%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : CAT010-4 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 : Mon Jun 24 04:40:13 EDT 2024
% Result : Unsatisfiable 32.38s 32.48s
% Output : CNFRefutation 32.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT010-4 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n008.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Jun 18 12:13:23 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.49/0.56 start to proof:theBenchmark
% 32.38/32.47 %-------------------------------------------
% 32.38/32.47 % File :CSE---1.7
% 32.38/32.47 % Problem :theBenchmark
% 32.38/32.47 % Transform :cnf
% 32.38/32.47 % Format :tptp:raw
% 32.38/32.47 % Command :java -jar mcs_scs.jar %d %s
% 32.38/32.47
% 32.38/32.47 % Result :Theorem 31.860000s
% 32.38/32.47 % Output :CNFRefutation 31.860000s
% 32.38/32.47 %-------------------------------------------
% 32.38/32.48 %--------------------------------------------------------------------------
% 32.38/32.48 % File : CAT010-4 : TPTP v8.2.0. Released v1.0.0.
% 32.38/32.48 % Domain : Category Theory
% 32.38/32.48 % Problem : If xy is defined, then codomain(xy) = codomain(x)
% 32.38/32.48 % Version : [Sco79] axioms : Reduced > Complete.
% 32.38/32.48 % English :
% 32.38/32.48
% 32.38/32.48 % Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% 32.38/32.48 % Source : [TPTP]
% 32.38/32.48 % Names :
% 32.38/32.48
% 32.38/32.48 % Status : Unsatisfiable
% 32.38/32.48 % Rating : 0.00 v6.0.0, 0.22 v5.5.0, 0.25 v5.4.0, 0.20 v5.3.0, 0.25 v5.1.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.4.0, 0.33 v3.3.0, 0.29 v3.2.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.43 v2.5.0, 0.20 v2.4.0, 0.17 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.60 v2.0.0
% 32.38/32.48 % Syntax : Number of clauses : 13 ( 5 unt; 0 nHn; 10 RR)
% 32.38/32.48 % Number of literals : 23 ( 8 equ; 11 neg)
% 32.38/32.48 % Maximal clause size : 3 ( 1 avg)
% 32.38/32.48 % Maximal term depth : 3 ( 1 avg)
% 32.38/32.48 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 32.38/32.48 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 32.38/32.48 % Number of variables : 19 ( 2 sgn)
% 32.38/32.48 % SPC : CNF_UNS_RFO_SEQ_HRN
% 32.38/32.48
% 32.38/32.48 % Comments : The dependent axioms have been removed.
% 32.38/32.48 %--------------------------------------------------------------------------
% 32.38/32.48 %----Include Scott's axioms for category theory
% 32.38/32.48 include('Axioms/CAT004-0.ax').
% 32.38/32.48 %--------------------------------------------------------------------------
% 32.38/32.48 cnf(ab_exists,hypothesis,
% 32.38/32.48 there_exists(compose(a,b)) ).
% 32.38/32.48
% 32.38/32.48 cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
% 32.38/32.48 codomain(compose(a,b)) != codomain(a) ).
% 32.38/32.48
% 32.38/32.48 %--------------------------------------------------------------------------
% 32.38/32.48 %-------------------------------------------
% 32.38/32.48 % Proof found
% 32.38/32.48 % SZS status Theorem for theBenchmark
% 32.38/32.48 % SZS output start Proof
% 32.38/32.49 %ClaNum:23(EqnAxiom:10)
% 32.38/32.49 %VarNum:40(SingletonVarNum:19)
% 32.38/32.49 %MaxLitNum:3
% 32.38/32.49 %MaxfuncDepth:2
% 32.38/32.49 %SharedTerms:7
% 32.38/32.49 %goalClause: 15
% 32.38/32.49 %singleGoalClaCount:1
% 32.38/32.49 [13]P1(f2(a4,a5))
% 32.38/32.49 [15]~E(f3(f2(a4,a5)),f3(a4))
% 32.38/32.49 [11]E(f2(x111,f1(x111)),x111)
% 32.38/32.49 [12]E(f2(f3(x121),x121),x121)
% 32.38/32.49 [14]E(f2(f2(x141,x142),x143),f2(x141,f2(x142,x143)))
% 32.38/32.49 [16]P1(x161)+~P1(f1(x161))
% 32.38/32.49 [17]P1(x171)+~P1(f3(x171))
% 32.38/32.49 [18]~P2(x181,x182)+E(x181,x182)
% 32.38/32.49 [20]P1(x201)+~P2(x201,x202)
% 32.38/32.49 [21]E(f3(x211),f1(x212))+~P1(f2(x212,x211))
% 32.38/32.49 [22]P1(f1(x221))+~P1(f2(x221,x222))
% 32.38/32.49 [19]~E(x191,x192)+~P1(x191)+P2(x191,x192)
% 32.38/32.49 [23]~E(f3(x232),f1(x231))+~P1(f1(x231))+P1(f2(x231,x232))
% 32.38/32.49 %EqnAxiom
% 32.38/32.49 [1]E(x11,x11)
% 32.38/32.49 [2]E(x22,x21)+~E(x21,x22)
% 32.38/32.49 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 32.38/32.49 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 32.38/32.49 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 32.38/32.49 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 32.38/32.49 [7]~E(x71,x72)+E(f3(x71),f3(x72))
% 32.38/32.49 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 32.38/32.49 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93)
% 32.38/32.49 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101)
% 32.38/32.49
% 32.38/32.49 %-------------------------------------------
% 32.38/32.50 cnf(24,plain,
% 32.38/32.50 (~P1(x241)+P2(x241,x241)),
% 32.38/32.50 inference(equality_inference,[],[19])).
