%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT017-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:00:43 PM UTC 2026
% Result : Unsatisfiable 4.07s 0.93s
% Output : Proof 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 32 unt; 0 def)
% Number of atoms : 48 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 32 ( 6 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t11,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t28,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t11]) ).
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(t13,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t25,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(orient,[status(thm)],[t13]) ).
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(t3,plain,
compose(codomain(X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t18,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t27,plain,
true = ifeq(there_exists(X1),true,there_exists(domain(codomain(X1))),true),
inference(cp,[status(thm)],[t25,t18]) ).
cnf(t238,plain,
ifeq(there_exists(X1),true,there_exists(domain(codomain(X1))),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f11,hypothesis,
there_exists(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_a_exists) ).
fof(f11_nnf,plain,
there_exists(a),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(a),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t0,plain,
there_exists(a) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t21,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t239,plain,
true = ifeq(true,true,there_exists(domain(codomain(a))),true),
inference(cp,[status(thm)],[t238,t21]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t283,plain,
true = there_exists(domain(codomain(a))),
inference(step,[status(thm)],[t239,t19]) ).
cnf(t246,plain,
there_exists(domain(codomain(a))) = true,
inference(orient,[status(thm)],[t283]) ).
cnf(t252,plain,
true = ifeq(true,true,there_exists(codomain(a)),true),
inference(cp,[status(thm)],[t28,t246]) ).
cnf(t284,plain,
true = there_exists(codomain(a)),
inference(step,[status(thm)],[t252,t19]) ).
cnf(t257,plain,
there_exists(codomain(a)) = true,
inference(orient,[status(thm)],[t284]) ).
cnf(f12,negated_conjecture,
~ there_exists(codomain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_exists) ).
fof(f12_nnf,plain,
~ there_exists(codomain(a)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ there_exists(codomain(a)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ there_exists(codomain(a)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
there_exists(codomain(a)) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t257]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT017-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 06:57:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.07/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.07/0.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------