TSTP Solution File: CAT010-10 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : 600s
% DateTime : Fri Jul 15 00:04:34 EDT 2022
% Result : Unsatisfiable 0.60s 0.77s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 35
% Syntax : Number of clauses : 97 ( 53 unt; 0 nHn; 65 RR)
% Number of literals : 162 ( 161 equ; 67 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 70 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom_001,axiom,
ifeq2(A,A,B,C) = B ).
cnf(ifeq_axiom_002,axiom,
ifeq(A,A,B,C) = B ).
cnf(domain_has_elements,axiom,
ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ).
cnf(composition_implies_domain,axiom,
ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ).
cnf(domain_codomain_composition1,axiom,
ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ).
cnf(associativity_of_compose,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ).
cnf(compose_domain,axiom,
compose(X,domain(X)) = X ).
cnf(compose_codomain,axiom,
compose(codomain(X),X) = X ).
cnf(ab_exists,hypothesis,
there_exists(compose(a,b)) = true ).
cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
codomain(compose(a,b)) != codomain(a) ).
cnf(refute_0_0,plain,
ifeq2(there_exists(compose(codomain(a),compose(codomain(a),X_54))),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(a))),bind(Y,$fot(compose(codomain(a),X_54)))]]) ).
cnf(refute_0_1,plain,
compose(codomain(a),compose(codomain(a),X_49)) = compose(compose(codomain(a),codomain(a)),X_49),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(codomain(a))),bind(Y,$fot(codomain(a))),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_2,plain,
compose(codomain(a),domain(codomain(a))) = codomain(a),
inference(subst,[],[compose_domain:[bind(X,$fot(codomain(a)))]]) ).
cnf(refute_0_3,plain,
ifeq2(there_exists(compose(codomain(X_24),X_24)),true,domain(codomain(X_24)),codomain(X_24)) = codomain(X_24),
inference(subst,[],[domain_codomain_composition1:[bind(X,$fot(codomain(X_24))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_4,plain,
compose(codomain(X_24),X_24) = X_24,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_5,plain,
( compose(codomain(X_24),X_24) != X_24
| ifeq2(there_exists(compose(codomain(X_24),X_24)),true,domain(codomain(X_24)),codomain(X_24)) != codomain(X_24)
| ifeq2(there_exists(X_24),true,domain(codomain(X_24)),codomain(X_24)) = codomain(X_24) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(codomain(X_24),X_24)),true,domain(codomain(X_24)),codomain(X_24)),codomain(X_24)) ),[0,0,0],$fot(X_24)]]) ).
cnf(refute_0_6,plain,
( ifeq2(there_exists(compose(codomain(X_24),X_24)),true,domain(codomain(X_24)),codomain(X_24)) != codomain(X_24)
| ifeq2(there_exists(X_24),true,domain(codomain(X_24)),codomain(X_24)) = codomain(X_24) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_24),X_24),X_24) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
ifeq2(there_exists(X_24),true,domain(codomain(X_24)),codomain(X_24)) = codomain(X_24),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(codomain(X_24),X_24)),true,domain(codomain(X_24)),codomain(X_24)),codomain(X_24)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
ifeq2(there_exists(a),true,domain(codomain(a)),codomain(a)) = codomain(a),
inference(subst,[],[refute_0_7:[bind(X_24,$fot(a))]]) ).
cnf(refute_0_9,plain,
ifeq(there_exists(domain(a)),true,there_exists(a),true) = true,
inference(subst,[],[domain_has_elements:[bind(X,$fot(a))]]) ).
cnf(refute_0_10,plain,
ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) = true,
inference(subst,[],[composition_implies_domain:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_11,plain,
( ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) != true
| there_exists(compose(a,b)) != true
| ifeq(true,true,there_exists(domain(a)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_12,plain,
( ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) != true
| ifeq(true,true,there_exists(domain(a)),true) = true ),
inference(resolve,[$cnf( $equal(there_exists(compose(a,b)),true) )],[ab_exists,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq(true,true,there_exists(domain(a)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true),true) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
ifeq(true,true,there_exists(domain(a)),true) = there_exists(domain(a)),
inference(subst,[],[ifeq_axiom_002:[bind(A,$fot(true)),bind(B,$fot(there_exists(domain(a)))),bind(C,$fot(true))]]) ).
