%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:04:37 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.53s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 47 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z,W] :
( Y = W
| ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f48,plain,
! [Y,W] :
( Y = W
| ! [X,Z] :
( ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f93,plain,
! [X0,X1] :
( X1 = additive_identity
| ~ sum(X0,X1,X0) ),
inference(resolution,[status(thm)],[f49,f22]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X1,X5,X3)
| ~ sum(X2,X4,X5)
| ~ product(X1,X4,X0)
| ~ product(X1,X2,X3)
| X0 = additive_identity ),
inference(resolution,[status(thm)],[f93,f37]) ).
fof(f176,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,X1)
| ~ product(X0,X2,multiply(X0,X1))
| multiply(X0,X1) = additive_identity ),
inference(resolution,[status(thm)],[f99,f23]) ).
fof(f180,plain,
! [X0,X1] :
( ~ sum(X1,X1,X1)
| multiply(X0,X1) = additive_identity ),
inference(resolution,[status(thm)],[f176,f23]) ).
fof(f182,plain,
! [X0] : multiply(X0,additive_identity) = additive_identity,
inference(resolution,[status(thm)],[f180,f21]) ).
fof(f194,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f182,f23]) ).
fof(f201,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 21 04:09:24 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.32 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.54 % Elapsed time: 0.220450 seconds
% 0.10/0.54 % CPU time: 1.472078 seconds
% 0.10/0.54 % Total memory used: 56.505 MB
% 0.10/0.54 % Net memory used: 53.862 MB
%------------------------------------------------------------------------------