%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 : Thu Sep 24 12:07:24 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.67s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 28 unt; 0 def)
% Number of atoms : 148 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 160 ( 81 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 129 ( 129 !; 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(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(f5,axiom,
! [X,Y,Xy,Z,Xyz,Yz] :
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ 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(f7,axiom,
! [Y,Z,Yz,X,Xy] :
( defined(Xy,Z)
| ~ defined(X,Yz)
| ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : identity_map(codomain(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(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,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [X1,X2,X3] :
( X1 = X3
| ~ product(c,X3,X2)
| ~ product(c,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(b,h,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(b,g,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X,Y] :
( defined(X,Y)
| ! [Z] : ~ product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f31,plain,
! [X,Xyz,Yz] :
( product(X,Yz,Xyz)
| ! [Y,Z] :
( ~ product(Y,Z,Yz)
| ! [Xy] :
( ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X5,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [Y,X] :
( defined(X,Y)
| ! [Yz] :
( ~ defined(X,Yz)
| ! [Z] : ~ product(Y,Z,Yz) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [Z,Xy] :
( defined(Xy,Z)
| ! [Yz,X] :
( ~ defined(X,Yz)
| ! [Y] :
( ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( defined(X4,X1)
| ~ defined(X3,X2)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [X,Z] :
( defined(X,Z)
| ! [Y] :
( ~ identity_map(Y)
| ~ defined(Y,Z)
| ~ defined(X,Y) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f40,plain,
! [X0,X1,X2] :
( defined(X0,X2)
| ~ identity_map(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0] : identity_map(codomain(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
! [X0] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f49,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
! [X1,X3] :
( X1 = X3
| ! [X2] :
( ~ product(c,X3,X2)
| ~ product(c,X1,X2) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ product(c,X2,X1)
| ~ product(c,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
product(b,h,d),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f55,plain,
product(b,g,d),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f56,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
defined(a,b),
inference(resolution,[status(thm)],[f51,f26]) ).
fof(f66,plain,
! [X0,X1,X2] :
( defined(codomain(X0),X2)
| ~ defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f46]) ).
fof(f68,plain,
! [X0,X1,X2] :
( defined(codomain(X0),X2)
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f66,f26]) ).
fof(f74,plain,
! [X0,X1,X2] :
( product(a,X2,X1)
| ~ product(b,X0,X2)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f32,f51]) ).
fof(f85,plain,
! [X0,X1] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(resolution,[status(thm)],[f34,f46]) ).
fof(f93,plain,
! [X0,X1] :
( defined(X1,g)
| ~ defined(X0,d)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f36,f55]) ).
fof(f94,plain,
! [X0,X1] :
( defined(X1,h)
| ~ defined(X0,d)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f36,f54]) ).
fof(f227,plain,
defined(codomain(b),d),
inference(resolution,[status(thm)],[f68,f55]) ).
fof(f284,plain,
defined(a,codomain(b)),
inference(resolution,[status(thm)],[f85,f64]) ).
fof(f312,plain,
! [X0] :
( defined(a,X0)
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),X0) ),
inference(resolution,[status(thm)],[f284,f40]) ).
fof(f316,plain,
! [X0] :
( defined(a,X0)
| ~ defined(codomain(b),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f42]) ).
fof(f414,plain,
( defined(c,g)
| ~ defined(a,d) ),
inference(resolution,[status(thm)],[f93,f51]) ).
fof(f450,plain,
( defined(c,h)
| ~ defined(a,d) ),
inference(resolution,[status(thm)],[f94,f51]) ).
fof(f2767,plain,
defined(a,d),
inference(resolution,[status(thm)],[f316,f227]) ).
fof(f2779,plain,
defined(c,h),
inference(backward_subsumption_resolution,[status(thm)],[f450,f2767]) ).
fof(f2780,plain,
defined(c,g),
inference(backward_subsumption_resolution,[status(thm)],[f414,f2767]) ).
fof(f2788,plain,
product(a,d,compose(a,d)),
inference(resolution,[status(thm)],[f2767,f24]) ).
fof(f2796,plain,
product(c,h,compose(c,h)),
inference(resolution,[status(thm)],[f2779,f24]) ).
fof(f2805,plain,
product(c,g,compose(c,g)),
inference(resolution,[status(thm)],[f2780,f24]) ).
fof(f4346,plain,
! [X0] :
( product(a,X0,compose(c,h))
| ~ product(b,h,X0) ),
inference(resolution,[status(thm)],[f2796,f74]) ).
fof(f4347,plain,
! [X0] :
( h = X0
| ~ product(c,X0,compose(c,h)) ),
inference(resolution,[status(thm)],[f2796,f53]) ).
fof(f4389,plain,
! [X0] :
( product(a,X0,compose(c,g))
| ~ product(b,g,X0) ),
inference(resolution,[status(thm)],[f2805,f74]) ).
fof(f4472,plain,
! [X0] :
( compose(a,d) = X0
| ~ product(a,d,X0) ),
inference(resolution,[status(thm)],[f2788,f50]) ).
fof(f10652,plain,
product(a,d,compose(c,h)),
inference(resolution,[status(thm)],[f4346,f54]) ).
fof(f10653,plain,
compose(a,d) = compose(c,h),
inference(resolution,[status(thm)],[f10652,f4472]) ).
fof(f10714,plain,
! [X0] :
( h = X0
| ~ product(c,X0,compose(a,d)) ),
inference(backward_demodulation,[status(thm)],[f10653,f4347]) ).
fof(f10826,plain,
product(a,d,compose(c,g)),
inference(resolution,[status(thm)],[f4389,f55]) ).
fof(f10827,plain,
compose(a,d) = compose(c,g),
inference(resolution,[status(thm)],[f10826,f4472]) ).
fof(f10891,plain,
product(c,g,compose(a,d)),
inference(backward_demodulation,[status(thm)],[f10827,f2805]) ).
fof(f10892,plain,
h = g,
inference(resolution,[status(thm)],[f10891,f10714]) ).
fof(f10915,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10892,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n008.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 13:55:45 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.67 % Refutation found
% 0.14/5.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.69 % Elapsed time: 0.292686 seconds
% 0.14/5.69 % CPU time: 2.112889 seconds
% 0.14/5.69 % Total memory used: 66.322 MB
% 0.14/5.69 % Net memory used: 61.475 MB
%------------------------------------------------------------------------------