cnf(refute_0_15,plain,
( ifeq(true,true,there_exists(domain(a)),true) != there_exists(domain(a))
| ifeq(true,true,there_exists(domain(a)),true) != true
| there_exists(domain(a)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,there_exists(domain(a)),true),true) ),[0],$fot(there_exists(domain(a)))]]) ).
cnf(refute_0_16,plain,
( ifeq(true,true,there_exists(domain(a)),true) != true
| there_exists(domain(a)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,there_exists(domain(a)),true),there_exists(domain(a))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
there_exists(domain(a)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,there_exists(domain(a)),true),true) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( ifeq(there_exists(domain(a)),true,there_exists(a),true) != true
| there_exists(domain(a)) != true
| ifeq(true,true,there_exists(a),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(there_exists(domain(a)),true,there_exists(a),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_19,plain,
( ifeq(there_exists(domain(a)),true,there_exists(a),true) != true
| ifeq(true,true,there_exists(a),true) = true ),
inference(resolve,[$cnf( $equal(there_exists(domain(a)),true) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
ifeq(true,true,there_exists(a),true) = true,
inference(resolve,[$cnf( $equal(ifeq(there_exists(domain(a)),true,there_exists(a),true),true) )],[refute_0_9,refute_0_19]) ).
cnf(refute_0_21,plain,
ifeq(true,true,there_exists(a),true) = there_exists(a),
inference(subst,[],[ifeq_axiom_002:[bind(A,$fot(true)),bind(B,$fot(there_exists(a))),bind(C,$fot(true))]]) ).
cnf(refute_0_22,plain,
( ifeq(true,true,there_exists(a),true) != there_exists(a)
| ifeq(true,true,there_exists(a),true) != true
| there_exists(a) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,there_exists(a),true),true) ),[0],$fot(there_exists(a))]]) ).
cnf(refute_0_23,plain,
( ifeq(true,true,there_exists(a),true) != true
| there_exists(a) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,there_exists(a),true),there_exists(a)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
there_exists(a) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,there_exists(a),true),true) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( ifeq2(there_exists(a),true,domain(codomain(a)),codomain(a)) != codomain(a)
| there_exists(a) != true
| ifeq2(true,true,domain(codomain(a)),codomain(a)) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(a),true,domain(codomain(a)),codomain(a)),codomain(a)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_26,plain,
( ifeq2(there_exists(a),true,domain(codomain(a)),codomain(a)) != codomain(a)
| ifeq2(true,true,domain(codomain(a)),codomain(a)) = codomain(a) ),
inference(resolve,[$cnf( $equal(there_exists(a),true) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
ifeq2(true,true,domain(codomain(a)),codomain(a)) = codomain(a),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(a),true,domain(codomain(a)),codomain(a)),codomain(a)) )],[refute_0_8,refute_0_26]) ).
cnf(refute_0_28,plain,
ifeq2(true,true,domain(codomain(a)),codomain(a)) = domain(codomain(a)),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(domain(codomain(a)))),bind(C,$fot(codomain(a)))]]) ).
cnf(refute_0_29,plain,
( ifeq2(true,true,domain(codomain(a)),codomain(a)) != codomain(a)
| ifeq2(true,true,domain(codomain(a)),codomain(a)) != domain(codomain(a))
| domain(codomain(a)) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,domain(codomain(a)),codomain(a)),codomain(a)) ),[0],$fot(domain(codomain(a)))]]) ).
cnf(refute_0_30,plain,
( ifeq2(true,true,domain(codomain(a)),codomain(a)) != codomain(a)
| domain(codomain(a)) = codomain(a) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,domain(codomain(a)),codomain(a)),domain(codomain(a))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
domain(codomain(a)) = codomain(a),
inference(resolve,[$cnf( $equal(ifeq2(true,true,domain(codomain(a)),codomain(a)),codomain(a)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( compose(codomain(a),domain(codomain(a))) != codomain(a)
| domain(codomain(a)) != codomain(a)
| compose(codomain(a),codomain(a)) = codomain(a) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(a),domain(codomain(a))),codomain(a)) ),[0,1],$fot(codomain(a))]]) ).
cnf(refute_0_33,plain,
( compose(codomain(a),domain(codomain(a))) != codomain(a)
| compose(codomain(a),codomain(a)) = codomain(a) ),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
compose(codomain(a),codomain(a)) = codomain(a),
inference(resolve,[$cnf( $equal(compose(codomain(a),domain(codomain(a))),codomain(a)) )],[refute_0_2,refute_0_33]) ).
