%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y,U,V] :
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Y,U,V] :
( equalish(U,V)
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
! [X,Y] :
( product(X,h(X,Y),Y)
| ~ equalish(X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [Y,W,Z] :
( product(W,Z,Y)
| ! [X] :
( ~ product(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f69,plain,
! [U,V] :
( equalish(U,V)
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [U,V] :
( equalish(U,V)
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f75,plain,
! [X] :
( ! [Y] : product(X,h(X,Y),Y)
| ~ equalish(X,additive_identity) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f76,plain,
! [X0,X1] :
( product(X0,h(X0,X1),X1)
| ~ equalish(X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
~ equalish(b,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f81,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(resolution,[status(thm)],[f56,f48]) ).
fof(f93,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f70,f81]) ).
fof(f98,plain,
! [X0] : equalish(X0,X0),
inference(resolution,[status(thm)],[f93,f81]) ).
fof(f103,plain,
! [X0] : product(additive_identity,h(additive_identity,X0),X0),
inference(resolution,[status(thm)],[f98,f76]) ).
fof(f307,plain,
! [X0,X1] :
( equalish(additive_identity,X1)
| ~ product(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f72,f73]) ).
fof(f310,plain,
! [X0] : equalish(additive_identity,X0),
inference(resolution,[status(thm)],[f307,f103]) ).
fof(f315,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ product(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f310,f47]) ).
fof(f340,plain,
! [X0,X1] : product(additive_identity,X0,X1),
inference(resolution,[status(thm)],[f315,f73]) ).
fof(f348,plain,
! [X0,X1,X2] :
( equalish(X2,X1)
| ~ product(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f340,f72]) ).
fof(f355,plain,
! [X0,X1] : equalish(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f348,f340]) ).
fof(f359,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f79,f355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:17:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.063407 seconds
% 0.12/0.43 % CPU time: 0.239146 seconds
% 0.12/0.43 % Total memory used: 31.060 MB
% 0.12/0.43 % Net memory used: 30.857 MB
%------------------------------------------------------------------------------