%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:04:45 PM UTC 2026
% Result : Unsatisfiable 27.83s 3.97s
% Output : CNFRefutation 27.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 26 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 46 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 120 ( 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X,Y,W,Z] :
( product(Y,W,Z)
| ~ product(X,W,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] : product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,U,V] :
( equalish(U,V)
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] : equalish(multiply(A,A),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B] : product(a,multiply(b,A),multiply(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [A] : product(A,A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,plain,
! [Y,W,Z] :
( product(Y,W,Z)
| ! [X] :
( ~ product(X,W,Z)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( product(X1,X2,X3)
| ~ product(X0,X2,X3)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [Y,W,Z] :
( product(W,Z,Y)
| ! [X] :
( ~ product(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f96,plain,
! [X,Z] :
( equalish(X,Z)
| ! [Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f97,plain,
! [X0,X1,X2] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f100,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f109,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f119,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f123,plain,
! [U,V] :
( equalish(U,V)
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f134,plain,
! [X0] : equalish(multiply(X0,X0),X0),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f143,plain,
! [X0,X1] : product(a,multiply(b,X0),multiply(X1,X0)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f168,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f169,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f171,plain,
~ equalish(c,d),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f182,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ product(X0,X1,multiply(X2,X2)) ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f184,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ product(multiply(X0,X0),X1,X2) ),
inference(resolution,[status(thm)],[f134,f90]) ).
fof(f202,plain,
! [X0,X1,X2] :
( product(c,X0,X2)
| ~ product(a,X1,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f110,f169]) ).
fof(f221,plain,
! [X0,X1,X2] :
( equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f100,f124]) ).
fof(f410,plain,
! [X0,X1] :
( product(c,X0,X1)
| ~ product(a,multiply(b,X0),X1) ),
inference(resolution,[status(thm)],[f202,f100]) ).
fof(f758,plain,
! [X0] : product(a,multiply(b,X0),X0),
inference(resolution,[status(thm)],[f182,f143]) ).
fof(f761,plain,
! [X0] : product(multiply(X0,X0),multiply(X0,X0),X0),
inference(resolution,[status(thm)],[f182,f168]) ).
fof(f801,plain,
! [X0,X1] : product(X0,X1,multiply(multiply(X0,X0),X1)),
inference(resolution,[status(thm)],[f184,f100]) ).
fof(f1261,plain,
! [X0] : equalish(multiply(additive_identity,X0),additive_identity),
inference(resolution,[status(thm)],[f221,f119]) ).
fof(f4371,plain,
! [X0,X1] : product(c,X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[f410,f143]) ).
fof(f4372,plain,
! [X0] : product(c,X0,X0),
inference(resolution,[status(thm)],[f410,f758]) ).
fof(f4444,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f4372,f124]) ).
fof(f5261,plain,
! [X0,X1] : equalish(X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[f4444,f4371]) ).
fof(f5370,plain,
! [X0,X1,X2] :
( equalish(X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f5261,f97]) ).
fof(f9515,plain,
! [X0] : equalish(X0,additive_identity),
inference(resolution,[status(thm)],[f5370,f1261]) ).
fof(f9561,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(additive_identity,X0) ),
inference(resolution,[status(thm)],[f9515,f97]) ).
fof(f9562,plain,
! [X0,X1,X2] :
( product(X0,X1,additive_identity)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f9515,f94]) ).
fof(f12338,plain,
! [X0,X1] : product(X0,X1,additive_identity),
inference(resolution,[status(thm)],[f9562,f801]) ).
fof(f12705,plain,
! [X0,X1,X2] :
( equalish(additive_identity,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f12338,f124]) ).
fof(f13860,plain,
! [X0] : equalish(additive_identity,X0),
inference(resolution,[status(thm)],[f12705,f761]) ).
fof(f13913,plain,
! [X0,X1] : equalish(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f9561,f13860]) ).
fof(f13954,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f171,f13913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:17:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 27.83/3.97 % Refutation found
% 27.83/3.97 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 27.83/3.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.83/4.00 % Elapsed time: 3.625537 seconds
% 27.83/4.00 % CPU time: 28.474636 seconds
% 27.83/4.00 % Total memory used: 196.131 MB
% 27.83/4.00 % Net memory used: 159.270 MB
%------------------------------------------------------------------------------