%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM847+1 : TPTP v9.3.1. Released v4.1.0.
% 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 01:41:49 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f59,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f60,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f159,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f180,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(backward_demodulation,[status(thm)],[f59,f58]) ).
fof(f227,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(backward_demodulation,[status(thm)],[f60,f59]) ).
fof(f276,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(forward_demodulation,[status(thm)],[f60,f180]) ).
fof(f362,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(forward_demodulation,[status(thm)],[f159,f227]) ).
fof(f363,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f362,f276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM847+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 03:12:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.063093 seconds
% 0.11/0.44 % CPU time: 0.176889 seconds
% 0.11/0.44 % Total memory used: 103.829 MB
% 0.11/0.44 % Net memory used: 103.774 MB
%------------------------------------------------------------------------------