%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : CAT009-4 : 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 : n010.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 2.52s 2.62s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT009-4 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Jun 18 12:24:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.47/0.56 start to proof:theBenchmark
% 2.52/2.61 %-------------------------------------------
% 2.52/2.61 % File :CSE---1.7
% 2.52/2.61 % Problem :theBenchmark
% 2.52/2.61 % Transform :cnf
% 2.52/2.61 % Format :tptp:raw
% 2.52/2.61 % Command :java -jar mcs_scs.jar %d %s
% 2.52/2.61
% 2.52/2.61 % Result :Theorem 2.020000s
% 2.52/2.61 % Output :CNFRefutation 2.020000s
% 2.52/2.61 %-------------------------------------------
% 2.52/2.61 %--------------------------------------------------------------------------
% 2.52/2.61 % File : CAT009-4 : TPTP v8.2.0. Released v1.0.0.
% 2.52/2.61 % Domain : Category Theory
% 2.52/2.61 % Problem : If xy is defined, then domain(xy) = domain(y)
% 2.52/2.61 % Version : [Sco79] axioms : Reduced > Complete.
% 2.52/2.61 % English :
% 2.52/2.61
% 2.52/2.61 % Refs : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% 2.52/2.61 % Source : [TPTP]
% 2.52/2.61 % Names :
% 2.52/2.61
% 2.52/2.61 % Status : Unsatisfiable
% 2.52/2.61 % Rating : 0.00 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.20 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.29 v4.1.0, 0.22 v4.0.1, 0.33 v3.7.0, 0.17 v3.3.0, 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, 0.44 v2.2.0, 0.57 v2.1.0, 0.60 v2.0.0
% 2.52/2.61 % Syntax : Number of clauses : 13 ( 5 unt; 0 nHn; 10 RR)
% 2.52/2.61 % Number of literals : 23 ( 8 equ; 11 neg)
% 2.52/2.61 % Maximal clause size : 3 ( 1 avg)
% 2.52/2.61 % Maximal term depth : 3 ( 1 avg)
% 2.52/2.61 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 2.52/2.61 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 2.52/2.61 % Number of variables : 19 ( 2 sgn)
% 2.52/2.61 % SPC : CNF_UNS_RFO_SEQ_HRN
% 2.52/2.61
% 2.52/2.61 % Comments : The dependent axioms have been removed. The ANL version has
% 2.52/2.62 % been extended to use all axioms.
% 2.52/2.62 %--------------------------------------------------------------------------
% 2.52/2.62 %----Include Scott's axioms for category theory
% 2.52/2.62 include('Axioms/CAT004-0.ax').
% 2.52/2.62 %--------------------------------------------------------------------------
% 2.52/2.62 cnf(ab_exists,hypothesis,
% 2.52/2.62 there_exists(compose(a,b)) ).
% 2.52/2.62
% 2.52/2.62 cnf(prove_domain_of_ab_equals_domain_of_b,negated_conjecture,
% 2.52/2.62 domain(compose(a,b)) != domain(b) ).
% 2.52/2.62
% 2.52/2.62 %--------------------------------------------------------------------------
% 2.52/2.62 %-------------------------------------------
% 2.52/2.62 % Proof found
% 2.52/2.62 % SZS status Theorem for theBenchmark
% 2.52/2.62 % SZS output start Proof
% 2.52/2.62 %ClaNum:23(EqnAxiom:10)
% 2.52/2.62 %VarNum:40(SingletonVarNum:19)
% 2.52/2.62 %MaxLitNum:3
% 2.52/2.62 %MaxfuncDepth:2
% 2.52/2.62 %SharedTerms:7
% 2.52/2.62 %goalClause: 15
% 2.52/2.62 %singleGoalClaCount:1
% 2.52/2.62 [13]P1(f2(a4,a5))
% 2.52/2.62 [15]~E(f1(f2(a4,a5)),f1(a5))
% 2.52/2.62 [11]E(f2(x111,f1(x111)),x111)
% 2.52/2.62 [12]E(f2(f3(x121),x121),x121)
% 2.52/2.62 [14]E(f2(f2(x141,x142),x143),f2(x141,f2(x142,x143)))
% 2.52/2.62 [16]P1(x161)+~P1(f1(x161))
% 2.52/2.62 [17]P1(x171)+~P1(f3(x171))
% 2.52/2.62 [18]~P2(x181,x182)+E(x181,x182)
% 2.52/2.62 [20]P1(x201)+~P2(x201,x202)
% 2.52/2.62 [21]E(f3(x211),f1(x212))+~P1(f2(x212,x211))
% 2.52/2.62 [22]P1(f1(x221))+~P1(f2(x221,x222))
% 2.52/2.62 [19]~E(x191,x192)+~P1(x191)+P2(x191,x192)
% 2.52/2.62 [23]~E(f3(x232),f1(x231))+~P1(f1(x231))+P1(f2(x231,x232))
% 2.52/2.62 %EqnAxiom
% 2.52/2.62 [1]E(x11,x11)
% 2.52/2.62 [2]E(x22,x21)+~E(x21,x22)
% 2.52/2.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.52/2.62 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 2.52/2.62 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 2.52/2.62 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 2.52/2.62 [7]~E(x71,x72)+E(f3(x71),f3(x72))
% 2.52/2.62 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 2.52/2.62 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93)
% 2.52/2.62 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101)
% 2.52/2.62
% 2.52/2.62 %-------------------------------------------
% 2.52/2.62 cnf(24,plain,
% 2.52/2.62 (~P1(x241)+P2(x241,x241)),
% 2.52/2.62 inference(equality_inference,[],[19])).
