%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : CAT010-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 : Tue Jul 15 06:16:19 AM UTC 2025
% Result : Unsatisfiable 37.11s 37.26s
% Output : CNFRefutation 37.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 14 RR)
% Number of literals : 31 ( 30 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
cnf(c2,axiom,
compose(codomain(X),X) = X,
file('theBenchmark.p',compose_codomain) ).
cnf(c3,axiom,
there_exists(compose(a,b)) = true,
file('theBenchmark.p',ab_exists) ).
cnf(c4,axiom,
ifeq2(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c6,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom_002) ).
cnf(c7,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('theBenchmark.p',associativity_of_compose) ).
cnf(c8,plain,
compose(compose(X,Y),Z) = compose(X,compose(Y,Z)),
inference(equational,[status(thm)],[c7]) ).
cnf(c12,plain,
compose(codomain(X),compose(X,Y)) = compose(X,Y),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c17,axiom,
ifeq(there_exists(X),true,equivalent(X,X),true) = true,
file('theBenchmark.p',existence_and_equality_implies_equivalence1) ).
cnf(c18,plain,
true = equivalent(compose(a,b),compose(a,b)),
inference(equational,[status(thm)],[c3,c6,c17]) ).
cnf(c19,axiom,
ifeq(there_exists(codomain(X)),true,there_exists(X),true) = true,
file('theBenchmark.p',codomain_has_elements) ).
cnf(c20,plain,
ifeq(there_exists(codomain(X)),equivalent(compose(a,b),compose(a,b)),there_exists(X),equivalent(compose(a,b),compose(a,b))) = equivalent(compose(a,b),compose(a,b)),
inference(equational,[status(thm)],[c18,c19]) ).
cnf(c21,axiom,
ifeq(there_exists(domain(X)),true,there_exists(X),true) = true,
file('theBenchmark.p',domain_has_elements) ).
cnf(c22,plain,
ifeq(there_exists(domain(X)),equivalent(compose(a,b),compose(a,b)),there_exists(X),equivalent(compose(a,b),compose(a,b))) = equivalent(compose(a,b),compose(a,b)),
inference(equational,[status(thm)],[c18,c21]) ).
cnf(c29,axiom,
ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true,
file('theBenchmark.p',composition_implies_domain) ).
cnf(c30,plain,
ifeq(there_exists(compose(X,Y)),equivalent(compose(a,b),compose(a,b)),there_exists(domain(X)),equivalent(compose(a,b),compose(a,b))) = equivalent(compose(a,b),compose(a,b)),
inference(equational,[status(thm)],[c18,c29]) ).
cnf(c31,plain,
there_exists(domain(a)) = equivalent(compose(a,b),compose(a,b)),
inference(equational,[status(thm)],[c3,c6,c18,c30]) ).
cnf(c32,plain,
there_exists(a) = equivalent(compose(a,b),compose(a,b)),
inference(equational,[status(thm)],[c6,c22,c31]) ).
cnf(c33,plain,
equivalent(compose(a,b),compose(a,b)) = equivalent(domain(a),domain(a)),
inference(equational,[status(thm)],[c6,c17,c18,c31]) ).
cnf(c34,plain,
equivalent(domain(a),domain(a)) = equivalent(a,a),
inference(equational,[status(thm)],[c6,c17,c18,c32,c33]) ).
cnf(c35,axiom,
ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y),
file('theBenchmark.p',domain_codomain_composition1) ).
cnf(c36,plain,
ifeq2(there_exists(compose(X,Y)),equivalent(a,a),domain(X),codomain(Y)) = codomain(Y),
inference(equational,[status(thm)],[c18,c33,c34,c35]) ).
cnf(c37,plain,
codomain(b) = domain(a),
inference(equational,[status(thm)],[c3,c4,c18,c33,c34,c36]) ).
cnf(c38,plain,
there_exists(b) = equivalent(a,a),
inference(equational,[status(thm)],[c6,c20,c31,c33,c34,c37]) ).
cnf(c41,plain,
equivalent(a,a) = equivalent(b,b),
inference(equational,[status(thm)],[c6,c17,c18,c33,c34,c38]) ).
cnf(c68,plain,
ifeq2(there_exists(X),equivalent(b,b),domain(codomain(X)),codomain(X)) = codomain(X),
inference(equational,[status(thm)],[c2,c36,c41]) ).
cnf(c69,plain,
domain(codomain(a)) = codomain(a),
inference(equational,[status(thm)],[c4,c32,c33,c34,c41,c68]) ).
cnf(c711,plain,
ifeq2(there_exists(compose(X,Y)),equivalent(b,b),domain(codomain(X)),codomain(compose(X,Y))) = codomain(compose(X,Y)),
inference(equational,[status(thm)],[c12,c36,c41]) ).
cnf(c712,plain,
codomain(compose(a,b)) = codomain(a),
inference(equational,[status(thm)],[c3,c4,c18,c33,c34,c41,c69,c711]) ).
cnf(g1,plain,
codomain(compose(a,b)) = codomain(a),
inference(equational,[status(thm)],[c712]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-10 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n001.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 : Mon Jul 14 04:38:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 37.11/37.26 % SZS status Unsatisfiable
% 37.11/37.26 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------