%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:06:21 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.71s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 27 unt; 0 def)
% Number of atoms : 83 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 77 ( 40 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f41,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f60,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f62,plain,
! [X0] : product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f63,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f64,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f86,plain,
inverse(inverse(x)) != x,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f91,plain,
! [X0,X1] :
( X1 = additive_identity
| ~ product(inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f67,f62]) ).
fof(f101,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f40,f65]) ).
fof(f134,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f41,f65]) ).
fof(f194,plain,
! [X0] : multiply(inverse(X0),X0) = additive_identity,
inference(resolution,[status(thm)],[f37,f91]) ).
fof(f241,plain,
! [X0,X1,X2,X3,X4] :
( sum(X2,X3,X4)
| ~ product(X0,multiplicative_identity,X4)
| ~ product(X0,X1,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f45,f60]) ).
fof(f249,plain,
! [X0,X1,X2,X3] :
( sum(X2,X3,X0)
| ~ product(X0,X1,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f241,f43]) ).
fof(f259,plain,
! [X0,X1,X2] :
( sum(multiply(X0,inverse(X1)),X2,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f249,f37]) ).
fof(f299,plain,
! [X0] : sum(multiply(X0,inverse(inverse(X0))),additive_identity,X0),
inference(resolution,[status(thm)],[f259,f63]) ).
fof(f310,plain,
! [X0] : X0 = multiply(X0,inverse(inverse(X0))),
inference(resolution,[status(thm)],[f299,f134]) ).
fof(f333,plain,
! [X0] : product(X0,inverse(inverse(X0)),X0),
inference(paramodulation,[status(thm)],[f310,f37]) ).
fof(f342,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,inverse(inverse(X0)),X1) ),
inference(resolution,[status(thm)],[f333,f67]) ).
fof(f354,plain,
! [X0,X1] :
( ~ product(inverse(inverse(X1)),X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f342,f39]) ).
fof(f362,plain,
! [X0] : multiply(inverse(inverse(X0)),X0) = X0,
inference(resolution,[status(thm)],[f354,f37]) ).
fof(f373,plain,
! [X0] : product(inverse(inverse(X0)),X0,X0),
inference(paramodulation,[status(thm)],[f362,f37]) ).
fof(f644,plain,
! [X0] : sum(multiply(inverse(inverse(X0)),inverse(X0)),X0,inverse(inverse(X0))),
inference(resolution,[status(thm)],[f373,f259]) ).
fof(f660,plain,
! [X0] : sum(additive_identity,X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f194,f644]) ).
fof(f663,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[f660,f101]) ).
fof(f678,plain,
x != x,
inference(backward_demodulation,[status(thm)],[f663,f86]) ).
fof(f703,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.41 % Computer : n014.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Mon Sep 21 13:47:50 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.43 % Drodi V4.1.1
% 0.09/0.71 % Refutation found
% 0.09/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.55/0.75 % Elapsed time: 0.316231 seconds
% 1.55/0.75 % CPU time: 2.128671 seconds
% 1.55/0.75 % Total memory used: 53.970 MB
% 1.55/0.75 % Net memory used: 52.190 MB
%------------------------------------------------------------------------------