%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 12:07:28 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 24 unt; 0 def)
% Number of atoms : 158 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 173 ( 88 ~; 85 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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; 0-2 aty)
% Number of variables : 150 ( 150 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( defined(X,Y)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Xy,Z,Yz] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : identity_map(domain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : identity_map(codomain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : defined(X,domain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : defined(codomain(X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : product(X,domain(X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] : product(codomain(X),X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
defined(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X,Y] :
( defined(X,Y)
| ! [Z] : ~ product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [Y,Z] :
( defined(Y,Z)
| ! [Xy] :
( ~ defined(Xy,Z)
| ! [X] : ~ product(X,Y,Xy) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X,Yz] :
( defined(X,Yz)
| ! [Xy,Z] :
( ~ defined(Xy,Z)
| ! [Y] :
( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4] :
( defined(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
! [Y,X] :
( defined(X,Y)
| ! [Yz] :
( ~ defined(X,Yz)
| ! [Z] : ~ product(Y,Z,Yz) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f38,plain,
! [X0] : identity_map(domain(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
! [X0] : identity_map(codomain(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
! [X0] : defined(X0,domain(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
! [X0] : defined(codomain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
! [X0] : product(X0,domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
! [X0] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
defined(b,a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
codomain(compose(b,a)) != codomain(b),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ defined(X0,X1)
| X2 = compose(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f21]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ identity_map(X1)
| ~ defined(X0,X1)
| X2 = X0
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f45]) ).
fof(f60,plain,
! [X0,X1,X2] :
( X2 = compose(X0,X1)
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f23]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ identity_map(X1)
| X2 = X0
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f23]) ).
fof(f71,plain,
! [X0] : X0 = compose(X0,domain(X0)),
inference(resolution,[status(thm)],[f60,f42]) ).
fof(f85,plain,
! [X0,X1] :
( ~ identity_map(X1)
| ~ defined(X1,X0)
| ~ identity_map(X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f61,f44]) ).
fof(f99,plain,
! [X0,X1] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f25,f42]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ defined(X0,X1)
| defined(X1,X2)
| ~ defined(compose(X0,X1),X2) ),
inference(resolution,[status(thm)],[f25,f21]) ).
fof(f103,plain,
! [X0,X1] :
( ~ identity_map(domain(X0))
| ~ identity_map(X1)
| X1 = domain(X0)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f99,f85]) ).
fof(f104,plain,
! [X0,X1] :
( ~ identity_map(X1)
| X1 = domain(X0)
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f38]) ).
fof(f109,plain,
! [X0,X1,X2] :
( defined(X0,X1)
| ~ defined(X2,X1)
| ~ product(X0,codomain(X1),X2) ),
inference(resolution,[status(thm)],[f27,f43]) ).
fof(f132,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f31,f43]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ defined(X1,X2)
| defined(X0,X1)
| ~ defined(X0,compose(X1,X2)) ),
inference(resolution,[status(thm)],[f31,f21]) ).
fof(f137,plain,
! [X0,X1] :
( ~ identity_map(codomain(X1))
| codomain(X1) = domain(X0)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f132,f104]) ).
fof(f138,plain,
! [X0,X1] :
( ~ identity_map(X0)
| ~ identity_map(codomain(X1))
| codomain(X1) = X0
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f132,f85]) ).
fof(f139,plain,
! [X0,X1] :
( codomain(X1) = domain(X0)
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f39]) ).
fof(f140,plain,
! [X0,X1] :
( ~ identity_map(X0)
| codomain(X1) = X0
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f39]) ).
fof(f147,plain,
! [X0,X1] :
( ~ defined(X1,X0)
| defined(X0,domain(compose(X1,X0))) ),
inference(resolution,[status(thm)],[f100,f40]) ).
fof(f152,plain,
! [X0,X1] :
( ~ identity_map(domain(compose(X0,X1)))
| domain(compose(X0,X1)) = domain(X1)
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f147,f104]) ).
fof(f156,plain,
! [X0,X1] :
( domain(compose(X0,X1)) = domain(X1)
| ~ defined(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f38]) ).
fof(f159,plain,
! [X0] :
( domain(X0) = domain(domain(X0))
| ~ defined(X0,domain(X0)) ),
inference(paramodulation,[status(thm)],[f71,f156]) ).
fof(f160,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f159,f40]) ).
fof(f163,plain,
! [X0,X1] :
( codomain(X1) = domain(X0)
| ~ defined(domain(X0),X1) ),
inference(paramodulation,[status(thm)],[f160,f139]) ).
fof(f219,plain,
! [X0] :
( defined(codomain(codomain(X0)),X0)
| ~ defined(codomain(X0),X0) ),
inference(resolution,[status(thm)],[f109,f43]) ).
fof(f223,plain,
! [X0] : defined(codomain(codomain(X0)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f219,f41]) ).
fof(f248,plain,
! [X0] :
( ~ identity_map(codomain(codomain(X0)))
| codomain(X0) = codomain(codomain(X0)) ),
inference(resolution,[status(thm)],[f223,f140]) ).
fof(f252,plain,
! [X0] : codomain(X0) = codomain(codomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f248,f39]) ).
fof(f260,plain,
! [X0,X1] :
( codomain(X1) = domain(X0)
| ~ defined(X0,codomain(X1)) ),
inference(paramodulation,[status(thm)],[f252,f139]) ).
fof(f267,plain,
! [X0] : defined(codomain(X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f252,f41]) ).
fof(f341,plain,
! [X0] : codomain(X0) = domain(codomain(X0)),
inference(resolution,[status(thm)],[f260,f267]) ).
fof(f355,plain,
! [X0,X1] :
( codomain(X1) = domain(codomain(X0))
| ~ defined(codomain(X0),X1) ),
inference(paramodulation,[status(thm)],[f341,f163]) ).
fof(f376,plain,
! [X0,X1] :
( codomain(X1) = codomain(X0)
| ~ defined(codomain(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f341,f355]) ).
fof(f1248,plain,
! [X0,X1] :
( ~ defined(X0,X1)
| defined(codomain(compose(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f134,f41]) ).
fof(f1279,plain,
! [X0,X1] :
( codomain(X0) = codomain(compose(X0,X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f1248,f376]) ).
fof(f1313,plain,
~ defined(b,a),
inference(resolution,[status(thm)],[f1279,f49]) ).
fof(f1318,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1313,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 : Mon Sep 21 13:55:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.14/0.53 % Refutation found
% 0.14/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.57 % Elapsed time: 0.195520 seconds
% 0.18/0.57 % CPU time: 1.318929 seconds
% 0.18/0.57 % Total memory used: 57.322 MB
% 0.18/0.57 % Net memory used: 54.911 MB
%------------------------------------------------------------------------------