%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : CAT002-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 04:40:07 EDT 2024
% Result : Unsatisfiable 63.41s 63.55s
% Output : CNFRefutation 63.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT002-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 12:01:24 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 63.41/63.54 %-------------------------------------------
% 63.41/63.54 % File :CSE---1.7
% 63.41/63.54 % Problem :theBenchmark
% 63.41/63.54 % Transform :cnf
% 63.41/63.54 % Format :tptp:raw
% 63.41/63.54 % Command :java -jar mcs_scs.jar %d %s
% 63.41/63.54
% 63.41/63.54 % Result :Theorem 62.890000s
% 63.41/63.54 % Output :CNFRefutation 62.890000s
% 63.41/63.54 %-------------------------------------------
% 63.41/63.55 %--------------------------------------------------------------------------
% 63.41/63.55 % File : CAT002-1 : TPTP v8.2.0. Released v1.0.0.
% 63.41/63.55 % Domain : Category Theory
% 63.41/63.55 % Problem : X and Y monomorphisms, XY well-defined => XY monomorphism
% 63.41/63.55 % Version : [Mit67] axioms.
% 63.41/63.55 % English : If x and y are monomorphisms and xy is well-defined then
% 63.41/63.55 % xy is a monomorphism.
% 63.41/63.55
% 63.41/63.55 % Refs : [Mit67] Mitchell (1967), Theory of Categories
% 63.41/63.55 % : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 63.41/63.55 % Source : [ANL]
% 63.41/63.55 % Names : C2 [MOW76]
% 63.41/63.55 % : p2.ver1.in [ANL]
% 63.41/63.55
% 63.41/63.55 % Status : Unsatisfiable
% 63.41/63.55 % Rating : 0.06 v8.2.0, 0.00 v7.5.0, 0.10 v7.4.0, 0.11 v7.3.0, 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, 0.29 v4.1.0, 0.11 v4.0.1, 0.17 v4.0.0, 0.33 v3.7.0, 0.17 v3.5.0, 0.00 v3.1.0, 0.22 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.3.0, 0.17 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 0.40 v2.0.0
% 63.41/63.55 % Syntax : Number of clauses : 24 ( 10 unt; 0 nHn; 18 RR)
% 63.41/63.55 % Number of literals : 55 ( 4 equ; 32 neg)
% 63.41/63.55 % Maximal clause size : 4 ( 2 avg)
% 63.41/63.55 % Maximal term depth : 2 ( 1 avg)
% 63.41/63.55 % Number of predicates : 4 ( 3 usr; 0 prp; 1-3 aty)
% 63.41/63.55 % Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% 63.41/63.55 % Number of variables : 58 ( 5 sgn)
% 63.41/63.55 % SPC : CNF_UNS_RFO_SEQ_HRN
% 63.41/63.55
% 63.41/63.55 % Comments :
% 63.41/63.55 %--------------------------------------------------------------------------
% 63.41/63.55 %----Include Mitchell's axioms for category theory
% 63.41/63.55 include('Axioms/CAT001-0.ax').
% 63.41/63.55 %--------------------------------------------------------------------------
% 63.41/63.55 cnf(cancellation_for_product1,hypothesis,
% 63.41/63.55 ( ~ product(a,X,W)
% 63.41/63.55 | ~ product(a,Y,W)
% 63.41/63.55 | X = Y ) ).
% 63.41/63.55
% 63.41/63.55 cnf(cancellation_for_product2,hypothesis,
% 63.41/63.55 ( ~ product(b,X,W)
% 63.41/63.55 | ~ product(b,Y,W)
% 63.41/63.55 | X = Y ) ).
% 63.41/63.55
% 63.41/63.55 cnf(ab_equals_c,hypothesis,
% 63.41/63.55 product(a,b,c) ).
% 63.41/63.55
% 63.41/63.55 cnf(ch_equals_d,hypothesis,
% 63.41/63.55 product(c,h,d) ).
% 63.41/63.55
% 63.41/63.55 cnf(cg_equals_d,hypothesis,
% 63.41/63.55 product(c,g,d) ).
% 63.41/63.55
% 63.41/63.55 cnf(prove_h_equals_g,negated_conjecture,
% 63.41/63.55 h != g ).
