%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 2.97s 1.06s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 60 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 60 ( 31 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,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(f17,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,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)],[f13]) ).
fof(f44,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)],[f43]) ).
fof(f51,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f56,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
product(a,b,aPb),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
product(a,c,aPc),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f60,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f62,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f52]) ).
fof(f69,plain,
multiply(a,b) = aPb,
inference(resolution,[status(thm)],[f57,f62]) ).
fof(f170,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ sum(multiply(X0,X3),X2,X5)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f44,f28]) ).
fof(f280,plain,
! [X0,X1] : product(X0,additive_inverse(X1),additive_inverse(multiply(X0,X1))),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f332,plain,
multiply(a,c) = aPc,
inference(resolution,[status(thm)],[f58,f62]) ).
fof(f1249,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X2,X4)
| ~ sum(multiply(X3,X0),additive_inverse(multiply(X3,X1)),X4)
| ~ sum(X0,additive_inverse(X1),X2) ),
inference(resolution,[status(thm)],[f280,f170]) ).
fof(f1358,plain,
! [X0,X1] :
( product(X0,bS_Ic,X1)
| ~ sum(multiply(X0,b),additive_inverse(multiply(X0,c)),X1) ),
inference(resolution,[status(thm)],[f1249,f56]) ).
fof(f1408,plain,
! [X0] :
( product(a,bS_Ic,X0)
| ~ sum(aPb,additive_inverse(multiply(a,c)),X0) ),
inference(paramodulation,[status(thm)],[f69,f1358]) ).
fof(f1410,plain,
! [X0] :
( product(a,bS_Ic,X0)
| ~ sum(aPb,additive_inverse(aPc),X0) ),
inference(forward_demodulation,[status(thm)],[f332,f1408]) ).
fof(f1412,plain,
product(a,bS_Ic,aPb_S_IaPc),
inference(resolution,[status(thm)],[f1410,f59]) ).
fof(f1415,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1412,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:12:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 2.97/1.06 % Refutation found
% 2.97/1.06 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.97/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.97/1.09 % Elapsed time: 0.709162 seconds
% 2.97/1.09 % CPU time: 5.311769 seconds
% 2.97/1.09 % Total memory used: 73.746 MB
% 2.97/1.09 % Net memory used: 68.260 MB
%------------------------------------------------------------------------------