%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT016-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 2.96s 0.87s
% Output : Proof 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 51 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 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 : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 35 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f17,hypothesis,
there_exists(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_a_exists) ).
fof(f17_nnf,plain,
there_exists(a),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(a),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
there_exists(a) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
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(hi9,axiom,
compose(X0,domain(X0)) = X0,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h0,plain,
equivalent(a,compose(a,domain(a))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi17,hi9]) ).
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(h1,plain,
there_exists(compose(a,domain(a))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h0]) ).
cnf(f5,axiom,
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/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(hi5,axiom,
ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t7,plain,
there_exists(domain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h1]) ).
cnf(t35,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f18,negated_conjecture,
~ there_exists(domain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_exists) ).
fof(f18_nnf,plain,
~ there_exists(domain(a)),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ there_exists(domain(a)),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ there_exists(domain(a)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
there_exists(domain(a)) != true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t35]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT016-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:00:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.96/0.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.96/0.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------