege,
% 2.02/2.11 % {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18,
% 2.02/2.11 % CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz,
% 2.02/2.11 % {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom.
% 2.02/2.11 % Show that CN-39 depends on the Church system.
% 2.02/2.11
% 2.02/2.11 % Refs : [Mor84] Morgan (1984), Logic Problems
% 2.02/2.11 % Source : [ANL]
% 2.02/2.11 % Names : morgan.two.ver1.in [ANL]
% 2.02/2.11
% 2.02/2.11 % Status : Unsatisfiable
% 2.02/2.11 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.00 v2.1.0, 0.00 v2.0.0
% 2.02/2.11 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 3 RR)
% 2.02/2.12 % Number of literals : 10 ( 0 equ; 5 neg)
% 2.02/2.12 % Maximal clause size : 3 ( 1 avg)
% 2.02/2.12 % Maximal term depth : 4 ( 2 avg)
% 2.02/2.12 % Number of predicates : 1 ( 1 usr; 0 prp; 1-1 aty)
% 2.02/2.12 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 2.02/2.12 % Number of variables : 12 ( 1 sgn)
% 2.02/2.12 % SPC : CNF_UNS_RFO_NEQ_HRN
% 2.02/2.12
% 2.02/2.12 % Comments : Transitivity of implies is supplied as an axiom
% 2.02/2.12 %--------------------------------------------------------------------------
% 2.02/2.12 cnf(condensed_detachment,axiom,
% 2.02/2.12 ( ~ is_a_theorem(implies(X,Y))
% 2.02/2.12 | ~ is_a_theorem(X)
% 2.02/2.12 | is_a_theorem(Y) ) ).
% 2.02/2.12
% 2.02/2.12 cnf(cn_18,axiom,
% 2.02/2.12 is_a_theorem(implies(X,implies(Y,X))) ).
% 2.02/2.12
% 2.02/2.12 cnf(cn_35,axiom,
% 2.02/2.12 is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ).
% 2.02/2.12
% 2.02/2.12 cnf(cn_49,axiom,
% 2.02/2.12 is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
% 2.02/2.12
% 2.02/2.12 cnf(transitivity,axiom,
% 2.02/2.12 ( ~ is_a_theorem(implies(X1,X2))
% 2.02/2.12 | ~ is_a_theorem(implies(X2,X3))
% 2.02/2.12 | is_a_theorem(implies(X1,X3)) ) ).
% 2.02/2.12
% 2.02/2.12 cnf(prove_cn_39,negated_conjecture,
% 2.02/2.12 ~ is_a_theorem(implies(not(not(a)),a)) ).
% 2.02/2.12
% 2.02/2.12 %--------------------------------------------------------------------------
% 2.02/2.12 %-------------------------------------------
% 2.02/2.12 % Proof found
% 2.02/2.12 % SZS status Theorem for theBenchmark
% 2.02/2.12 % SZS output start Proof
% 2.02/2.12 %ClaNum:6(EqnAxiom:0)
% 2.02/2.12 %VarNum:24(SingletonVarNum:12)
% 2.02/2.12 %MaxLitNum:3
% 2.02/2.12 %MaxfuncDepth:3
% 2.02/2.12 %SharedTerms:5
% 2.02/2.12 %goalClause: 4
% 2.02/2.12 %singleGoalClaCount:1
% 2.02/2.12 [4]~P1(f1(f3(f3(a2)),a2))
% 2.02/2.12 [1]P1(f1(x11,f1(x12,x11)))
% 2.02/2.12 [2]P1(f1(f1(f3(x21),f3(x22)),f1(x22,x21)))
% 2.02/2.12 [3]P1(f1(f1(x31,f1(x32,x33)),f1(f1(x31,x32),f1(x31,x33))))
% 2.02/2.12 [5]P1(x51)+~P1(x52)+~P1(f1(x52,x51))
% 2.02/2.12 [6]~P1(f1(x61,x63))+P1(f1(x61,x62))+~P1(f1(x63,x62))
% 2.02/2.12 %EqnAxiom
% 2.02/2.12
% 2.02/2.12 %-------------------------------------------
% 2.02/2.12 cnf(7,plain,
% 2.02/2.12 (~P1(a2)),
% 2.02/2.12 inference(scs_inference,[],[4,1,5])).
% 2.02/2.12 cnf(8,plain,
% 2.02/2.12 (P1(f1(x81,f1(x82,x81)))),
% 2.02/2.12 inference(rename_variables,[],[1])).