% 2.52/2.62 cnf(27,plain,
% 2.52/2.62 (E(x271,f2(x271,f1(x271)))),
% 2.52/2.62 inference(scs_inference,[],[15,11,18,2])).
% 2.52/2.62 cnf(28,plain,
% 2.52/2.62 (~E(f2(a4,a5),a5)),
% 2.52/2.62 inference(scs_inference,[],[15,11,18,2,4])).
% 2.52/2.62 cnf(29,plain,
% 2.52/2.62 (E(f3(a5),f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[15,11,13,18,2,4,21])).
% 2.52/2.62 cnf(31,plain,
% 2.52/2.62 (P2(f2(a4,a5),f2(f2(a4,a5),f1(f2(a4,a5))))),
% 2.52/2.62 inference(scs_inference,[],[15,11,13,18,2,4,21,19])).
% 2.52/2.62 cnf(33,plain,
% 2.52/2.62 (~E(f1(f2(a4,a5)),f2(f3(f1(a5)),f1(a5)))),
% 2.52/2.62 inference(scs_inference,[],[15,11,12,13,18,2,4,21,19,3])).
% 2.52/2.62 cnf(36,plain,
% 2.52/2.62 (P2(f2(a4,a5),f2(a4,a5))),
% 2.52/2.62 inference(scs_inference,[],[15,11,12,13,18,2,4,21,19,3,8,10])).
% 2.52/2.62 cnf(41,plain,
% 2.52/2.62 (E(f1(a4),f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[33,29,18,2])).
% 2.52/2.62 cnf(42,plain,
% 2.52/2.62 (E(f3(a5),f2(f1(a4),f1(f1(a4))))),
% 2.52/2.62 inference(scs_inference,[],[27,33,29,18,2,3])).
% 2.52/2.62 cnf(44,plain,
% 2.52/2.62 (~P1(f3(a5))+P1(f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[27,33,29,18,2,3,8])).
% 2.52/2.62 cnf(45,plain,
% 2.52/2.62 (~P2(f3(a5),x451)+P1(f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[27,33,29,18,2,3,8,20])).
% 2.52/2.62 cnf(47,plain,
% 2.52/2.62 (~E(f2(a4,a5),f3(a5))+P1(f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[27,33,31,29,18,2,3,8,20,9])).
% 2.52/2.62 cnf(48,plain,
% 2.52/2.62 (~P2(f2(a4,a5),a5)),
% 2.52/2.62 inference(scs_inference,[],[28,18])).
% 2.52/2.62 cnf(50,plain,
% 2.52/2.62 (E(f2(f1(a4),f1(f1(a4))),f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[28,42,18,2])).
% 2.52/2.62 cnf(51,plain,
% 2.52/2.62 (~E(f2(f2(a4,a5),f1(f2(a4,a5))),a5)),
% 2.52/2.62 inference(scs_inference,[],[28,42,31,18,2,10])).
% 2.52/2.62 cnf(52,plain,
% 2.52/2.62 (E(f2(f3(f1(a4)),f1(a4)),f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[28,42,41,31,12,18,2,10,3])).
% 2.52/2.62 cnf(55,plain,
% 2.52/2.62 (~P2(f3(a5),x551)+P1(f2(f1(a4),f1(f1(a4))))),
% 2.52/2.62 inference(scs_inference,[],[28,42,41,31,12,18,2,10,3,8,20])).
% 2.52/2.62 cnf(61,plain,
% 2.52/2.62 (~P1(f2(f1(a4),f1(f1(a4))))+P1(f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[50,52,51,18,2,8])).
% 2.52/2.62 cnf(66,plain,
% 2.52/2.62 (E(x661,f2(f3(x661),x661))),
% 2.52/2.62 inference(scs_inference,[],[12,2])).
% 2.52/2.62 cnf(68,plain,
% 2.52/2.62 (E(f1(a4),f2(f3(a5),f1(f3(a5))))),
% 2.52/2.62 inference(scs_inference,[],[41,27,13,12,2,8,3])).
% 2.52/2.62 cnf(70,plain,
% 2.52/2.62 (E(f2(f3(a5),f1(f3(a5))),f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[68,2])).
% 2.52/2.62 cnf(75,plain,
% 2.52/2.62 (~P2(f1(a4),x751)+P1(f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[41,66,68,36,13,2,9,8,22,20])).
