%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT011-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:00:39 PM UTC 2026
% Result : Unsatisfiable 6.92s 1.49s
% Output : Proof 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 30 unt; 0 def)
% Number of atoms : 92 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 38 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
compose(X,domain(X)) = X,
file('/export/starexec/sandbox2/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(f6,axiom,
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/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(p37,plain,
( domain(X0) = codomain(domain(X0))
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c9,c6]) ).
cnf(f3,axiom,
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f3_nnf,plain,
! [X] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f17,hypothesis,
there_exists(domain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_domain_exists) ).
fof(f17_nnf,plain,
there_exists(domain(a)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(domain(a)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p19,plain,
there_exists(a),
inference(resolution,[status(thm)],[c3,c17]) ).
cnf(p358,plain,
domain(a) = codomain(domain(a)),
inference(resolution,[status(thm)],[p37,p19]) ).
cnf(f10,axiom,
compose(codomain(X),X) = X,
file('/export/starexec/sandbox2/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(f5,axiom,
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f5_nnf,plain,
! [X,Y] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p26,plain,
( there_exists(domain(codomain(X0)))
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c10,c5]) ).
cnf(p39,plain,
there_exists(domain(codomain(domain(a)))),
inference(resolution,[status(thm)],[p26,c17]) ).
cnf(p57,plain,
there_exists(codomain(domain(a))),
inference(resolution,[status(thm)],[p39,c3]) ).
cnf(f2,axiom,
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
fof(f2_nnf,plain,
! [X,Y] :
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( equivalent(X0,X1)
| X0 != X1
| ~ there_exists(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p20,plain,
( equivalent(X0,X0)
| ~ there_exists(X0) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p64,plain,
equivalent(codomain(domain(a)),codomain(domain(a))),
inference(resolution,[status(thm)],[p57,p20]) ).
cnf(p412,plain,
equivalent(codomain(domain(a)),domain(a)),
inference(superposition,[status(thm)],[p358,p64]) ).
cnf(f1,axiom,
( X = Y
| ~ equivalent(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
fof(f1_nnf,plain,
! [X,Y] :
( X = Y
| ~ equivalent(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( X = Y
| ~ equivalent(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = X1
| ~ equivalent(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p413,plain,
codomain(domain(a)) = domain(a),
inference(resolution,[status(thm)],[p412,c1]) ).
cnf(f13,axiom,
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_codomain) ).
fof(f13_nnf,plain,
! [X,Y] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( there_exists(codomain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p117,plain,
( there_exists(codomain(X0))
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c9,c13]) ).
cnf(p65,plain,
there_exists(domain(codomain(codomain(domain(a))))),
inference(resolution,[status(thm)],[p57,p26]) ).
cnf(p111,plain,
there_exists(codomain(codomain(domain(a)))),
inference(resolution,[status(thm)],[p65,c3]) ).
cnf(p157,plain,
there_exists(codomain(codomain(codomain(domain(a))))),
inference(resolution,[status(thm)],[p117,p111]) ).
cnf(p195,plain,
there_exists(codomain(codomain(codomain(codomain(domain(a)))))),
inference(resolution,[status(thm)],[p157,p117]) ).
cnf(p429,plain,
there_exists(codomain(codomain(codomain(domain(a))))),
inference(demodulation,[status(thm)],[p413,p195]) ).
cnf(p38,plain,
( domain(codomain(X0)) = codomain(X0)
| ~ there_exists(X0) ),
inference(superposition,[status(thm)],[c10,c6]) ).
cnf(p593,plain,
domain(domain(a)) = domain(a),
inference(resolution,[status(thm)],[p429,p38]) ).
cnf(f18,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
fof(f18_nnf,plain,
domain(domain(a)) != domain(a),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
domain(domain(a)) != domain(a),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
domain(domain(a)) != domain(a),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p594,plain,
domain(a) != domain(a),
inference(demodulation,[status(thm)],[p593,c18]) ).
cnf(p641,plain,
$false,
inference(equality_resolution,[status(thm)],[p594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT011-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 06:55:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.92/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.92/1.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------