%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:04:38 PM UTC 2026
% Result : Unsatisfiable 1.23s 0.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 42 ( 24 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X] : product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f68,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(V3,X,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f76,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f78,plain,
product(a,b,d),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f79,plain,
product(additive_inverse(a),b,c),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f80,plain,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f379,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X1,additive_identity)
| ~ sum(X0,X2,X3)
| ~ product(X2,X1,d)
| ~ product(X0,X1,c) ),
inference(resolution,[status(thm)],[f69,f80]) ).
fof(f803,plain,
! [X0,X1] :
( ~ product(additive_identity,X1,additive_identity)
| ~ product(X0,X1,d)
| ~ product(additive_inverse(X0),X1,c) ),
inference(resolution,[status(thm)],[f379,f53]) ).
fof(f825,plain,
! [X0,X1] :
( ~ product(X0,X1,d)
| ~ product(additive_inverse(X0),X1,c) ),
inference(forward_subsumption_resolution,[status(thm)],[f803,f76]) ).
fof(f1227,plain,
~ product(a,b,d),
inference(resolution,[status(thm)],[f825,f79]) ).
fof(f1235,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1227,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:10:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 1.23/0.71 % Refutation found
% 1.23/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.23/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.23/0.74 % Elapsed time: 0.361994 seconds
% 1.23/0.74 % CPU time: 2.620831 seconds
% 1.23/0.74 % Total memory used: 76.452 MB
% 1.23/0.74 % Net memory used: 71.877 MB
%------------------------------------------------------------------------------