% 2.52/2.62 cnf(77,plain,
% 2.52/2.62 (E(f2(x771,f2(x772,x773)),f2(f2(x771,x772),x773))),
% 2.52/2.62 inference(scs_inference,[],[14,2])).
% 2.52/2.62 cnf(83,plain,
% 2.52/2.62 (~P2(f1(a4),x831)+P1(f2(f3(a5),f1(f3(a5))))),
% 2.52/2.62 inference(scs_inference,[],[68,13,14,2,8,45,47,18,22,20])).
% 2.52/2.62 cnf(104,plain,
% 2.52/2.62 (~P1(f2(f3(a5),f1(f3(a5))))+P1(f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[70,8])).
% 2.52/2.62 cnf(113,plain,
% 2.52/2.62 (P2(f1(a4),f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[13,24,22])).
% 2.52/2.62 cnf(114,plain,
% 2.52/2.62 (P1(f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[113,75])).
% 2.52/2.62 cnf(115,plain,
% 2.52/2.62 (P1(f2(f3(a5),f1(f3(a5))))),
% 2.52/2.62 inference(scs_inference,[],[113,83])).
% 2.52/2.62 cnf(118,plain,
% 2.52/2.62 (P2(f3(a5),f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[41,113,10,9])).
% 2.52/2.62 cnf(119,plain,
% 2.52/2.62 (E(f2(f3(x1191),x1191),f2(x1191,f1(x1191)))),
% 2.52/2.62 inference(scs_inference,[],[12,41,27,113,10,9,3])).
% 2.52/2.62 cnf(121,plain,
% 2.52/2.62 (P1(f2(f1(a4),f1(f1(a4))))),
% 2.52/2.62 inference(scs_inference,[],[12,41,27,113,10,9,3,55])).
% 2.52/2.62 cnf(126,plain,
% 2.52/2.62 (P1(f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[114,44])).
% 2.52/2.62 cnf(128,plain,
% 2.52/2.62 (P1(f3(a5))),
% 2.52/2.62 inference(scs_inference,[],[121,61])).
% 2.52/2.62 cnf(137,plain,
% 2.52/2.62 (P1(f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[115,104])).
% 2.52/2.62 cnf(141,plain,
% 2.52/2.62 (P1(a4)),
% 2.52/2.62 inference(scs_inference,[],[126,16])).
% 2.52/2.62 cnf(166,plain,
% 2.52/2.62 (E(f3(x1661),f3(f2(f3(x1661),x1661)))),
% 2.52/2.62 inference(scs_inference,[],[12,7,2])).
% 2.52/2.62 cnf(169,plain,
% 2.52/2.62 (E(x1691,f2(f3(x1691),x1691))),
% 2.52/2.62 inference(rename_variables,[],[66])).
% 2.52/2.62 cnf(172,plain,
% 2.52/2.62 (E(f2(f3(x1721),x1721),x1721)),
% 2.52/2.62 inference(rename_variables,[],[12])).
% 2.52/2.62 cnf(175,plain,
% 2.52/2.62 (P2(f2(f3(a4),a4),f2(f3(a4),a4))),
% 2.52/2.62 inference(scs_inference,[],[12,66,169,166,128,141,2,19,10,8,9])).
% 2.52/2.62 cnf(177,plain,
% 2.52/2.62 (P1(f2(f3(a5),a5))),
% 2.52/2.62 inference(scs_inference,[],[12,66,169,166,128,141,2,19,10,8,9,17])).
% 2.52/2.62 cnf(181,plain,
% 2.52/2.62 (E(f2(f3(f3(a5)),f3(a5)),f1(f3(a5)))),
% 2.52/2.62 inference(scs_inference,[],[12,172,66,169,166,128,141,2,19,10,8,9,17,21,3])).
% 2.52/2.62 cnf(186,plain,
% 2.52/2.62 (E(f2(f3(x1861),x1861),x1861)),
% 2.52/2.62 inference(rename_variables,[],[12])).
% 2.52/2.62 cnf(198,plain,
% 2.52/2.62 (~E(f1(f2(a4,a5)),f3(f1(a5)))),
% 2.52/2.62 inference(scs_inference,[],[12,186,15,48,119,181,177,175,2,19,10,8,9,5,21,18,3])).
% 2.52/2.62 cnf(374,plain,
% 2.52/2.62 (~P1(f2(f2(a4,a5),f1(a5)))),
% 2.52/2.62 inference(scs_inference,[],[198,2,21])).
% 2.52/2.62 cnf(452,plain,
% 2.52/2.62 (~P2(f3(f2(a5,f1(a5))),f1(a4))),
% 2.52/2.62 inference(scs_inference,[],[77,374,137,8,20,23,18])).
% 2.52/2.62 cnf(459,plain,
% 2.52/2.62 ($false),
% 2.52/2.62 inference(scs_inference,[],[452,27,118,9,7]),
% 2.52/2.62 ['proof']).
% 2.52/2.62 % SZS output end Proof
% 2.52/2.62 % Total time :2.020000s
%------------------------------------------------------------------------------