%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD008-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 12:21:51 PM UTC 2026
% Result : Unsatisfiable 94.72s 12.48s
% Output : CNFRefutation 94.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 13 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 241 ( 141 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f31,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)],[f30]) ).
fof(f32,plain,
! [W,X,V] :
( ~ sum(X,V,W)
| ! [Z,Y] :
( ~ sum(Y,Z,V)
| ! [U] :
( ~ sum(X,Y,U)
| sum(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X5,X2,X4)
| ~ sum(X5,X0,X3)
| sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| defined(add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f49,plain,
! [X0,X1] :
( defined(add(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,additive_identity)
| ~ sum(X2,additive_inverse(add(a,b)),X1)
| ~ sum(X0,X1,add(additive_inverse(a),additive_inverse(b))) ),
inference(resolution,[status(thm)],[f33,f71]) ).
fof(f98,plain,
! [X0] :
( ~ sum(X0,additive_inverse(add(a,b)),additive_inverse(b))
| ~ sum(additive_inverse(a),X0,additive_identity)
| ~ defined(additive_inverse(a))
| ~ defined(additive_inverse(b)) ),
inference(resolution,[status(thm)],[f89,f57]) ).
fof(f171,plain,
! [X0] :
( ~ defined(b)
| ~ sum(X0,additive_inverse(add(a,b)),additive_inverse(b))
| ~ sum(additive_inverse(a),X0,additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[f98,f51]) ).
fof(f172,plain,
! [X0] :
( ~ sum(X0,additive_inverse(add(a,b)),additive_inverse(b))
| ~ defined(additive_inverse(a))
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f70]) ).
fof(f173,plain,
! [X0] :
( ~ defined(a)
| ~ sum(X0,additive_inverse(add(a,b)),additive_inverse(b))
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(resolution,[status(thm)],[f172,f51]) ).
fof(f174,plain,
! [X0] :
( ~ sum(additive_inverse(a),X0,additive_identity)
| ~ sum(X0,additive_inverse(add(a,b)),additive_inverse(b)) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f69]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( ~ sum(additive_inverse(a),X3,additive_identity)
| ~ sum(X0,X2,X3)
| ~ sum(X2,additive_inverse(add(a,b)),X1)
| ~ sum(X0,X1,additive_inverse(b)) ),
inference(resolution,[status(thm)],[f174,f33]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ defined(a)
| ~ sum(X0,X2,a)
| ~ sum(X2,additive_inverse(add(a,b)),X1)
| ~ sum(X0,X1,additive_inverse(b)) ),
inference(resolution,[status(thm)],[f175,f35]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,additive_inverse(b))
| ~ sum(X2,X0,a)
| ~ sum(X0,additive_inverse(add(a,b)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f69]) ).
fof(f194,plain,
! [X0] :
( ~ defined(a)
| ~ sum(additive_identity,X0,additive_inverse(b))
| ~ sum(a,additive_inverse(add(a,b)),X0) ),
inference(resolution,[status(thm)],[f188,f34]) ).
fof(f198,plain,
! [X0] :
( ~ sum(a,additive_inverse(add(a,b)),X0)
| ~ sum(additive_identity,X0,additive_inverse(b)) ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f69]) ).
fof(f199,plain,
( ~ defined(additive_inverse(add(a,b)))
| ~ defined(a)
| ~ sum(additive_identity,add(a,additive_inverse(add(a,b))),additive_inverse(b)) ),
inference(resolution,[status(thm)],[f198,f57]) ).
fof(f203,plain,
( ~ sum(additive_identity,add(a,additive_inverse(add(a,b))),additive_inverse(b))
| ~ defined(additive_inverse(add(a,b))) ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f69]) ).
fof(f354,plain,
( ~ sum(additive_identity,add(a,additive_inverse(add(a,b))),additive_inverse(b))
| ~ defined(add(a,b)) ),
inference(resolution,[status(thm)],[f203,f51]) ).
fof(f359,plain,
( ~ defined(a)
| ~ defined(b)
| ~ sum(additive_identity,add(a,additive_inverse(add(a,b))),additive_inverse(b)) ),
inference(resolution,[status(thm)],[f354,f49]) ).
fof(f360,plain,
( ~ defined(a)
| ~ sum(additive_identity,add(a,additive_inverse(add(a,b))),additive_inverse(b)) ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f70]) ).
fof(f361,plain,
~ sum(additive_identity,add(a,additive_inverse(add(a,b))),additive_inverse(b)),
inference(forward_subsumption_resolution,[status(thm)],[f360,f69]) ).
fof(f362,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,additive_inverse(b))
| ~ sum(X1,add(a,additive_inverse(add(a,b))),X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f361,f33]) ).
