%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:22:08 PM UTC 2026
% Result : Unsatisfiable 138.60s 17.99s
% Output : CNFRefutation 65.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 29 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 212 ( 105 ~; 107 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 134 !; 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(f14,axiom,
defined(additive_identity),
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(f21,axiom,
! [X,Y] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| sum(additive_identity,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
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,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,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(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,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(f34,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f58,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| sum(additive_identity,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f65,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [V,Y,Z] :
( ~ sum(Y,Z,V)
| ! [U,X] :
( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
! [X0] :
( less_or_equal(X0,X0)
| ~ defined(X0)
| ~ defined(X0)
| less_or_equal(X0,X0) ),
inference(resolution,[status(thm)],[f65,f63]) ).
fof(f83,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f78]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ sum(add(b,additive_inverse(a)),X2,X1)
| ~ sum(additive_identity,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f67,f72]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( ~ defined(X2)
| ~ sum(X2,X3,X1)
| ~ sum(X2,X3,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f67,f83]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1)
| ~ sum(X0,additive_identity,additive_identity)
| sum(X0,X1,X1) ),
inference(resolution,[status(thm)],[f32,f61]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( ~ defined(X1)
| ~ sum(X3,additive_identity,X2)
| ~ sum(X3,additive_inverse(X1),X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f36]) ).
fof(f201,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_inverse(X0),additive_identity) ),
inference(resolution,[status(thm)],[f37,f36]) ).
fof(f202,plain,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f37,f61]) ).
fof(f203,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f37,f35]) ).
fof(f204,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ defined(X1)
| sum(X0,X1,add(X1,X0)) ),
inference(resolution,[status(thm)],[f37,f58]) ).
fof(f229,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),additive_identity,additive_inverse(X0)) ),
inference(resolution,[status(thm)],[f203,f52]) ).
fof(f230,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f203,f71]) ).
fof(f231,plain,
sum(a,additive_identity,a),
inference(resolution,[status(thm)],[f203,f70]) ).
fof(f232,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f203,f51]) ).
fof(f234,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f230,f37]) ).
fof(f244,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f231,f37]) ).
fof(f270,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,b,b) ),
inference(resolution,[status(thm)],[f234,f32]) ).
fof(f292,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(resolution,[status(thm)],[f201,f51]) ).
fof(f311,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f292,f37]) ).
fof(f358,plain,
! [X0] :
( sum(additive_identity,additive_inverse(X0),additive_inverse(X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f229,f37]) ).
fof(f394,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,b,add(b,X0)) ),
inference(resolution,[status(thm)],[f204,f71]) ).
fof(f401,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),b,add(b,additive_inverse(X0))) ),
inference(resolution,[status(thm)],[f394,f52]) ).
fof(f730,plain,
sum(additive_inverse(additive_identity),b,b),
inference(resolution,[status(thm)],[f270,f311]) ).
fof(f745,plain,
! [X0,X1,X2] :
( ~ sum(X2,b,X1)
| ~ sum(X0,X2,additive_inverse(additive_identity))
| sum(X0,X1,b) ),
inference(resolution,[status(thm)],[f730,f32]) ).
fof(f1169,plain,
! [X0,X1] :
( ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0)
| sum(additive_identity,X0,X0) ),
inference(resolution,[status(thm)],[f174,f232]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X2,additive_inverse(a),X0)
| sum(X0,a,X1) ),
inference(resolution,[status(thm)],[f188,f70]) ).
fof(f2821,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X2,X1)
| ~ sum(additive_identity,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f102,f51]) ).
fof(f3077,plain,
! [X0] :
( ~ sum(additive_identity,additive_inverse(additive_identity),X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f2821,f292]) ).
fof(f3079,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ sum(additive_identity,additive_inverse(X1),X0)
| less_or_equal(X0,additive_inverse(X1)) ),
inference(resolution,[status(thm)],[f2821,f358]) ).
fof(f3128,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_inverse(additive_identity),additive_identity) ),
inference(resolution,[status(thm)],[f3077,f358]) ).
fof(f3135,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f3128,f51]) ).
fof(f3149,plain,
( ~ less_or_equal(additive_identity,additive_inverse(additive_identity))
| sum(additive_identity,additive_identity,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[f3135,f202]) ).
fof(f4406,plain,
! [X0] :
( ~ sum(additive_identity,additive_inverse(a),X0)
| less_or_equal(X0,additive_inverse(a)) ),
inference(resolution,[status(thm)],[f3079,f70]) ).
fof(f4407,plain,
! [X0] :
( ~ sum(additive_identity,additive_inverse(additive_identity),X0)
| less_or_equal(X0,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[f3079,f51]) ).
fof(f4467,plain,
( ~ defined(a)
| less_or_equal(additive_inverse(a),additive_inverse(a)) ),
inference(resolution,[status(thm)],[f4406,f358]) ).
fof(f4473,plain,
less_or_equal(additive_inverse(a),additive_inverse(a)),
inference(forward_subsumption_resolution,[status(thm)],[f4467,f70]) ).
fof(f4480,plain,
( ~ less_or_equal(additive_inverse(a),additive_inverse(a))
| sum(additive_identity,additive_inverse(a),additive_inverse(a)) ),
inference(resolution,[status(thm)],[f4473,f1169]) ).
fof(f4494,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(forward_subsumption_resolution,[status(thm)],[f4480,f4473]) ).
fof(f4535,plain,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(resolution,[status(thm)],[f4407,f292]) ).
fof(f7851,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(forward_subsumption_resolution,[status(thm)],[f3149,f4535]) ).
fof(f15465,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(additive_inverse(a),a,X0) ),
inference(resolution,[status(thm)],[f1830,f4494]) ).
fof(f15796,plain,
sum(additive_inverse(a),a,additive_inverse(additive_identity)),
inference(resolution,[status(thm)],[f15465,f7851]) ).
fof(f15816,plain,
sum(a,additive_inverse(a),additive_inverse(additive_identity)),
inference(resolution,[status(thm)],[f15796,f37]) ).
fof(f25197,plain,
! [X0] :
( ~ sum(additive_inverse(a),b,X0)
| sum(a,X0,b) ),
inference(resolution,[status(thm)],[f745,f15816]) ).
fof(f25230,plain,
( ~ defined(a)
| sum(a,add(b,additive_inverse(a)),b) ),
inference(resolution,[status(thm)],[f25197,f401]) ).
fof(f25233,plain,
sum(a,add(b,additive_inverse(a)),b),
inference(forward_subsumption_resolution,[status(thm)],[f25230,f70]) ).
fof(f25262,plain,
sum(add(b,additive_inverse(a)),a,b),
inference(resolution,[status(thm)],[f25233,f37]) ).
fof(f25306,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f25262,f101]) ).
fof(f25327,plain,
less_or_equal(a,b),
inference(resolution,[status(thm)],[f25306,f244]) ).
fof(f25332,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f25327,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 15:44:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 138.60/17.99 % Refutation found
% 138.60/17.99 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 138.60/17.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 65.66/18.05 % Elapsed time: 17.662621 seconds
% 65.66/18.05 % CPU time: 139.595542 seconds
% 65.66/18.05 % Total memory used: 545.704 MB
% 65.66/18.05 % Net memory used: 481.754 MB
%------------------------------------------------------------------------------