%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:07:25 PM UTC 2026
% Result : Unsatisfiable 0.17s 6.13s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 27 unt; 0 def)
% Number of atoms : 138 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 146 ( 74 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 113 ( 113 !; 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(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(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(f10,axiom,
! [X] : identity_map(domain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : defined(X,domain(X)),
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,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [X,W,Y] :
( X = Y
| ~ product(Y,c,W)
| ~ product(X,c,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(h,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(g,a,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(f27,plain,
! [Y,Z] :
( defined(Y,Z)
| ! [Xy] :
( ~ defined(Xy,Z)
| ! [X] : ~ product(X,Y,Xy) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
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(f37,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(f38,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)],[f37]) ).
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(f41,plain,
! [X0] : identity_map(domain(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
! [X0] : defined(X0,domain(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f48,plain,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
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,
! [X,Y] :
( X = Y
| ! [W] :
( ~ product(Y,c,W)
| ~ product(X,c,W) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ product(X2,c,X1)
| ~ product(X0,c,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
product(h,a,d),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f55,plain,
product(g,a,d),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f56,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
defined(a,b),
inference(resolution,[status(thm)],[f26,f51]) ).
fof(f97,plain,
! [X0] :
( defined(a,X0)
| ~ defined(d,X0) ),
inference(resolution,[status(thm)],[f28,f55]) ).
fof(f102,plain,
! [X0,X1] :
( defined(g,X1)
| ~ defined(d,X0)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f30,f55]) ).
fof(f103,plain,
! [X0,X1] :
( defined(h,X1)
| ~ defined(d,X0)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f30,f54]) ).
fof(f111,plain,
defined(a,domain(d)),
inference(resolution,[status(thm)],[f97,f43]) ).
fof(f112,plain,
( product(a,domain(d),a)
| ~ identity_map(domain(d)) ),
inference(resolution,[status(thm)],[f111,f48]) ).
fof(f115,plain,
product(a,domain(d),a),
inference(forward_subsumption_resolution,[status(thm)],[f112,f41]) ).
fof(f118,plain,
! [X0] :
( defined(domain(d),X0)
| ~ defined(a,X0) ),
inference(resolution,[status(thm)],[f115,f28]) ).
fof(f122,plain,
( defined(g,c)
| ~ defined(d,b) ),
inference(resolution,[status(thm)],[f102,f51]) ).
fof(f132,plain,
defined(domain(d),b),
inference(resolution,[status(thm)],[f118,f59]) ).
fof(f139,plain,
( defined(h,c)
| ~ defined(d,b) ),
inference(resolution,[status(thm)],[f103,f51]) ).
fof(f220,plain,
! [X0,X1,X2] :
( product(X2,b,X1)
| ~ product(X0,a,X2)
| ~ product(X0,c,X1) ),
inference(resolution,[status(thm)],[f38,f51]) ).
fof(f411,plain,
! [X0,X1] :
( defined(X0,X1)
| ~ identity_map(domain(X0))
| ~ defined(domain(X0),X1) ),
inference(resolution,[status(thm)],[f40,f43]) ).
fof(f420,plain,
! [X0,X1] :
( defined(X0,X1)
| ~ defined(domain(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f41]) ).
fof(f745,plain,
defined(d,b),
inference(resolution,[status(thm)],[f420,f132]) ).
fof(f750,plain,
defined(h,c),
inference(backward_subsumption_resolution,[status(thm)],[f139,f745]) ).
fof(f751,plain,
defined(g,c),
inference(backward_subsumption_resolution,[status(thm)],[f122,f745]) ).
fof(f766,plain,
product(h,c,compose(h,c)),
inference(resolution,[status(thm)],[f750,f24]) ).
fof(f773,plain,
product(g,c,compose(g,c)),
inference(resolution,[status(thm)],[f751,f24]) ).
fof(f4328,plain,
! [X0] :
( product(X0,b,compose(h,c))
| ~ product(h,a,X0) ),
inference(resolution,[status(thm)],[f766,f220]) ).
fof(f4329,plain,
! [X0] :
( h = X0
| ~ product(X0,c,compose(h,c)) ),
inference(resolution,[status(thm)],[f766,f53]) ).
fof(f4345,plain,
! [X0] :
( product(X0,b,compose(g,c))
| ~ product(g,a,X0) ),
inference(resolution,[status(thm)],[f773,f220]) ).
fof(f11430,plain,
product(d,b,compose(h,c)),
inference(resolution,[status(thm)],[f4328,f54]) ).
fof(f11450,plain,
! [X0] :
( compose(h,c) = X0
| ~ product(d,b,X0) ),
inference(resolution,[status(thm)],[f11430,f50]) ).
fof(f11759,plain,
product(d,b,compose(g,c)),
inference(resolution,[status(thm)],[f4345,f55]) ).
fof(f11762,plain,
compose(h,c) = compose(g,c),
inference(resolution,[status(thm)],[f11759,f11450]) ).
fof(f11818,plain,
product(g,c,compose(h,c)),
inference(backward_demodulation,[status(thm)],[f11762,f773]) ).
fof(f11821,plain,
h = g,
inference(resolution,[status(thm)],[f11818,f4329]) ).
fof(f11840,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11821,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n013.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 21 13:55:11 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.17/5.40 % Drodi V4.1.1
% 0.17/6.13 % Refutation found
% 0.17/6.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/6.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.50/6.15 % Elapsed time: 0.743486 seconds
% 0.50/6.15 % CPU time: 5.612776 seconds
% 0.50/6.15 % Total memory used: 72.245 MB
% 0.50/6.15 % Net memory used: 65.749 MB
%------------------------------------------------------------------------------