%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT013-3 : 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 01:00:40 PM UTC 2026
% Result : Unsatisfiable 4.13s 0.92s
% Output : Proof 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 25 unt; 0 def)
% Number of atoms : 61 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 40 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(hi4,axiom,
ifeq(there_exists(codomain(X0)),true,there_exists(X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
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(hi17,axiom,
there_exists(codomain(a)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h0,plain,
there_exists(a) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi17]) ).
cnf(f2,axiom,
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
file('/export/starexec/sandbox/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(hi2,axiom,
ifeq(there_exists(X0),true,ifeq(X0,X1,equivalent(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
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(hi10,axiom,
compose(codomain(X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h7,plain,
equivalent(a,compose(codomain(a),a)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,hi10]) ).
cnf(f11,axiom,
( there_exists(Y)
| ~ equivalent(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
fof(f11_nnf,plain,
! [X,Y] :
( there_exists(Y)
| ~ equivalent(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( there_exists(Y)
| ~ equivalent(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( there_exists(X1)
| ~ equivalent(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(equivalent(X0,X1),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h34,plain,
there_exists(compose(codomain(a),a)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h7]) ).
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(hi6,axiom,
ifeq(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t11,plain,
domain(codomain(a)) = codomain(a),
inference(hyper_resolution,[status(thm)],[hi6,h34]) ).
cnf(t136,plain,
domain(codomain(a)) = codomain(a),
inference(orient,[status(thm)],[t11]) ).
cnf(f18,negated_conjecture,
domain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_codomain_is_codomain) ).
fof(f18_nnf,plain,
domain(codomain(a)) != codomain(a),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
domain(codomain(a)) != codomain(a),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
domain(codomain(a)) != codomain(a),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
domain(codomain(a)) != codomain(a),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
codomain(a) != codomain(a),
inference(rw,[status(thm)],[goal_0,t136]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 06:55:50 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.13/0.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.13/0.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------