%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT014-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 01:00:41 PM UTC 2026
% Result : Unsatisfiable 10.48s 7.02s
% Output : Proof 10.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 21 unt; 0 def)
% Number of atoms : 41 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
compose(codomain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f10_nnf,plain,
! [X] : compose(codomain(X),X) = X,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : compose(codomain(X),X) = X,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f6,axiom,
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f6_nnf,plain,
! [X,Y] :
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p39,plain,
( domain(codomain(X0)) = codomain(X0)
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c10,c6]) ).
cnf(f4,axiom,
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f4_nnf,plain,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f17,hypothesis,
there_exists(codomain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_codomain_exists) ).
fof(f17_nnf,plain,
there_exists(codomain(a)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(codomain(a)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p19,plain,
there_exists(a),
inference(resolution,[status(thm)],[c4,c17]) ).
cnf(p406,plain,
domain(codomain(a)) = codomain(a),
inference(resolution,[status(thm)],[p39,p19]) ).
cnf(f9,axiom,
compose(X,domain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f9_nnf,plain,
! [X] : compose(X,domain(X)) = X,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : compose(X,domain(X)) = X,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
compose(X0,domain(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p38,plain,
( domain(X0) = codomain(domain(X0))
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c9,c6]) ).
cnf(p316,plain,
domain(codomain(a)) = codomain(domain(codomain(a))),
inference(resolution,[status(thm)],[p38,c17]) ).
cnf(p441,plain,
codomain(a) = codomain(codomain(a)),
inference(demodulation,[status(thm)],[p406,p316]) ).
cnf(f18,negated_conjecture,
codomain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
fof(f18_nnf,plain,
codomain(codomain(a)) != codomain(a),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
codomain(codomain(a)) != codomain(a),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
codomain(codomain(a)) != codomain(a),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p593,plain,
codomain(a) != codomain(a),
inference(superposition,[status(thm)],[p441,c18]) ).
cnf(p597,plain,
$false,
inference(equality_resolution,[status(thm)],[p593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT014-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.40 % Computer : n004.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Fri Sep 25 06:56:27 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.48/7.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.48/7.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------