cnf(refute_0_35,plain,
( compose(codomain(a),codomain(a)) != codomain(a)
| compose(codomain(a),compose(codomain(a),X_49)) != compose(compose(codomain(a),codomain(a)),X_49)
| compose(codomain(a),compose(codomain(a),X_49)) = compose(codomain(a),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(a),compose(codomain(a),X_49)),compose(compose(codomain(a),codomain(a)),X_49)) ),[1,0],$fot(codomain(a))]]) ).
cnf(refute_0_36,plain,
( compose(codomain(a),compose(codomain(a),X_49)) != compose(compose(codomain(a),codomain(a)),X_49)
| compose(codomain(a),compose(codomain(a),X_49)) = compose(codomain(a),X_49) ),
inference(resolve,[$cnf( $equal(compose(codomain(a),codomain(a)),codomain(a)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
compose(codomain(a),compose(codomain(a),X_49)) = compose(codomain(a),X_49),
inference(resolve,[$cnf( $equal(compose(codomain(a),compose(codomain(a),X_49)),compose(compose(codomain(a),codomain(a)),X_49)) )],[refute_0_1,refute_0_36]) ).
cnf(refute_0_38,plain,
compose(codomain(a),compose(codomain(a),X_54)) = compose(codomain(a),X_54),
inference(subst,[],[refute_0_37:[bind(X_49,$fot(X_54))]]) ).
cnf(refute_0_39,plain,
( compose(codomain(a),compose(codomain(a),X_54)) != compose(codomain(a),X_54)
| ifeq2(there_exists(compose(codomain(a),compose(codomain(a),X_54))),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) != codomain(compose(codomain(a),X_54))
| ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),compose(codomain(a),X_54))),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),codomain(compose(codomain(a),X_54))) ),[0,0,0],$fot(compose(codomain(a),X_54))]]) ).
cnf(refute_0_40,plain,
( ifeq2(there_exists(compose(codomain(a),compose(codomain(a),X_54))),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) != codomain(compose(codomain(a),X_54))
| ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)) ),
inference(resolve,[$cnf( $equal(compose(codomain(a),compose(codomain(a),X_54)),compose(codomain(a),X_54)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),compose(codomain(a),X_54))),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),codomain(compose(codomain(a),X_54))) )],[refute_0_0,refute_0_40]) ).
cnf(refute_0_42,plain,
ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),
introduced(tautology,[refl,[$fot(ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))))]]) ).
cnf(refute_0_43,plain,
( domain(codomain(a)) != codomain(a)
| ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) != ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54)))
| ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54)))) ),[1,2],$fot(codomain(a))]]) ).
cnf(refute_0_44,plain,
( domain(codomain(a)) != codomain(a)
| ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))) ),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54)))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) = ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))),
inference(resolve,[$cnf( $equal(domain(codomain(a)),codomain(a)) )],[refute_0_31,refute_0_44]) ).
cnf(refute_0_46,plain,
( ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) != codomain(compose(codomain(a),X_54))
| ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) != ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54)))
| ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),codomain(compose(codomain(a),X_54))) ),[0],$fot(ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))))]]) ).
cnf(refute_0_47,plain,
( ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))) != codomain(compose(codomain(a),X_54))
| ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)) ),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
ifeq2(there_exists(compose(codomain(a),X_54)),true,codomain(a),codomain(compose(codomain(a),X_54))) = codomain(compose(codomain(a),X_54)),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),X_54)),true,domain(codomain(a)),codomain(compose(codomain(a),X_54))),codomain(compose(codomain(a),X_54))) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
ifeq2(there_exists(compose(codomain(a),compose(a,X_61))),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = codomain(compose(codomain(a),compose(a,X_61))),
inference(subst,[],[refute_0_48:[bind(X_54,$fot(compose(a,X_61)))]]) ).
cnf(refute_0_50,plain,
compose(codomain(X_48),compose(X_48,X_49)) = compose(compose(codomain(X_48),X_48),X_49),
inference(subst,[],[associativity_of_compose:[bind(X,$fot(codomain(X_48))),bind(Y,$fot(X_48)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_51,plain,
compose(codomain(X_48),X_48) = X_48,
inference(subst,[],[compose_codomain:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_52,plain,
( compose(codomain(X_48),X_48) != X_48
| compose(codomain(X_48),compose(X_48,X_49)) != compose(compose(codomain(X_48),X_48),X_49)
| compose(codomain(X_48),compose(X_48,X_49)) = compose(X_48,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(compose(codomain(X_48),compose(X_48,X_49)),compose(compose(codomain(X_48),X_48),X_49)) ),[1,0],$fot(X_48)]]) ).
