%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT013-1 : 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 01:00:40 PM UTC 2026
% Result : Unsatisfiable 5.14s 1.20s
% Output : Proof 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 27 unt; 0 def)
% Number of atoms : 51 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 48 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity1) ).
fof(f15_nnf,plain,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(defined(X0,X1),true,ifeq(identity_map(X0),true,product(X0,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f11,axiom,
defined(X,domain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
fof(f11_nnf,plain,
! [X] : defined(X,domain(X)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : defined(X,domain(X)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
defined(X0,domain(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
defined(X0,domain(X0)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f10,axiom,
identity_map(codomain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
fof(f10_nnf,plain,
! [X] : identity_map(codomain(X)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : identity_map(codomain(X)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
identity_map(codomain(X0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
identity_map(codomain(X0)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h0,plain,
product(codomain(V0),domain(codomain(V0)),domain(codomain(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi11,hi10]) ).
cnf(f17,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f17_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f13,axiom,
product(X,domain(X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_domain) ).
fof(f13_nnf,plain,
! [X] : product(X,domain(X),X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : product(X,domain(X),X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
product(X0,domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
product(X0,domain(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t4,plain,
domain(codomain(X1)) = codomain(X1),
inference(hyper_resolution,[status(thm)],[hi17,hi13,h0]) ).
cnf(t417,plain,
domain(codomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t4]) ).
cnf(f18,negated_conjecture,
domain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox2/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,t417]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 06:56:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.14/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.14/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------