% 32.38/32.50 cnf(27,plain,
% 32.38/32.50 (E(x271,f2(x271,f1(x271)))),
% 32.38/32.50 inference(scs_inference,[],[15,11,18,2])).
% 32.38/32.50 cnf(28,plain,
% 32.38/32.50 (~E(f2(a4,a5),a4)),
% 32.38/32.50 inference(scs_inference,[],[15,11,18,2,7])).
% 32.38/32.50 cnf(29,plain,
% 32.38/32.50 (E(f3(a5),f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[15,11,13,18,2,7,21])).
% 32.38/32.50 cnf(31,plain,
% 32.38/32.50 (P2(f2(a4,a5),f2(f2(a4,a5),f1(f2(a4,a5))))),
% 32.38/32.50 inference(scs_inference,[],[15,11,13,18,2,7,21,19])).
% 32.38/32.50 cnf(33,plain,
% 32.38/32.50 (~E(f3(f2(a4,a5)),f2(f3(f3(a4)),f3(a4)))),
% 32.38/32.50 inference(scs_inference,[],[15,11,12,13,18,2,7,21,19,3])).
% 32.38/32.50 cnf(36,plain,
% 32.38/32.50 (P2(f2(a4,a5),f2(a4,a5))),
% 32.38/32.50 inference(scs_inference,[],[15,11,12,13,18,2,7,21,19,3,8,10])).
% 32.38/32.50 cnf(41,plain,
% 32.38/32.50 (E(f1(a4),f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[33,29,18,2])).
% 32.38/32.50 cnf(42,plain,
% 32.38/32.50 (E(f3(a5),f2(f1(a4),f1(f1(a4))))),
% 32.38/32.50 inference(scs_inference,[],[27,33,29,18,2,3])).
% 32.38/32.50 cnf(44,plain,
% 32.38/32.50 (~P1(f3(a5))+P1(f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[27,33,29,18,2,3,8])).
% 32.38/32.50 cnf(45,plain,
% 32.38/32.50 (~P2(f3(a5),x451)+P1(f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[27,33,29,18,2,3,8,20])).
% 32.38/32.50 cnf(48,plain,
% 32.38/32.50 (~P2(f2(a4,a5),a4)),
% 32.38/32.50 inference(scs_inference,[],[28,18])).
% 32.38/32.50 cnf(50,plain,
% 32.38/32.50 (E(f2(f1(a4),f1(f1(a4))),f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[28,42,18,2])).
% 32.38/32.50 cnf(51,plain,
% 32.38/32.50 (~E(f2(f2(a4,a5),f1(f2(a4,a5))),a4)),
% 32.38/32.50 inference(scs_inference,[],[28,42,31,18,2,10])).
% 32.38/32.50 cnf(52,plain,
% 32.38/32.50 (E(f2(f3(f1(a4)),f1(a4)),f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[28,42,41,31,12,18,2,10,3])).
% 32.38/32.50 cnf(55,plain,
% 32.38/32.50 (~P2(f3(a5),x551)+P1(f2(f1(a4),f1(f1(a4))))),
% 32.38/32.50 inference(scs_inference,[],[28,42,41,31,12,18,2,10,3,8,20])).