% 63.41/63.55
% 63.41/63.55 %--------------------------------------------------------------------------
% 63.41/63.55 %-------------------------------------------
% 63.41/63.55 % Proof found
% 63.41/63.55 % SZS status Theorem for theBenchmark
% 63.41/63.55 % SZS output start Proof
% 63.41/63.56 %ClaNum:37(EqnAxiom:13)
% 63.41/63.56 %VarNum:120(SingletonVarNum:58)
% 63.41/63.56 %MaxLitNum:4
% 63.41/63.56 %MaxfuncDepth:1
% 63.41/63.56 %SharedTerms:10
% 63.41/63.56 %goalClause: 23
% 63.41/63.56 %singleGoalClaCount:1
% 63.41/63.56 [18]P3(a3,a4,a5)
% 63.41/63.56 [19]P3(a5,a8,a6)
% 63.41/63.56 [20]P3(a5,a9,a6)
% 63.41/63.56 [23]~E(a9,a8)
% 63.41/63.56 [14]P1(f1(x141))
% 63.41/63.56 [15]P1(f2(x151))
% 63.41/63.56 [16]P2(x161,f1(x161))
% 63.41/63.56 [17]P2(f2(x171),x171)
% 63.41/63.56 [21]P3(x211,f1(x211),x211)
% 63.41/63.56 [22]P3(f2(x221),x221,x221)
% 63.41/63.56 [28]~P2(x281,x282)+P3(x281,x282,f7(x281,x282))
% 63.41/63.56 [27]P2(x271,x272)+~P3(x271,x272,x273)
% 63.41/63.56 [25]~P1(x251)+~P2(x251,x252)+P3(x251,x252,x252)
% 63.41/63.56 [26]~P1(x262)+~P2(x261,x262)+P3(x261,x262,x261)
% 63.41/63.56 [31]E(x311,x312)+~P3(a3,x311,x313)+~P3(a3,x312,x313)
% 63.41/63.56 [32]E(x321,x322)+~P3(a4,x321,x323)+~P3(a4,x322,x323)
% 63.41/63.56 [29]P2(x291,x292)+~P3(x292,x294,x293)+~P2(x291,x293)
% 63.41/63.56 [30]P2(x301,x302)+~P3(x304,x301,x303)+~P2(x303,x302)
% 63.41/63.56 [33]~P3(x333,x334,x331)+E(x331,x332)+~P3(x333,x334,x332)
% 63.41/63.56 [24]~P2(x243,x242)+~P2(x241,x243)+P2(x241,x242)+~P1(x243)
% 63.41/63.56 [34]~P3(x345,x342,x344)+P2(x341,x342)+~P3(x343,x345,x341)+~P2(x343,x344)
% 63.41/63.56 [35]~P3(x351,x355,x353)+P2(x351,x352)+~P3(x355,x354,x352)+~P2(x353,x354)
% 63.41/63.56 [36]~P3(x366,x362,x365)+P3(x361,x362,x363)+~P3(x364,x365,x363)+~P3(x364,x366,x361)
% 63.41/63.56 [37]~P3(x371,x376,x374)+P3(x371,x372,x373)+~P3(x374,x375,x373)+~P3(x376,x375,x372)
% 63.41/63.56 %EqnAxiom
% 63.41/63.56 [1]E(x11,x11)
% 63.41/63.56 [2]E(x22,x21)+~E(x21,x22)
% 63.41/63.56 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 63.41/63.56 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 63.41/63.56 [5]~E(x51,x52)+E(f2(x51),f2(x52))
% 63.41/63.56 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 63.41/63.56 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 63.41/63.56 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 63.41/63.56 [9]P3(x92,x93,x94)+~E(x91,x92)+~P3(x91,x93,x94)
% 63.41/63.56 [10]P3(x103,x102,x104)+~E(x101,x102)+~P3(x103,x101,x104)
% 63.41/63.56 [11]P3(x113,x114,x112)+~E(x111,x112)+~P3(x113,x114,x111)
% 63.41/63.56 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 63.41/63.56 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 63.41/63.56
% 63.41/63.56 %-------------------------------------------
% 63.41/63.57 cnf(38,plain,
% 63.41/63.57 (P2(f1(x381),f1(x381))),
% 63.41/63.57 inference(scs_inference,[],[21,16,30])).
