%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:36:23 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.24s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 40 RR)
% Number of literals : 60 ( 59 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 36 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
cnf(c2,axiom,
ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
cnf(c3,plain,
ifeq2(there_exists(compose(codomain(codomain(a)),compose(a,b))),true,domain(codomain(codomain(a))),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
codomain(compose(a,b)) = ifeq2(there_exists(compose(codomain(codomain(a)),compose(a,b))),true,domain(codomain(codomain(a))),codomain(compose(a,b))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
compose(X2,compose(Y2,Z)) = compose(compose(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
cnf(c6,plain,
compose(codomain(X3),compose(X3,X2)) = compose(compose(codomain(X3),X3),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
compose(codomain(X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
compose(compose(codomain(X3),X3),X2) = compose(X3,X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
compose(codomain(X3),compose(X3,X2)) = compose(X3,X2),
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
compose(X3,X2) = compose(codomain(X3),compose(X3,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
compose(codomain(codomain(X3)),compose(X3,X2)) = compose(codomain(codomain(X3)),compose(codomain(X3),compose(X3,X2))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
compose(codomain(codomain(X3)),compose(codomain(X3),compose(X3,X2))) = compose(codomain(X3),compose(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c13,plain,
compose(codomain(codomain(X3)),compose(codomain(X3),compose(X3,X2))) = compose(X3,X2),
inference(transitivity,[status(thm)],[c12,c9]) ).
cnf(c14,plain,
compose(codomain(codomain(X3)),compose(X3,X2)) = compose(X3,X2),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
compose(codomain(codomain(a)),compose(a,b)) = compose(a,b),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
there_exists(compose(codomain(codomain(a)),compose(a,b))) = there_exists(compose(a,b)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq2(there_exists(compose(codomain(codomain(a)),compose(a,b))),true,domain(codomain(codomain(a))),codomain(compose(a,b))) = ifeq2(there_exists(compose(a,b)),true,domain(codomain(codomain(a))),codomain(compose(a,b))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
ifeq2(there_exists(compose(a,b)),true,domain(codomain(codomain(a))),codomain(compose(a,b))) = ifeq2(true,true,domain(codomain(codomain(a))),codomain(compose(a,b))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c21,plain,
ifeq2(true,true,domain(codomain(codomain(a))),codomain(compose(a,b))) = domain(codomain(codomain(a))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq2(true,true,domain(codomain(codomain(a))),codomain(a)) = domain(codomain(codomain(a))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c23,plain,
domain(codomain(codomain(a))) = ifeq2(true,true,domain(codomain(codomain(a))),codomain(a)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(c25,plain,
ifeq(true,true,there_exists(a),true) = there_exists(a),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
there_exists(a) = ifeq(true,true,there_exists(a),true),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(true,true,there_exists(domain(a)),true) = there_exists(domain(a)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c28,plain,
there_exists(domain(a)) = ifeq(true,true,there_exists(domain(a)),true),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
true = there_exists(compose(a,b)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c30,plain,
ifeq(true,true,there_exists(domain(a)),true) = ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
ifeq(there_exists(compose(X2,Y2)),true,there_exists(domain(X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
cnf(c32,plain,
ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) = true,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(true,true,there_exists(domain(a)),true) = true,
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
there_exists(domain(a)) = true,
inference(transitivity,[status(thm)],[c28,c33]) ).
cnf(c35,plain,
true = there_exists(domain(a)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(true,true,there_exists(a),true) = ifeq(there_exists(domain(a)),true,there_exists(a),true),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
ifeq(there_exists(domain(X2)),true,there_exists(X2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
cnf(c38,plain,
ifeq(there_exists(domain(a)),true,there_exists(a),true) = true,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq(true,true,there_exists(a),true) = true,
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
there_exists(a) = true,
inference(transitivity,[status(thm)],[c26,c39]) ).
cnf(c41,plain,
true = there_exists(a),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq2(true,true,domain(codomain(codomain(a))),codomain(a)) = ifeq2(there_exists(a),true,domain(codomain(codomain(a))),codomain(a)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
X2 = compose(codomain(X2),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c44,plain,
compose(codomain(codomain(X2)),X2) = compose(codomain(codomain(X2)),compose(codomain(X2),X2)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
compose(codomain(codomain(X2)),compose(codomain(X2),X2)) = compose(codomain(X2),X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c46,plain,
compose(codomain(codomain(X2)),compose(codomain(X2),X2)) = X2,
inference(transitivity,[status(thm)],[c45,c7]) ).
cnf(c47,plain,
compose(codomain(codomain(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
compose(codomain(codomain(a)),a) = a,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
a = compose(codomain(codomain(a)),a),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
there_exists(a) = there_exists(compose(codomain(codomain(a)),a)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq2(there_exists(a),true,domain(codomain(codomain(a))),codomain(a)) = ifeq2(there_exists(compose(codomain(codomain(a)),a)),true,domain(codomain(codomain(a))),codomain(a)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq2(there_exists(compose(codomain(codomain(a)),a)),true,domain(codomain(codomain(a))),codomain(a)) = codomain(a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
ifeq2(there_exists(a),true,domain(codomain(codomain(a))),codomain(a)) = codomain(a),
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
ifeq2(true,true,domain(codomain(codomain(a))),codomain(a)) = codomain(a),
inference(transitivity,[status(thm)],[c42,c53]) ).
cnf(c55,plain,
domain(codomain(codomain(a))) = codomain(a),
inference(transitivity,[status(thm)],[c23,c54]) ).
cnf(c56,plain,
ifeq2(true,true,domain(codomain(codomain(a))),codomain(compose(a,b))) = codomain(a),
inference(transitivity,[status(thm)],[c21,c55]) ).
cnf(c57,plain,
ifeq2(there_exists(compose(a,b)),true,domain(codomain(codomain(a))),codomain(compose(a,b))) = codomain(a),
inference(transitivity,[status(thm)],[c19,c56]) ).
cnf(c58,plain,
ifeq2(there_exists(compose(codomain(codomain(a)),compose(a,b))),true,domain(codomain(codomain(a))),codomain(compose(a,b))) = codomain(a),
inference(transitivity,[status(thm)],[c17,c57]) ).
cnf(c59,plain,
codomain(compose(a,b)) = codomain(a),
inference(transitivity,[status(thm)],[c4,c58]) ).
cnf(c60,plain,
$false,
inference(resolution,[status(thm)],[c1,c59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n002.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Mon Sep 28 21:15:51 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.24 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.09/0.24
% 0.09/0.24 % SZS status Unsatisfiable
% 0.09/0.24
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.52/0.27
% 0.52/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------