% 32.38/32.50 cnf(60,plain,
% 32.38/32.50 (E(f3(a5),f2(f3(f1(a4)),f1(a4)))),
% 32.38/32.50 inference(scs_inference,[],[52,51,18,2])).
% 32.38/32.50 cnf(61,plain,
% 32.38/32.50 (~P1(f2(f1(a4),f1(f1(a4))))+P1(f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[50,52,51,18,2,8])).
% 32.38/32.50 cnf(67,plain,
% 32.38/32.50 (E(x671,f2(f3(x671),x671))),
% 32.38/32.50 inference(scs_inference,[],[12,2])).
% 32.38/32.50 cnf(74,plain,
% 32.38/32.50 (~P2(f1(a4),x741)+P1(f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[41,67,13,36,14,2,9,8,22,20])).
% 32.38/32.50 cnf(94,plain,
% 32.38/32.50 (E(f2(f3(a5),f1(f3(a5))),f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[11,29,3])).
% 32.38/32.50 cnf(96,plain,
% 32.38/32.50 (E(f1(a4),f2(f3(a5),f1(f3(a5))))),
% 32.38/32.50 inference(scs_inference,[],[11,29,3,2])).
% 32.38/32.50 cnf(97,plain,
% 32.38/32.50 (~P1(f2(f3(a5),f1(f3(a5))))+P1(f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[11,29,3,2,8])).
% 32.38/32.50 cnf(101,plain,
% 32.38/32.50 (P2(f1(a4),f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[13,24,22])).
% 32.38/32.50 cnf(102,plain,
% 32.38/32.50 (P1(f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[101,74])).
% 32.38/32.50 cnf(104,plain,
% 32.38/32.50 (P2(f1(a4),f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[41,101,10])).
% 32.38/32.50 cnf(105,plain,
% 32.38/32.50 (P2(f3(a5),f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[41,101,10,9])).
% 32.38/32.50 cnf(106,plain,
% 32.38/32.50 (P1(f2(f1(a4),f1(f1(a4))))),
% 32.38/32.50 inference(scs_inference,[],[41,101,10,9,55])).
% 32.38/32.50 cnf(111,plain,
% 32.38/32.50 (~P1(f1(a4))+P1(f2(f3(a5),f1(f3(a5))))),
% 32.38/32.50 inference(scs_inference,[],[11,41,96,101,10,9,55,19,8])).
% 32.38/32.50 cnf(120,plain,
% 32.38/32.50 (P1(f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[102,44])).
% 32.38/32.50 cnf(121,plain,
% 32.38/32.50 (P1(f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[105,45])).
% 32.38/32.50 cnf(122,plain,
% 32.38/32.50 (P1(f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[106,61])).
% 32.38/32.50 cnf(132,plain,
% 32.38/32.50 (P1(f2(f3(a5),f1(f3(a5))))),
% 32.38/32.50 inference(scs_inference,[],[120,111])).
% 32.38/32.50 cnf(133,plain,
% 32.38/32.50 (P1(a4)),
% 32.38/32.50 inference(scs_inference,[],[120,16])).
% 32.38/32.50 cnf(135,plain,
% 32.38/32.50 (P1(a5)),
% 32.38/32.50 inference(scs_inference,[],[102,120,16,17])).
% 32.38/32.50 cnf(142,plain,
% 32.38/32.50 (P1(f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[132,97])).
% 32.38/32.50 cnf(152,plain,
% 32.38/32.50 (P2(f3(a5),f2(f1(a4),f1(f1(a4))))),
% 32.38/32.50 inference(scs_inference,[],[42,122,19])).
% 32.38/32.50 cnf(155,plain,
% 32.38/32.50 (E(f1(x1551),f1(f2(x1551,f1(x1551))))),
% 32.38/32.50 inference(scs_inference,[],[11,4,2])).
% 32.38/32.50 cnf(158,plain,
% 32.38/32.50 (E(x1581,f2(f3(x1581),x1581))),
% 32.38/32.50 inference(rename_variables,[],[67])).
% 32.38/32.50 cnf(165,plain,
% 32.38/32.50 (P1(f2(a4,f1(a4)))),
% 32.38/32.50 inference(scs_inference,[],[60,67,158,155,121,133,104,2,19,10,9,8,16])).
% 32.38/32.50 cnf(167,plain,
% 32.38/32.50 (E(f3(f1(a4)),f1(a4))),
% 32.38/32.50 inference(scs_inference,[],[60,67,158,155,121,133,104,2,19,10,9,8,16,21])).