% 63.41/63.57 cnf(41,plain,
% 63.41/63.57 (P3(a5,f1(a4),a5)),
% 63.41/63.57 inference(scs_inference,[],[21,16,18,30,36])).
% 63.41/63.57 cnf(44,plain,
% 63.41/63.57 (P3(f2(a3),a5,a5)),
% 63.41/63.57 inference(scs_inference,[],[21,22,16,18,30,36,37])).
% 63.41/63.57 cnf(56,plain,
% 63.41/63.57 (P3(f2(x561),x561,x561)),
% 63.41/63.57 inference(rename_variables,[],[22])).
% 63.41/63.57 cnf(58,plain,
% 63.41/63.57 (P2(f1(a4),f1(a5))),
% 63.41/63.57 inference(scs_inference,[],[38,41,22,16,29,30])).
% 63.41/63.57 cnf(61,plain,
% 63.41/63.57 (P2(a5,f1(a4))),
% 63.41/63.57 inference(scs_inference,[],[17,38,41,22,56,16,29,30,34])).
% 63.41/63.57 cnf(63,plain,
% 63.41/63.57 (P3(f2(x631),x631,x631)),
% 63.41/63.57 inference(rename_variables,[],[22])).
% 63.41/63.57 cnf(65,plain,
% 63.41/63.57 (P3(f2(f2(a3)),a5,a5)),
% 63.41/63.57 inference(scs_inference,[],[17,38,41,44,22,56,63,16,29,30,34,37])).
% 63.41/63.57 cnf(68,plain,
% 63.41/63.57 (P3(a5,f1(f1(a4)),a5)),
% 63.41/63.57 inference(scs_inference,[],[17,38,41,44,22,56,63,16,21,29,30,34,37,36])).
% 63.41/63.57 cnf(85,plain,
% 63.41/63.57 (P2(f2(f2(a3)),a5)),
% 63.41/63.57 inference(scs_inference,[],[17,61,65,41,29,35])).
% 63.41/63.57 cnf(87,plain,
% 63.41/63.57 (P3(a6,f1(a8),a6)),
% 63.41/63.57 inference(scs_inference,[],[17,61,65,19,21,41,29,35,36])).
% 63.41/63.57 cnf(90,plain,
% 63.41/63.57 (P3(f2(f2(a3)),a6,a6)),
% 63.41/63.57 inference(scs_inference,[],[17,61,65,19,21,41,29,35,36,37])).
% 63.41/63.57 cnf(100,plain,
% 63.41/63.57 (P3(f2(x1001),x1001,x1001)),
% 63.41/63.57 inference(rename_variables,[],[22])).
% 63.41/63.57 cnf(102,plain,
% 63.41/63.57 (P2(a5,f1(f1(a4)))),
% 63.41/63.57 inference(scs_inference,[],[17,58,61,68,22,100,30,29,34])).
% 63.41/63.57 cnf(106,plain,
% 63.41/63.57 (P3(a6,f1(f1(a8)),a6)),
% 63.41/63.57 inference(scs_inference,[],[17,58,61,68,87,22,100,21,30,29,34,36])).
% 63.41/63.57 cnf(109,plain,
% 63.41/63.57 (P3(f2(a3),a6,a6)),
% 63.41/63.57 inference(scs_inference,[],[17,58,61,68,87,20,44,22,100,21,30,29,34,36,37])).
% 63.41/63.57 cnf(127,plain,
% 63.41/63.57 (P2(f2(a3),a5)),
% 63.41/63.57 inference(scs_inference,[],[17,61,90,44,41,29,35])).
% 63.41/63.57 cnf(146,plain,
% 63.41/63.57 (P2(f2(a3),a6)),
% 63.41/63.57 inference(scs_inference,[],[17,16,109,102,18,21,30,29,35])).
% 63.41/63.57 cnf(150,plain,
% 63.41/63.57 (P2(a3,a4)),
% 63.41/63.57 inference(scs_inference,[],[17,16,109,102,18,127,22,21,30,29,35,34])).
% 63.41/63.57 cnf(174,plain,
% 63.41/63.57 (P3(f2(x1741),x1741,x1741)),
% 63.41/63.57 inference(rename_variables,[],[22])).
