TSTP Solution File: CAT007-3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : CAT007-3 : 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 : n015.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 : Wed Aug 30 18:13:42 EDT 2023
% Result : Unsatisfiable 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT007-3 : 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
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 00:25:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.54 start to proof:theBenchmark
% 0.20/0.58 %-------------------------------------------
% 0.20/0.58 % File :CSE---1.6
% 0.20/0.58 % Problem :theBenchmark
% 0.20/0.58 % Transform :cnf
% 0.20/0.58 % Format :tptp:raw
% 0.20/0.58 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.58
% 0.20/0.58 % Result :Theorem 0.000000s
% 0.20/0.58 % Output :CNFRefutation 0.000000s
% 0.20/0.58 %-------------------------------------------
% 0.20/0.59 %--------------------------------------------------------------------------
% 0.20/0.59 % File : CAT007-3 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.59 % Domain : Category Theory
% 0.20/0.59 % Problem : If domain(x) = codomain(y) then xy is defined
% 0.20/0.59 % Version : [Sco79] axioms : Reduced > Complete.
% 0.20/0.59 % English :
% 0.20/0.59
% 0.20/0.59 % Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 0.20/0.59 % : [Sco79] Scott (1979), Identity and Existence in Intuitionist L
% 0.20/0.59 % Source : [ANL]
% 0.20/0.59 % Names : p7.ver3.in [ANL]
% 0.20/0.59
% 0.20/0.59 % Status : Unsatisfiable
% 0.20/0.59 % Rating : 0.00 v2.0.0
% 0.20/0.59 % Syntax : Number of clauses : 12 ( 5 unt; 2 nHn; 9 RR)
% 0.20/0.59 % Number of literals : 23 ( 0 equ; 9 neg)
% 0.20/0.59 % Maximal clause size : 3 ( 1 avg)
% 0.20/0.59 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.59 % Number of predicates : 2 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.59 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.20/0.59 % Number of variables : 15 ( 0 sgn)
% 0.20/0.59 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.20/0.59
% 0.20/0.59 % Comments : In Scott's axiom system, this is an axiom; but
% 0.20/0.59 % it is dependant, vis. proof included.
% 0.20/0.59 % : Axioms simplified by Art Quaife.
% 0.20/0.59 %--------------------------------------------------------------------------
% 0.20/0.59 cnf(reflexivity,axiom,
% 0.20/0.59 equalish(X,X) ).
% 0.20/0.59
% 0.20/0.59 cnf(symmetry,axiom,
% 0.20/0.59 ( ~ equalish(X,Y)
% 0.20/0.59 | equalish(Y,X) ) ).
% 0.20/0.59
% 0.20/0.59 cnf(transitivity,axiom,
% 0.20/0.59 ( ~ equalish(X,Y)
% 0.20/0.59 | ~ equalish(Y,Z)
% 0.20/0.59 | equalish(X,Z) ) ).
% 0.20/0.59
% 0.20/0.59 %----Supply the axioms upon which it is dependant.
% 0.20/0.59
% 0.20/0.59 %----Category theory axioms
% 0.20/0.59 cnf(domain_has_elements,axiom,
% 0.20/0.59 ( ~ there_exists(domain(X))
% 0.20/0.59 | there_exists(X) ) ).
% 0.20/0.59
% 0.20/0.59 cnf(domain_codomain_composition2,axiom,
% 0.20/0.59 ( ~ there_exists(domain(X))
% 0.20/0.59 | ~ equalish(domain(X),codomain(Y))
% 0.20/0.59 | there_exists(compose(X,Y)) ) ).
% 0.20/0.59
% 0.20/0.59 %----Axiom of indiscernibles
% 0.20/0.59 cnf(indiscernibles1,axiom,
% 0.20/0.59 ( there_exists(f1(X,Y))
% 0.20/0.59 | equalish(X,Y) ) ).
% 0.20/0.59
% 0.20/0.59 cnf(indiscernibles2,axiom,
% 0.20/0.59 ( equalish(X,f1(X,Y))
% 0.20/0.59 | equalish(Y,f1(X,Y))
% 0.20/0.59 | equalish(X,Y) ) ).
% 0.20/0.59
% 0.20/0.59 cnf(indiscernibles3,axiom,
% 0.20/0.59 ( ~ equalish(X,f1(X,Y))
% 0.20/0.59 | ~ equalish(Y,f1(X,Y))
% 0.20/0.59 | equalish(X,Y) ) ).
% 0.20/0.59
% 0.20/0.59 cnf(domain_of_c2_exists,hypothesis,
% 0.20/0.59 there_exists(domain(c2)) ).
% 0.20/0.59
% 0.20/0.59 cnf(domain_of_c1_exists,hypothesis,
% 0.20/0.59 there_exists(domain(c1)) ).
% 0.20/0.59
% 0.20/0.59 cnf(domain_of_c2_equals_codomain_of_c1,hypothesis,
% 0.20/0.59 equalish(domain(c2),codomain(c1)) ).
% 0.20/0.59
% 0.20/0.59 cnf(prove_c1_c2_is_defined,negated_conjecture,
% 0.20/0.59 ~ there_exists(compose(c2,c1)) ).
% 0.20/0.59
% 0.20/0.59 %--------------------------------------------------------------------------
% 0.20/0.59 %-------------------------------------------
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark
% 0.20/0.59 % SZS output start Proof
% 0.20/0.59 %ClaNum:12(EqnAxiom:0)
% 0.20/0.59 %VarNum:39(SingletonVarNum:15)
% 0.20/0.59 %MaxLitNum:3
% 0.20/0.59 %MaxfuncDepth:1
% 0.20/0.59 %SharedTerms:10
% 0.20/0.59 %goalClause: 5
% 0.20/0.59 %singleGoalClaCount:1
% 0.20/0.59 [1]P1(f3(a1))
% 0.20/0.59 [2]P1(f3(a2))
% 0.20/0.59 [4]P2(f3(a1),f4(a2))
% 0.20/0.59 [5]~P1(f5(a1,a2))
% 0.20/0.59 [3]P2(x31,x31)
% 0.20/0.59 [6]P1(x61)+~P1(f3(x61))
% 0.20/0.59 [7]~P2(x72,x71)+P2(x71,x72)
% 0.20/0.59 [8]P2(x81,x82)+P1(f6(x81,x82))
% 0.20/0.59 [10]~P2(f3(x101),f4(x102))+~P1(f3(x101))+P1(f5(x101,x102))
% 0.20/0.59 [11]P2(x111,x112)+P2(x112,f6(x111,x112))+P2(x111,f6(x111,x112))
% 0.20/0.59 [12]P2(x121,x122)+~P2(x122,f6(x121,x122))+~P2(x121,f6(x121,x122))
% 0.20/0.59 [9]~P2(x91,x93)+P2(x91,x92)+~P2(x93,x92)
% 0.20/0.59 %EqnAxiom
% 0.20/0.59
% 0.20/0.59 %-------------------------------------------
% 0.20/0.59 cnf(13,plain,
% 0.20/0.59 ($false),
% 0.20/0.59 inference(scs_inference,[],[4,1,5,10]),
% 0.20/0.59 ['proof']).
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time :0.000000s
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