% 32.38/32.50 cnf(171,plain,
% 32.38/32.50 (P2(f2(a4,f1(a4)),a4)),
% 32.38/32.50 inference(scs_inference,[],[11,167,165,2,19])).
% 32.38/32.50 cnf(178,plain,
% 32.38/32.50 (~E(f1(a4),a5)),
% 32.38/32.50 inference(scs_inference,[],[11,48,67,167,165,142,2,19,10,9,8,6])).
% 32.38/32.50 cnf(179,plain,
% 32.38/32.50 (~P2(f2(a4,f1(a4)),f2(a4,a5))),
% 32.38/32.50 inference(scs_inference,[],[11,48,67,167,165,142,2,19,10,9,8,6,18])).
% 32.38/32.50 cnf(190,plain,
% 32.38/32.50 (~E(a5,f2(f3(a5),f1(f3(a5))))),
% 32.38/32.50 inference(scs_inference,[],[179,67,94,171,36,178,135,18,19,10,9,6,3])).
% 32.38/32.50 cnf(194,plain,
% 32.38/32.50 (~E(a5,f3(a5))),
% 32.38/32.50 inference(scs_inference,[],[27,190,18,3])).
% 32.38/32.50 cnf(202,plain,
% 32.38/32.50 (~E(a5,f2(f1(a4),f1(f1(a4))))),
% 32.38/32.50 inference(scs_inference,[],[50,194,18,3])).
% 32.38/32.50 cnf(297,plain,
% 32.38/32.50 (P1(f2(f3(a4),a4))),
% 32.38/32.50 inference(scs_inference,[],[120,67,16,8])).
% 32.38/32.50 cnf(300,plain,
% 32.38/32.50 (E(f1(f3(a4)),f3(a4))),
% 32.38/32.50 inference(scs_inference,[],[297,21,2])).
% 32.38/32.50 cnf(301,plain,
% 32.38/32.50 (E(f2(f3(f3(a4)),f3(a4)),f1(f3(a4)))),
% 32.38/32.50 inference(scs_inference,[],[12,297,21,2,3])).
% 32.38/32.50 cnf(309,plain,
% 32.38/32.50 (~E(f3(f2(a4,a5)),f1(f3(a4)))),
% 32.38/32.50 inference(scs_inference,[],[15,301,300,2,3])).
% 32.38/32.50 cnf(617,plain,
% 32.38/32.50 (E(f2(f3(a5),x6171),f2(f1(a4),x6171))),
% 32.38/32.50 inference(scs_inference,[],[13,21,5])).
% 32.38/32.50 cnf(618,plain,
% 32.38/32.50 (E(f2(f1(a4),x6181),f2(f3(a5),x6181))),
% 32.38/32.50 inference(scs_inference,[],[617,2])).
% 32.38/32.50 cnf(619,plain,
% 32.38/32.50 (~E(a5,f2(f3(a5),f1(f1(a4))))),
% 32.38/32.50 inference(scs_inference,[],[202,617,2,3])).
% 32.38/32.50 cnf(623,plain,
% 32.38/32.50 (~P1(f1(f2(f3(a4),f2(a4,a5))))),
% 32.38/32.50 inference(scs_inference,[],[309,21,16])).
% 32.38/32.50 cnf(632,plain,
% 32.38/32.50 (~P1(f2(f3(a4),f2(a4,a5)))),
% 32.38/32.50 inference(scs_inference,[],[27,190,618,619,623,22,20,18,3,8])).
% 32.38/32.50 cnf(1010,plain,
% 32.38/32.50 (~P2(f2(f2(f3(a4),a4),a5),x10101)),
% 32.38/32.50 inference(scs_inference,[],[632,14,8,20])).
% 32.38/32.50 cnf(1395,plain,
% 32.38/32.50 (~E(f3(a5),f2(f2(f3(a4),a4),a5))),
% 32.38/32.50 inference(scs_inference,[],[1010,152,9])).
% 32.38/32.50 cnf(1400,plain,
% 32.38/32.50 (~E(f2(a4,a5),f2(f2(f3(a4),a4),a5))),
% 32.38/32.50 inference(scs_inference,[],[1010,31,1395,18,9])).
% 32.38/32.50 cnf(1402,plain,
% 32.38/32.50 ($false),
% 32.38/32.50 inference(scs_inference,[],[67,1400,5]),
% 32.38/32.50 ['proof']).
% 32.38/32.50 % SZS output end Proof
% 32.38/32.50 % Total time :31.860000s
%------------------------------------------------------------------------------