% 2.02/2.12 cnf(9,plain,
% 2.02/2.12 (P1(f1(f1(f3(x91),f3(x92)),f1(x93,f1(x92,x91))))),
% 2.02/2.12 inference(scs_inference,[],[4,1,8,2,5,6])).
% 2.02/2.12 cnf(12,plain,
% 2.02/2.12 (P1(f1(f1(f3(f1(x121,x122)),f3(x123)),f1(f1(x123,x121),f1(x123,x122))))),
% 2.02/2.12 inference(scs_inference,[],[3,2,6])).
% 2.02/2.12 cnf(17,plain,
% 2.02/2.12 (~P1(f1(f1(f1(x171,x172),f1(x171,x171)),a2))),
% 2.02/2.12 inference(scs_inference,[],[1,7,3,5,6])).
% 2.02/2.12 cnf(20,plain,
% 2.02/2.12 (P1(f1(f3(x201),f1(x201,x202)))),
% 2.02/2.12 inference(scs_inference,[],[1,2,6])).
% 2.02/2.12 cnf(29,plain,
% 2.02/2.12 (P1(f1(f3(x291),f1(x291,x292)))),
% 2.02/2.12 inference(rename_variables,[],[20])).
% 2.02/2.12 cnf(31,plain,
% 2.02/2.12 (~P1(f1(f1(f3(a2),x311),a2))),
% 2.02/2.12 inference(scs_inference,[],[20,29,17,4,5,6])).
% 2.02/2.12 cnf(54,plain,
% 2.02/2.12 (P1(f1(f1(f3(x541),x541),f1(f3(x541),x542)))),
% 2.02/2.12 inference(scs_inference,[],[20,3,5])).
% 2.02/2.12 cnf(58,plain,
% 2.02/2.12 (~P1(f1(f1(x581,a2),a2))),
% 2.02/2.12 inference(scs_inference,[],[20,31,3,2,5,6])).
% 2.02/2.12 cnf(62,plain,
% 2.02/2.12 (~P1(f1(f3(f3(a2)),f3(a2)))),
% 2.02/2.12 inference(scs_inference,[],[54,4,5])).
% 2.02/2.12 cnf(68,plain,
% 2.02/2.12 (P1(f1(f3(x681),f1(x682,f1(x681,x683))))),
% 2.02/2.12 inference(scs_inference,[],[20,1,6])).
% 2.02/2.12 cnf(73,plain,
% 2.02/2.12 (P1(f1(f1(f3(x731),x732),f1(f3(x731),f1(x731,x733))))),
% 2.02/2.12 inference(scs_inference,[],[68,3,5])).
% 2.02/2.12 cnf(87,plain,
% 2.02/2.12 (~P1(f1(f1(f3(x871),f1(x871,x872)),f1(f3(f3(a2)),f3(a2))))),
% 2.02/2.12 inference(scs_inference,[],[20,62,5])).
% 2.02/2.12 cnf(89,plain,
% 2.02/2.12 (P1(f1(f3(f3(x891)),f1(x892,x891)))),
% 2.02/2.12 inference(scs_inference,[],[20,62,2,5,6])).
% 2.02/2.12 cnf(113,plain,
% 2.02/2.12 (~P1(f1(f3(f3(a2)),f1(f1(f3(a2),x1131),f3(a2))))),
% 2.02/2.12 inference(scs_inference,[],[87,3,5])).
% 2.02/2.12 cnf(128,plain,
% 2.02/2.12 (~P1(f1(f1(x1281,a2),f1(f1(f3(a2),x1282),f3(a2))))),
% 2.02/2.12 inference(scs_inference,[],[113,89,6])).
% 2.02/2.12 cnf(139,plain,
% 2.02/2.12 (P1(f1(f1(f3(f1(x1391,x1392)),f1(x1391,x1392)),f1(f1(x1393,x1391),f1(x1393,x1392))))),
% 2.02/2.12 inference(scs_inference,[],[54,12,6])).
% 2.02/2.12 cnf(155,plain,
% 2.02/2.12 (P1(f1(f1(f3(x1551),x1551),f1(x1552,f1(x1553,x1551))))),
% 2.02/2.12 inference(scs_inference,[],[54,9,6])).
