%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.22s 0.94s
% Output : CNFRefutation 0.22s
% 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(f3,axiom,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ 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(f19,hypothesis,
! [X,W,Y] :
( X = Y
| ~ product(a,Y,W)
| ~ product(a,X,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [X,W,Y] :
( X = Y
| ~ product(b,Y,W)
| ~ product(b,X,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(c,h,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
product(c,g,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(f28,plain,
! [Y,Z] :
( defined(Y,Z)
| ! [Xy] :
( ~ defined(Xy,Z)
| ! [X] : ~ product(X,Y,Xy) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,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(f33,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)],[f32]) ).
fof(f52,plain,
! [X,Y] :
( X = Y
| ! [W] :
( ~ product(a,Y,W)
| ~ product(a,X,W) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ product(a,X2,X1)
| ~ product(a,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X,Y] :
( X = Y
| ! [W] :
( ~ product(b,Y,W)
| ~ product(b,X,W) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f55,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ product(b,X2,X1)
| ~ product(b,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
product(c,h,d),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
product(c,g,d),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
h != g,
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
defined(c,g),
inference(resolution,[status(thm)],[f27,f58]) ).
fof(f65,plain,
defined(c,h),
inference(resolution,[status(thm)],[f27,f57]) ).
fof(f98,plain,
! [X0] :
( defined(b,X0)
| ~ defined(c,X0) ),
inference(resolution,[status(thm)],[f29,f56]) ).
fof(f109,plain,
! [X0,X1,X2] :
( product(a,X2,X1)
| ~ product(b,X0,X2)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f33,f56]) ).
fof(f146,plain,
defined(b,h),
inference(resolution,[status(thm)],[f98,f65]) ).
fof(f147,plain,
defined(b,g),
inference(resolution,[status(thm)],[f98,f64]) ).
fof(f151,plain,
product(b,h,compose(b,h)),
inference(resolution,[status(thm)],[f146,f25]) ).
fof(f154,plain,
product(b,g,compose(b,g)),
inference(resolution,[status(thm)],[f147,f25]) ).
fof(f1067,plain,
! [X0] :
( product(a,X0,d)
| ~ product(b,g,X0) ),
inference(resolution,[status(thm)],[f109,f58]) ).
fof(f1068,plain,
! [X0] :
( product(a,X0,d)
| ~ product(b,h,X0) ),
inference(resolution,[status(thm)],[f109,f57]) ).
fof(f1681,plain,
product(a,compose(b,h),d),
inference(resolution,[status(thm)],[f151,f1068]) ).
fof(f1683,plain,
! [X0] :
( h = X0
| ~ product(b,X0,compose(b,h)) ),
inference(resolution,[status(thm)],[f151,f55]) ).
fof(f1705,plain,
product(a,compose(b,g),d),
inference(resolution,[status(thm)],[f154,f1067]) ).
fof(f5156,plain,
! [X0] :
( compose(b,h) = X0
| ~ product(a,X0,d) ),
inference(resolution,[status(thm)],[f1681,f53]) ).
fof(f8058,plain,
compose(b,h) = compose(b,g),
inference(resolution,[status(thm)],[f5156,f1705]) ).
fof(f8075,plain,
product(b,g,compose(b,h)),
inference(backward_demodulation,[status(thm)],[f8058,f154]) ).
fof(f8077,plain,
h = g,
inference(resolution,[status(thm)],[f8075,f1683]) ).
fof(f8100,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8077,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.67 % Computer : n026.cluster.edu
% 0.19/0.67 % Model : x86_64 x86_64
% 0.19/0.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.67 % Memory : 8046.5625MB
% 0.19/0.67 % OS : Linux 6.8.0-71-generic
% 0.19/0.67 % CPULimit : 300
% 0.19/0.67 % WCLimit : 300
% 0.19/0.67 % DateTime : Mon Sep 21 13:57:53 UTC 2026
% 0.19/0.67 % CPUTime :
% 0.19/0.68 % Drodi V4.1.1
% 0.22/0.94 % Refutation found
% 0.22/0.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/0.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.99 % Elapsed time: 0.298133 seconds
% 0.22/0.99 % CPU time: 2.052568 seconds
% 0.22/0.99 % Total memory used: 58.064 MB
% 0.22/0.99 % Net memory used: 55.657 MB
%------------------------------------------------------------------------------