fof(f390,plain,
! [X0,X1,X2] :
( ~ sum(X2,add(a,additive_inverse(add(a,b))),X0)
| ~ sum(X1,X2,additive_identity)
| ~ sum(X0,X1,additive_inverse(b)) ),
inference(resolution,[status(thm)],[f362,f36]) ).
fof(f407,plain,
! [X0] :
( ~ sum(X0,add(a,additive_inverse(add(a,b))),additive_identity)
| ~ sum(additive_inverse(b),X0,additive_identity)
| ~ defined(additive_inverse(b)) ),
inference(resolution,[status(thm)],[f390,f34]) ).
fof(f747,plain,
! [X0] :
( ~ defined(b)
| ~ sum(X0,add(a,additive_inverse(add(a,b))),additive_identity)
| ~ sum(additive_inverse(b),X0,additive_identity) ),
inference(resolution,[status(thm)],[f407,f51]) ).
fof(f748,plain,
! [X0] :
( ~ sum(X0,add(a,additive_inverse(add(a,b))),additive_identity)
| ~ sum(additive_inverse(b),X0,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f747,f70]) ).
fof(f749,plain,
( ~ defined(b)
| ~ sum(b,add(a,additive_inverse(add(a,b))),additive_identity) ),
inference(resolution,[status(thm)],[f748,f35]) ).
fof(f753,plain,
~ sum(b,add(a,additive_inverse(add(a,b))),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f749,f70]) ).
fof(f756,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,additive_identity)
| ~ sum(b,X0,X2)
| ~ sum(X0,X1,add(a,additive_inverse(add(a,b)))) ),
inference(resolution,[status(thm)],[f753,f31]) ).
fof(f796,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,add(a,additive_inverse(add(a,b))))
| ~ sum(X2,b,X0)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f756,f36]) ).
fof(f841,plain,
! [X0] :
( ~ defined(additive_inverse(add(a,b)))
| ~ defined(a)
| ~ sum(a,b,X0)
| ~ sum(X0,additive_inverse(add(a,b)),additive_identity) ),
inference(resolution,[status(thm)],[f796,f57]) ).
fof(f845,plain,
! [X0] :
( ~ sum(a,b,X0)
| ~ defined(additive_inverse(add(a,b)))
| ~ sum(X0,additive_inverse(add(a,b)),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f841,f69]) ).
fof(f1220,plain,
! [X0] :
( ~ sum(a,b,X0)
| ~ sum(X0,additive_inverse(add(a,b)),additive_identity)
| ~ defined(add(a,b)) ),
inference(resolution,[status(thm)],[f845,f51]) ).
fof(f1221,plain,
! [X0] :
( ~ defined(a)
| ~ defined(b)
| ~ sum(a,b,X0)
| ~ sum(X0,additive_inverse(add(a,b)),additive_identity) ),
inference(resolution,[status(thm)],[f1220,f49]) ).
fof(f1222,plain,
! [X0] :
( ~ sum(X0,additive_inverse(add(a,b)),additive_identity)
| ~ defined(a)
| ~ sum(a,b,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1221,f70]) ).
fof(f1223,plain,
! [X0] :
( ~ sum(a,b,X0)
| ~ sum(X0,additive_inverse(add(a,b)),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f1222,f69]) ).
fof(f1224,plain,
( ~ defined(b)
| ~ defined(a)
| ~ sum(add(a,b),additive_inverse(add(a,b)),additive_identity) ),
inference(resolution,[status(thm)],[f1223,f57]) ).
fof(f1228,plain,
( ~ sum(add(a,b),additive_inverse(add(a,b)),additive_identity)
| ~ defined(b) ),
inference(forward_subsumption_resolution,[status(thm)],[f1224,f69]) ).
fof(f1234,plain,
~ sum(add(a,b),additive_inverse(add(a,b)),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f1228,f70]) ).
fof(f1237,plain,
~ sum(additive_inverse(add(a,b)),add(a,b),additive_identity),
inference(resolution,[status(thm)],[f1234,f36]) ).
fof(f1238,plain,
~ defined(add(a,b)),
inference(resolution,[status(thm)],[f1237,f35]) ).
fof(f1242,plain,
( ~ defined(a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[f1238,f49]) ).
fof(f1243,plain,
~ defined(a),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f70]) ).
fof(f1244,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1243,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD008-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 15:37:39 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 94.72/12.48 % Refutation found
% 94.72/12.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 94.72/12.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.96/12.54 % Elapsed time: 12.081874 seconds
% 13.96/12.54 % CPU time: 95.521133 seconds
% 13.96/12.54 % Total memory used: 340.558 MB
% 13.96/12.54 % Net memory used: 302.801 MB
%------------------------------------------------------------------------------