%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:04:45 PM UTC 2026
% Result : Unsatisfiable 35.77s 4.99s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 19 unt; 0 def)
% Number of atoms : 70 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 68 ( 35 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,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)],[f12]) ).
fof(f44,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)],[f43]) ).
fof(f53,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f59,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f60,plain,
sum(b,c,d),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
product(d,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
product(b,a,l),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f63,plain,
product(c,a,n),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
~ sum(l,n,additive_identity),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( sum(X1,X2,X3)
| ~ product(X0,d,X3)
| ~ product(X0,c,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f44,f60]) ).
fof(f255,plain,
! [X0] :
( X0 = n
| ~ product(c,a,X0) ),
inference(resolution,[status(thm)],[f54,f63]) ).
fof(f256,plain,
! [X0] :
( X0 = l
| ~ product(b,a,X0) ),
inference(resolution,[status(thm)],[f54,f62]) ).
fof(f257,plain,
! [X0] :
( X0 = additive_identity
| ~ product(d,a,X0) ),
inference(resolution,[status(thm)],[f54,f61]) ).
fof(f296,plain,
! [X0] :
( ~ product(a,c,X0)
| X0 = n ),
inference(resolution,[status(thm)],[f255,f59]) ).
fof(f303,plain,
! [X0] :
( ~ product(a,b,X0)
| X0 = l ),
inference(resolution,[status(thm)],[f256,f59]) ).
fof(f310,plain,
! [X0] :
( ~ product(a,d,X0)
| X0 = additive_identity ),
inference(resolution,[status(thm)],[f257,f59]) ).
fof(f322,plain,
multiply(a,c) = n,
inference(resolution,[status(thm)],[f296,f30]) ).
fof(f331,plain,
multiply(a,b) = l,
inference(resolution,[status(thm)],[f303,f30]) ).
fof(f336,plain,
product(a,b,l),
inference(paramodulation,[status(thm)],[f331,f30]) ).
fof(f355,plain,
multiply(a,d) = additive_identity,
inference(resolution,[status(thm)],[f310,f30]) ).
fof(f360,plain,
product(a,d,additive_identity),
inference(paramodulation,[status(thm)],[f355,f30]) ).
fof(f1390,plain,
! [X0,X1,X2] :
( sum(X1,multiply(X0,c),X2)
| ~ product(X0,d,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f167,f30]) ).
fof(f12334,plain,
! [X0] :
( sum(X0,multiply(a,c),additive_identity)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f1390,f360]) ).
fof(f12342,plain,
! [X0] :
( sum(X0,n,additive_identity)
| ~ product(a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f322,f12334]) ).
fof(f15456,plain,
sum(l,n,additive_identity),
inference(resolution,[status(thm)],[f12342,f336]) ).
fof(f15463,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f15456,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n009.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:14:58 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 35.77/4.99 % Refutation found
% 35.77/4.99 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 35.77/4.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.14/5.03 % Elapsed time: 4.652449 seconds
% 7.14/5.03 % CPU time: 36.643913 seconds
% 7.14/5.03 % Total memory used: 212.056 MB
% 7.14/5.03 % Net memory used: 183.438 MB
%------------------------------------------------------------------------------