cnf(refute_0_53,plain,
( compose(codomain(X_48),compose(X_48,X_49)) != compose(compose(codomain(X_48),X_48),X_49)
| compose(codomain(X_48),compose(X_48,X_49)) = compose(X_48,X_49) ),
inference(resolve,[$cnf( $equal(compose(codomain(X_48),X_48),X_48) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
compose(codomain(X_48),compose(X_48,X_49)) = compose(X_48,X_49),
inference(resolve,[$cnf( $equal(compose(codomain(X_48),compose(X_48,X_49)),compose(compose(codomain(X_48),X_48),X_49)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
compose(codomain(a),compose(a,X_61)) = compose(a,X_61),
inference(subst,[],[refute_0_54:[bind(X_48,$fot(a)),bind(X_49,$fot(X_61))]]) ).
cnf(refute_0_56,plain,
( compose(codomain(a),compose(a,X_61)) != compose(a,X_61)
| ifeq2(there_exists(compose(codomain(a),compose(a,X_61))),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = codomain(compose(codomain(a),compose(a,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),compose(a,X_61))),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),codomain(compose(codomain(a),compose(a,X_61)))) ),[0,0,0],$fot(compose(a,X_61))]]) ).
cnf(refute_0_57,plain,
( ifeq2(there_exists(compose(codomain(a),compose(a,X_61))),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = codomain(compose(codomain(a),compose(a,X_61))) ),
inference(resolve,[$cnf( $equal(compose(codomain(a),compose(a,X_61)),compose(a,X_61)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = codomain(compose(codomain(a),compose(a,X_61))),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(codomain(a),compose(a,X_61))),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),codomain(compose(codomain(a),compose(a,X_61)))) )],[refute_0_49,refute_0_57]) ).
cnf(refute_0_59,plain,
codomain(compose(codomain(a),compose(a,X_61))) = codomain(compose(codomain(a),compose(a,X_61))),
introduced(tautology,[refl,[$fot(codomain(compose(codomain(a),compose(a,X_61))))]]) ).
cnf(refute_0_60,plain,
( codomain(compose(codomain(a),compose(a,X_61))) != codomain(compose(codomain(a),compose(a,X_61)))
| compose(codomain(a),compose(a,X_61)) != compose(a,X_61)
| codomain(compose(codomain(a),compose(a,X_61))) = codomain(compose(a,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(codomain(compose(codomain(a),compose(a,X_61))),codomain(compose(codomain(a),compose(a,X_61)))) ),[1,0],$fot(compose(a,X_61))]]) ).
cnf(refute_0_61,plain,
( compose(codomain(a),compose(a,X_61)) != compose(a,X_61)
| codomain(compose(codomain(a),compose(a,X_61))) = codomain(compose(a,X_61)) ),
inference(resolve,[$cnf( $equal(codomain(compose(codomain(a),compose(a,X_61))),codomain(compose(codomain(a),compose(a,X_61)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
codomain(compose(codomain(a),compose(a,X_61))) = codomain(compose(a,X_61)),
inference(resolve,[$cnf( $equal(compose(codomain(a),compose(a,X_61)),compose(a,X_61)) )],[refute_0_55,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),
introduced(tautology,[refl,[$fot(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))))]]) ).
cnf(refute_0_64,plain,
( codomain(compose(codomain(a),compose(a,X_61))) != codomain(compose(a,X_61))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61))))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61))))) ),[1,3],$fot(codomain(compose(a,X_61)))]]) ).
cnf(refute_0_65,plain,
( codomain(compose(codomain(a),compose(a,X_61))) != codomain(compose(a,X_61))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) ),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61))))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) = ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))),
inference(resolve,[$cnf( $equal(codomain(compose(codomain(a),compose(a,X_61))),codomain(compose(a,X_61))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) = codomain(compose(codomain(a),compose(a,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),codomain(compose(codomain(a),compose(a,X_61)))) ),[0],$fot(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))))]]) ).
