%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 60 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
sum(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
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(f31,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
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,c,d),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
sum(b,c,d),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f57,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f65,plain,
! [X0,X1,X2] :
( sum(b,X1,X2)
| ~ sum(d,X0,X2)
| ~ sum(c,X0,X1) ),
inference(resolution,[status(thm)],[f28,f49]) ).
fof(f66,plain,
! [X0,X1,X2] :
( sum(a,X1,X2)
| ~ sum(d,X0,X2)
| ~ sum(c,X0,X1) ),
inference(resolution,[status(thm)],[f28,f48]) ).
fof(f73,plain,
! [X0] :
( sum(b,additive_identity,X0)
| ~ sum(d,additive_inverse(c),X0) ),
inference(resolution,[status(thm)],[f65,f26]) ).
fof(f84,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f45,f22]) ).
fof(f85,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f57]) ).
fof(f145,plain,
! [X0] :
( sum(a,additive_identity,X0)
| ~ sum(d,additive_inverse(c),X0) ),
inference(resolution,[status(thm)],[f66,f26]) ).
fof(f221,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f85,f24]) ).
fof(f312,plain,
sum(b,additive_identity,add(additive_inverse(c),d)),
inference(resolution,[status(thm)],[f73,f57]) ).
fof(f314,plain,
sum(b,additive_identity,add(d,additive_inverse(c))),
inference(forward_demodulation,[status(thm)],[f221,f312]) ).
fof(f315,plain,
b = add(d,additive_inverse(c)),
inference(resolution,[status(thm)],[f314,f84]) ).
fof(f326,plain,
sum(d,additive_inverse(c),b),
inference(paramodulation,[status(thm)],[f315,f24]) ).
fof(f830,plain,
sum(a,additive_identity,b),
inference(resolution,[status(thm)],[f145,f326]) ).
fof(f838,plain,
a = b,
inference(resolution,[status(thm)],[f830,f84]) ).
fof(f849,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f838,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 04:09:57 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.43 % Refutation found
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.077330 seconds
% 0.10/0.46 % CPU time: 0.296208 seconds
% 0.10/0.46 % Total memory used: 45.777 MB
% 0.10/0.46 % Net memory used: 45.289 MB
%------------------------------------------------------------------------------