%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:06:17 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.74s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 18 unt; 0 def)
% Number of atoms : 57 ( 5 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 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 : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ product(x,x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,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(f33,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)],[f32]) ).
fof(f48,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f52,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
~ product(x,x,x),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f68,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f124,plain,
! [X0,X1,X2,X3,X4] :
( sum(additive_identity,X2,X4)
| ~ product(X0,X3,X4)
| ~ sum(inverse(X0),X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f51]) ).
fof(f226,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f952,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,multiply(X1,X0),X3)
| ~ product(X0,X2,X3)
| ~ sum(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f124,f68]) ).
fof(f1245,plain,
! [X0,X1] :
( sum(additive_identity,multiply(X0,X0),X1)
| ~ product(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f952,f48]) ).
fof(f1264,plain,
! [X0] : sum(additive_identity,multiply(X0,X0),X0),
inference(resolution,[status(thm)],[f1245,f58]) ).
fof(f1275,plain,
! [X0] : multiply(X0,X0) = X0,
inference(resolution,[status(thm)],[f1264,f226]) ).
fof(f1320,plain,
! [X0] : product(X0,X0,X0),
inference(paramodulation,[status(thm)],[f1275,f68]) ).
fof(f1323,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f1320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n007.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 13:43:51 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.24/0.74 % Refutation found
% 0.24/0.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.78 % Elapsed time: 0.295235 seconds
% 0.24/0.78 % CPU time: 1.932597 seconds
% 0.24/0.78 % Total memory used: 52.733 MB
% 0.24/0.78 % Net memory used: 50.941 MB
%------------------------------------------------------------------------------