%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT007-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 01:00:38 PM UTC 2026
% Result : Unsatisfiable 3.80s 0.94s
% Output : Proof 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 18 unt; 0 def)
% Number of atoms : 30 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 10 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y))
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f4_nnf,plain,
! [X,Y] :
( there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y))
| ~ there_exists(domain(X)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y))
| ~ there_exists(domain(X)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( there_exists(compose(X0,X1))
| ~ equalish(domain(X0),codomain(X1))
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(there_exists(domain(X0)),true,ifeq(equalish(domain(X0),codomain(X1)),true,there_exists(compose(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f8,hypothesis,
there_exists(domain(c2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_c2_exists) ).
fof(f8_nnf,plain,
there_exists(domain(c2)),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
there_exists(domain(c2)),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,axiom,
there_exists(domain(c2)) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f10,hypothesis,
equalish(domain(c2),codomain(c1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_c2_equals_codomain_of_c1) ).
fof(f10_nnf,plain,
equalish(domain(c2),codomain(c1)),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
equalish(domain(c2),codomain(c1)),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
equalish(domain(c2),codomain(c1)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t10,plain,
there_exists(compose(c2,c1)) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi8,hi10]) ).
cnf(t31,plain,
there_exists(compose(c2,c1)) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f11,negated_conjecture,
~ there_exists(compose(c2,c1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c1_c2_is_defined) ).
fof(f11_nnf,plain,
~ there_exists(compose(c2,c1)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ there_exists(compose(c2,c1)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ there_exists(compose(c2,c1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
there_exists(compose(c2,c1)) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t31]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 06:51:23 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.80/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.80/0.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------