%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 47 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
sum(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
sum(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [X,V,W] :
( sum(X,V,W)
| ! [U,Z] :
( ~ sum(U,Z,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f44,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
sum(a,b,d),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
sum(a,c,d),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
b != c,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f148,plain,
! [X0,X1,X2] :
( sum(X0,d,X2)
| ~ sum(X1,c,X2)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[f28,f49]) ).
fof(f150,plain,
! [X0,X1,X2] :
( sum(X0,d,X2)
| ~ sum(X1,b,X2)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[f28,f48]) ).
fof(f209,plain,
! [X0] :
( sum(X0,d,c)
| ~ sum(X0,a,additive_identity) ),
inference(resolution,[status(thm)],[f148,f21]) ).
fof(f218,plain,
sum(additive_inverse(a),d,c),
inference(resolution,[status(thm)],[f209,f25]) ).
fof(f226,plain,
! [X0] :
( X0 = c
| ~ sum(additive_inverse(a),d,X0) ),
inference(resolution,[status(thm)],[f218,f45]) ).
fof(f249,plain,
! [X0] :
( sum(X0,d,b)
| ~ sum(X0,a,additive_identity) ),
inference(resolution,[status(thm)],[f150,f21]) ).
fof(f316,plain,
sum(additive_inverse(a),d,b),
inference(resolution,[status(thm)],[f249,f25]) ).
fof(f317,plain,
b = c,
inference(resolution,[status(thm)],[f316,f226]) ).
fof(f328,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f317,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:14:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.084197 seconds
% 0.15/0.46 % CPU time: 0.394098 seconds
% 0.15/0.46 % Total memory used: 33.966 MB
% 0.15/0.46 % Net memory used: 33.718 MB
%------------------------------------------------------------------------------