% 2.02/2.12 cnf(163,plain,
% 2.02/2.12 (~P1(f1(f1(f3(a2),x1631),f1(a2,f3(a2))))),
% 2.02/2.12 inference(scs_inference,[],[62,128,68,3,6,5])).
% 2.02/2.12 cnf(168,plain,
% 2.02/2.12 (~P1(f1(f1(f3(f3(x1681)),f1(x1682,x1681)),f1(f1(x1683,a2),a2)))),
% 2.02/2.12 inference(scs_inference,[],[58,89,5])).
% 2.02/2.12 cnf(179,plain,
% 2.02/2.12 (P1(f1(f3(x1791),f1(f1(x1792,x1791),f1(x1792,x1793))))),
% 2.02/2.12 inference(scs_inference,[],[68,139,6])).
% 2.02/2.12 cnf(206,plain,
% 2.02/2.12 (~P1(f3(a2))),
% 2.02/2.12 inference(scs_inference,[],[68,163,5])).
% 2.02/2.12 cnf(217,plain,
% 2.02/2.12 (P1(f1(f1(f3(x2171),x2171),f1(f3(x2172),f1(x2172,x2173))))),
% 2.02/2.12 inference(scs_inference,[],[73,155,206,5,6])).
% 2.02/2.12 cnf(232,plain,
% 2.02/2.12 (P1(f1(x2321,f1(x2322,f1(x2323,x2321))))),
% 2.02/2.12 inference(scs_inference,[],[155,1,6])).
% 2.02/2.12 cnf(244,plain,
% 2.02/2.12 (P1(f1(x2441,f1(f3(x2442),f1(x2442,x2443))))),
% 2.02/2.12 inference(scs_inference,[],[232,217,6])).
% 2.02/2.12 cnf(264,plain,
% 2.02/2.12 (P1(f1(f1(x2641,f3(x2642)),f1(x2641,f1(x2642,x2643))))),
% 2.02/2.12 inference(scs_inference,[],[244,139,5])).
% 2.02/2.12 cnf(309,plain,
% 2.02/2.12 (P1(f1(f1(f3(f1(x3091,x3092)),f3(x3091)),f1(f1(x3093,x3091),f1(x3093,x3092))))),
% 2.02/2.12 inference(scs_inference,[],[139,264,6])).
% 2.02/2.12 cnf(331,plain,
% 2.02/2.12 (~P1(f1(f1(f3(x3311),f1(x3311,x3312)),f1(f1(x3313,a2),a2)))),
% 2.02/2.12 inference(scs_inference,[],[168,244,6])).
% 2.02/2.12 cnf(373,plain,
% 2.02/2.12 (~P1(f1(f3(f1(a2,f3(a2))),f3(a2)))),
% 2.02/2.12 inference(scs_inference,[],[309,128,5])).
% 2.02/2.12 cnf(411,plain,
% 2.02/2.12 (P1(f1(f1(x4111,x4112),f1(x4111,f1(x4113,x4111))))),
% 2.02/2.12 inference(scs_inference,[],[232,373,179,3,6,5])).
% 2.02/2.12 cnf(433,plain,
% 2.02/2.12 (P1(f1(f1(x4331,x4332),f1(f1(x4331,x4333),f1(x4331,x4331))))),
% 2.02/2.12 inference(scs_inference,[],[411,3,6])).
% 2.02/2.12 cnf(447,plain,
% 2.02/2.12 (P1(f1(f1(f1(x4471,x4472),x4473),f1(f1(x4471,x4472),f1(x4471,x4472))))),
% 2.02/2.12 inference(scs_inference,[],[433,411,5])).
% 2.02/2.12 cnf(465,plain,
% 2.02/2.12 (P1(f1(f1(x4651,x4652),f1(x4651,x4652)))),
% 2.02/2.12 inference(scs_inference,[],[433,447,5])).
% 2.02/2.12 cnf(505,plain,
% 2.02/2.12 (P1(f1(f1(f1(x5051,x5052),x5051),f1(f1(x5051,x5052),x5052)))),
% 2.02/2.12 inference(scs_inference,[],[465,3,5])).
% 2.02/2.12 cnf(509,plain,
% 2.02/2.12 ($false),
% 2.02/2.12 inference(scs_inference,[],[505,331,232,6]),
% 2.02/2.12 ['proof']).
% 2.02/2.13 % SZS output end Proof
% 2.02/2.13 % Total time :1.480000s
%------------------------------------------------------------------------------