%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:07:26 PM UTC 2026
% Result : Unsatisfiable 5.04s 1.08s
% Output : CNFRefutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 20 unt; 0 def)
% Number of atoms : 82 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 41 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 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(f6,axiom,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Y,Z,Yz,X,Xyz,Xy] :
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
! [X,W,Y] :
( X = Y
| ~ product(Y,a,W)
| ~ product(X,a,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [X,W,Y] :
( X = Y
| ~ product(Y,b,W)
| ~ product(X,b,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(h,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
product(g,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X,Y] :
( defined(X,Y)
| ! [Z] : ~ product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f34,plain,
! [Y,X] :
( defined(X,Y)
| ! [Yz] :
( ~ defined(X,Yz)
| ! [Z] : ~ product(Y,Z,Yz) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [Z,Xyz,Xy] :
( product(Xy,Z,Xyz)
| ! [Y,X] :
( ~ product(X,Y,Xy)
| ! [Yz] :
( ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f52,plain,
! [X,Y] :
( X = Y
| ! [W] :
( ~ product(Y,a,W)
| ~ product(X,a,W) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ product(X2,a,X1)
| ~ product(X0,a,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X,Y] :
( X = Y
| ! [W] :
( ~ product(Y,b,W)
| ~ product(X,b,W) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f55,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ product(X2,b,X1)
| ~ product(X0,b,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
product(h,c,d),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
product(g,c,d),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f75,plain,
defined(h,c),
inference(resolution,[status(thm)],[f57,f27]) ).
fof(f84,plain,
defined(g,c),
inference(resolution,[status(thm)],[f58,f27]) ).
fof(f87,plain,
! [X0] :
( defined(X0,a)
| ~ defined(X0,c) ),
inference(resolution,[status(thm)],[f35,f56]) ).
fof(f108,plain,
! [X0,X1,X2] :
( product(X2,b,X1)
| ~ product(X0,a,X2)
| ~ product(X0,c,X1) ),
inference(resolution,[status(thm)],[f39,f56]) ).
fof(f241,plain,
defined(g,a),
inference(resolution,[status(thm)],[f87,f84]) ).
fof(f242,plain,
defined(h,a),
inference(resolution,[status(thm)],[f87,f75]) ).
fof(f248,plain,
product(g,a,compose(g,a)),
inference(resolution,[status(thm)],[f241,f25]) ).
fof(f259,plain,
product(h,a,compose(h,a)),
inference(resolution,[status(thm)],[f242,f25]) ).
fof(f581,plain,
! [X0] :
( product(X0,b,d)
| ~ product(g,a,X0) ),
inference(resolution,[status(thm)],[f108,f58]) ).
fof(f582,plain,
! [X0] :
( product(X0,b,d)
| ~ product(h,a,X0) ),
inference(resolution,[status(thm)],[f108,f57]) ).
fof(f3064,plain,
product(compose(g,a),b,d),
inference(resolution,[status(thm)],[f248,f581]) ).
fof(f3115,plain,
product(compose(h,a),b,d),
inference(resolution,[status(thm)],[f259,f582]) ).
fof(f3117,plain,
! [X0] :
( h = X0
| ~ product(X0,a,compose(h,a)) ),
inference(resolution,[status(thm)],[f259,f53]) ).
fof(f4323,plain,
! [X0] :
( compose(g,a) = X0
| ~ product(X0,b,d) ),
inference(resolution,[status(thm)],[f3064,f55]) ).
fof(f5856,plain,
compose(g,a) = compose(h,a),
inference(resolution,[status(thm)],[f4323,f3115]) ).
fof(f5875,plain,
product(g,a,compose(h,a)),
inference(backward_demodulation,[status(thm)],[f5856,f248]) ).
fof(f5880,plain,
h = g,
inference(resolution,[status(thm)],[f5875,f3117]) ).
fof(f5898,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5880,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:57:02 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 5.04/1.08 % Refutation found
% 5.04/1.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.04/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.04/1.09 % Elapsed time: 0.719136 seconds
% 5.04/1.09 % CPU time: 5.397285 seconds
% 5.04/1.09 % Total memory used: 74.156 MB
% 5.04/1.09 % Net memory used: 67.232 MB
%------------------------------------------------------------------------------