%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:04:38 PM UTC 2026
% Result : Unsatisfiable 2.84s 0.82s
% Output : CNFRefutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 49 ( 28 ~; 21 |; 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 : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B,C] :
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,plain,
! [X,V3,V4] :
( product(X,V3,V4)
| ! [V1,V2] :
( ~ sum(V1,V2,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f72,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f83,plain,
! [X0,X1,X2] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f86,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
product(a,b,aPb),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
product(a,c,aPc),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( ~ sum(X1,X3,aPb_S_IaPc)
| ~ sum(X0,X2,bS_Ic)
| ~ product(a,X2,X3)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f72,f90]) ).
fof(f314,plain,
! [X0,X1] :
( ~ sum(X0,X1,bS_Ic)
| ~ product(a,X1,additive_inverse(aPc))
| ~ product(a,X0,aPb) ),
inference(resolution,[status(thm)],[f216,f89]) ).
fof(f325,plain,
! [X0] :
( ~ sum(b,X0,bS_Ic)
| ~ product(a,X0,additive_inverse(aPc)) ),
inference(resolution,[status(thm)],[f314,f87]) ).
fof(f333,plain,
! [X0] :
( ~ product(a,X0,aPc)
| ~ sum(b,additive_inverse(X0),bS_Ic) ),
inference(resolution,[status(thm)],[f325,f83]) ).
fof(f341,plain,
~ sum(b,additive_inverse(c),bS_Ic),
inference(resolution,[status(thm)],[f333,f88]) ).
fof(f349,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f341,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-2 : 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 : n009.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 04:10:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 2.84/0.82 % Refutation found
% 2.84/0.82 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.84/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.84/0.83 % Elapsed time: 0.455435 seconds
% 2.84/0.83 % CPU time: 3.316026 seconds
% 2.84/0.83 % Total memory used: 81.877 MB
% 2.84/0.83 % Net memory used: 76.195 MB
%------------------------------------------------------------------------------