% 63.41/63.57 cnf(176,plain,
% 63.41/63.57 (P2(f2(f2(a3)),a6)),
% 63.41/63.57 inference(scs_inference,[],[106,109,61,16,146,22,174,30,29,35])).
% 63.41/63.57 cnf(177,plain,
% 63.41/63.57 (P3(f2(x1771),x1771,x1771)),
% 63.41/63.57 inference(rename_variables,[],[22])).
% 63.41/63.57 cnf(179,plain,
% 63.41/63.57 (P2(a6,f1(f1(a8)))),
% 63.41/63.57 inference(scs_inference,[],[106,17,109,61,16,146,22,174,177,30,29,35,34])).
% 63.41/63.57 cnf(198,plain,
% 63.41/63.57 (P2(x1981,f1(x1981))),
% 63.41/63.57 inference(rename_variables,[],[16])).
% 63.41/63.57 cnf(203,plain,
% 63.41/63.57 (P2(a6,f1(a8))),
% 63.41/63.57 inference(scs_inference,[],[87,16,198,179,22,21,30,29,35])).
% 63.41/63.57 cnf(223,plain,
% 63.41/63.57 (P2(f2(a6),a5)),
% 63.41/63.57 inference(scs_inference,[],[19,17,16,30,29])).
% 63.41/63.57 cnf(226,plain,
% 63.41/63.57 (P2(a5,a8)),
% 63.41/63.57 inference(scs_inference,[],[19,17,16,203,21,30,29,35])).
% 63.41/63.57 cnf(248,plain,
% 63.41/63.57 (P2(a5,a9)),
% 63.41/63.57 inference(scs_inference,[],[20,65,176,16,226,22,30,29,34])).
% 63.41/63.57 cnf(298,plain,
% 63.41/63.57 (P3(x2981,f1(x2981),x2981)),
% 63.41/63.57 inference(rename_variables,[],[21])).
% 63.41/63.57 cnf(302,plain,
% 63.41/63.57 (P2(a6,f1(a9))),
% 63.41/63.57 inference(scs_inference,[],[109,20,146,248,21,298,30,29,34])).
% 63.41/63.57 cnf(368,plain,
% 63.41/63.57 (P3(x3681,f1(x3681),x3681)),
% 63.41/63.57 inference(rename_variables,[],[21])).
% 63.41/63.57 cnf(371,plain,
% 63.41/63.57 (P3(x3711,f1(x3711),x3711)),
% 63.41/63.57 inference(rename_variables,[],[21])).
% 63.41/63.57 cnf(373,plain,
% 63.41/63.57 (~E(a8,a9)),
% 63.41/63.57 inference(scs_inference,[],[23,150,21,368,371,33,30,11])).
% 63.41/63.57 cnf(383,plain,
% 63.41/63.57 (P2(f1(f2(x3831)),x3831)),
% 63.41/63.57 inference(scs_inference,[],[17,21,30])).
% 63.41/63.57 cnf(437,plain,
% 63.41/63.57 (P2(a5,f2(a9))),
% 63.41/63.57 inference(scs_inference,[],[22,248,29])).
% 63.41/63.57 cnf(502,plain,
% 63.41/63.57 (P2(f1(a8),f1(a9))),
% 63.41/63.57 inference(scs_inference,[],[87,302,30])).
% 63.41/63.57 cnf(1382,plain,
% 63.41/63.57 (P2(f2(a6),a3)),
% 63.41/63.57 inference(scs_inference,[],[18,223,29])).
% 63.41/63.57 cnf(1384,plain,
% 63.41/63.57 (P2(a4,a8)),
% 63.41/63.57 inference(scs_inference,[],[18,226,223,29,30])).
% 63.41/63.57 cnf(1388,plain,
% 63.41/63.57 (~P3(f2(f2(a3)),a3,x13881)+P2(x13881,a4)),
% 63.41/63.57 inference(scs_inference,[],[18,85,226,223,29,30,12,13,34])).
% 63.41/63.57 cnf(1398,plain,
% 63.41/63.57 (P2(a4,a9)),
% 63.41/63.57 inference(scs_inference,[],[18,248,383,29,30])).