cnf(refute_0_68,plain,
( ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) = codomain(compose(codomain(a),compose(a,X_61))) ),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( codomain(compose(codomain(a),compose(a,X_61))) != codomain(compose(a,X_61))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) = codomain(compose(a,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))),codomain(compose(codomain(a),compose(a,X_61)))) ),[1],$fot(codomain(compose(a,X_61)))]]) ).
cnf(refute_0_70,plain,
( ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) = codomain(compose(a,X_61)) ),
inference(resolve,[$cnf( $equal(codomain(compose(codomain(a),compose(a,X_61))),codomain(compose(a,X_61))) )],[refute_0_62,refute_0_69]) ).
cnf(refute_0_71,plain,
( ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))) != codomain(compose(codomain(a),compose(a,X_61)))
| ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) = codomain(compose(a,X_61)) ),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))),codomain(compose(codomain(a),compose(a,X_61)))) )],[refute_0_68,refute_0_70]) ).
cnf(refute_0_72,plain,
ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(a,X_61))) = codomain(compose(a,X_61)),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(a,X_61)),true,codomain(a),codomain(compose(codomain(a),compose(a,X_61)))),codomain(compose(codomain(a),compose(a,X_61)))) )],[refute_0_58,refute_0_71]) ).
cnf(refute_0_73,plain,
ifeq2(there_exists(compose(a,b)),true,codomain(a),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(subst,[],[refute_0_72:[bind(X_61,$fot(b))]]) ).
cnf(refute_0_74,plain,
( ifeq2(there_exists(compose(a,b)),true,codomain(a),codomain(compose(a,b))) != codomain(compose(a,b))
| there_exists(compose(a,b)) != true
| ifeq2(true,true,codomain(a),codomain(compose(a,b))) = codomain(compose(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(there_exists(compose(a,b)),true,codomain(a),codomain(compose(a,b))),codomain(compose(a,b))) ),[0,0],$fot(true)]]) ).
cnf(refute_0_75,plain,
( ifeq2(there_exists(compose(a,b)),true,codomain(a),codomain(compose(a,b))) != codomain(compose(a,b))
| ifeq2(true,true,codomain(a),codomain(compose(a,b))) = codomain(compose(a,b)) ),
inference(resolve,[$cnf( $equal(there_exists(compose(a,b)),true) )],[ab_exists,refute_0_74]) ).
cnf(refute_0_76,plain,
ifeq2(true,true,codomain(a),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(resolve,[$cnf( $equal(ifeq2(there_exists(compose(a,b)),true,codomain(a),codomain(compose(a,b))),codomain(compose(a,b))) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
ifeq2(true,true,codomain(a),codomain(compose(a,b))) = codomain(a),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(codomain(a))),bind(C,$fot(codomain(compose(a,b))))]]) ).
cnf(refute_0_78,plain,
( ifeq2(true,true,codomain(a),codomain(compose(a,b))) != codomain(a)
| ifeq2(true,true,codomain(a),codomain(compose(a,b))) != codomain(compose(a,b))
| codomain(a) = codomain(compose(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,codomain(a),codomain(compose(a,b))),codomain(compose(a,b))) ),[0],$fot(codomain(a))]]) ).
cnf(refute_0_79,plain,
( ifeq2(true,true,codomain(a),codomain(compose(a,b))) != codomain(compose(a,b))
| codomain(a) = codomain(compose(a,b)) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,codomain(a),codomain(compose(a,b))),codomain(a)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
codomain(a) = codomain(compose(a,b)),
inference(resolve,[$cnf( $equal(ifeq2(true,true,codomain(a),codomain(compose(a,b))),codomain(compose(a,b))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_82,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_83,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( codomain(a) != codomain(compose(a,b))
| codomain(compose(a,b)) = codomain(a) ),
inference(subst,[],[refute_0_83:[bind(X0,$fot(codomain(a))),bind(Y0,$fot(codomain(compose(a,b))))]]) ).
cnf(refute_0_85,plain,
codomain(a) != codomain(compose(a,b)),
inference(resolve,[$cnf( $equal(codomain(compose(a,b)),codomain(a)) )],[refute_0_84,prove_codomain_of_ab_equals_codomain_of_a]) ).
cnf(refute_0_86,plain,
$false,
inference(resolve,[$cnf( $equal(codomain(a),codomain(compose(a,b))) )],[refute_0_80,refute_0_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.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 : 600
% 0.13/0.34 % DateTime : Sun May 29 22:26:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.77
% 0.60/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.78
%------------------------------------------------------------------------------