% 63.41/63.57 cnf(2034,plain,
% 63.41/63.57 (P2(a9,f1(a8))),
% 63.41/63.57 inference(scs_inference,[],[20,203,30])).
% 63.41/63.57 cnf(2385,plain,
% 63.41/63.57 (P2(f1(a6),f1(a9))),
% 63.41/63.57 inference(scs_inference,[],[21,302,30])).
% 63.41/63.57 cnf(2413,plain,
% 63.41/63.57 (P2(f1(a5),a9)),
% 63.41/63.57 inference(scs_inference,[],[21,248,30])).
% 63.41/63.57 cnf(2455,plain,
% 63.41/63.57 (P2(f1(a5),f2(a9))),
% 63.41/63.57 inference(scs_inference,[],[21,437,30])).
% 63.41/63.57 cnf(3204,plain,
% 63.41/63.57 (P2(f2(x32041),f2(x32041))),
% 63.41/63.57 inference(scs_inference,[],[22,17,29])).
% 63.41/63.57 cnf(4784,plain,
% 63.41/63.57 (~E(a6,a3)+P2(a6,a4)),
% 63.41/63.57 inference(scs_inference,[],[90,1388,10])).
% 63.41/63.57 cnf(4792,plain,
% 63.41/63.57 (~P3(a3,f1(a3),a6)+P2(a6,a4)),
% 63.41/63.57 inference(scs_inference,[],[21,4784,33])).
% 63.41/63.57 cnf(4793,plain,
% 63.41/63.57 (~P3(a3,x47931,a6)+~E(x47931,f1(a3))+P2(a6,a4)),
% 63.41/63.57 inference(scs_inference,[],[4792,10])).
% 63.41/63.57 cnf(4947,plain,
% 63.41/63.57 (P3(a4,a8,f7(a4,a8))),
% 63.41/63.57 inference(scs_inference,[],[1384,28])).
% 63.41/63.57 cnf(4950,plain,
% 63.41/63.57 (P1(f1(x49501))),
% 63.41/63.57 inference(rename_variables,[],[14])).
% 63.41/63.57 cnf(4952,plain,
% 63.41/63.57 (~P3(a4,a9,f7(a4,a8))),
% 63.41/63.57 inference(scs_inference,[],[14,373,2385,1384,28,26,32])).
% 63.41/63.57 cnf(4960,plain,
% 63.41/63.57 (P3(x49601,f1(x49601),x49601)),
% 63.41/63.57 inference(rename_variables,[],[21])).
% 63.41/63.57 cnf(4962,plain,
% 63.41/63.57 (P2(f7(a4,a8),f1(a8))),
% 63.41/63.57 inference(scs_inference,[],[14,4950,373,2455,2413,2385,2034,1384,21,4960,28,26,32,25,24,37,34])).
% 63.41/63.57 cnf(4969,plain,
% 63.41/63.57 (P3(a4,a9,f7(a4,a9))),
% 63.41/63.57 inference(scs_inference,[],[1398,28])).
% 63.41/63.57 cnf(4974,plain,
% 63.41/63.57 (P1(f1(x49741))),
% 63.41/63.57 inference(rename_variables,[],[14])).
% 63.41/63.57 cnf(4984,plain,
% 63.41/63.57 (P3(x49841,f1(x49841),x49841)),
% 63.41/63.57 inference(rename_variables,[],[21])).
% 63.41/63.57 cnf(4989,plain,
% 63.41/63.57 (~E(f7(a4,a8),f7(a4,a9))),
% 63.41/63.57 inference(scs_inference,[],[14,4974,4962,4952,15,1382,1398,23,502,21,4984,28,32,26,25,11,24,36,37,2])).
% 63.41/63.57 cnf(5744,plain,
% 63.41/63.57 (~P3(a3,f7(a4,a9),a6)),
% 63.41/63.57 inference(scs_inference,[],[19,4947,3204,4989,15,18,26,37,4793,31])).
% 63.41/63.57 cnf(5798,plain,
% 63.41/63.57 ($false),
% 63.41/63.57 inference(scs_inference,[],[20,5744,2385,4969,14,18,25,37]),
% 63.41/63.57 ['proof']).
% 63.41/63.57 % SZS output end Proof
% 63.41/63.57 % Total time :62.890000s
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