TSTP Solution File: NUM852+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:30:50 EDT 2023
% Result : Theorem 0.14s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 43 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 (; 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Vd470,Vd471] :
( greater(Vd470,Vd471)
=> vmul(Vd470,vd469) = vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f23,plain,
greater(vd481,vd480),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
! [Vd470,Vd471] :
( ~ greater(Vd470,Vd471)
| greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f28,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater(vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)),vmul(X1,vd469)) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [Vd470,Vd471] :
( ~ greater(Vd470,Vd471)
| vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) = vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(vplus(X1,vskolem9(X0,X1)),vd469) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)) ),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
! [Vd470,Vd471] :
( ~ greater(Vd470,Vd471)
| vmul(Vd470,vd469) = vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(X0,vd469) = vmul(vplus(X1,vskolem9(X0,X1)),vd469) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f37,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f61,plain,
~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(paramodulation,[status(thm)],[f37,f22]) ).
fof(f631,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater(vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X0,X1))),vmul(X1,vd469)) ),
inference(forward_demodulation,[status(thm)],[f37,f28]) ).
fof(f632,plain,
greater(vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),vmul(vd480,vd469)),
inference(resolution,[status(thm)],[f631,f23]) ).
fof(f633,plain,
greater(vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),vmul(vd480,vd469)),
inference(forward_demodulation,[status(thm)],[f37,f632]) ).
fof(f634,plain,
greater(vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),vmul(vd469,vd480)),
inference(forward_demodulation,[status(thm)],[f37,f633]) ).
fof(f635,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vplus(vmul(X1,vd469),vmul(vskolem9(X0,X1),vd469)) ),
inference(forward_demodulation,[status(thm)],[f37,f30]) ).
fof(f636,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vplus(vmul(X1,vd469),vmul(vd469,vskolem9(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f37,f635]) ).
fof(f637,plain,
vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vplus(vmul(vd480,vd469),vmul(vd469,vskolem9(vd481,vd480))),
inference(resolution,[status(thm)],[f636,f23]) ).
fof(f638,plain,
vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vplus(vmul(vd469,vd480),vmul(vd469,vskolem9(vd481,vd480))),
inference(forward_demodulation,[status(thm)],[f37,f637]) ).
fof(f639,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| vmul(X0,vd469) = vmul(vd469,vplus(X1,vskolem9(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f37,f32]) ).
fof(f640,plain,
vmul(vd481,vd469) = vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))),
inference(resolution,[status(thm)],[f639,f23]) ).
fof(f691,plain,
greater(vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))),vmul(vd469,vd480)),
inference(backward_demodulation,[status(thm)],[f638,f634]) ).
fof(f1164,plain,
greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(forward_demodulation,[status(thm)],[f640,f691]) ).
fof(f1165,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1164,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% 0.05/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32 % Computer : n013.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Tue May 30 09:47:20 EDT 2023
% 0.09/0.32 % CPUTime :
% 0.09/0.33 % Drodi V3.5.1
% 0.14/0.48 % Refutation found
% 0.14/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.174303 seconds
% 0.14/0.50 % CPU time: 0.916518 seconds
% 0.14/0.50 % Memory used: 65.519 MB
%------------------------------------------------------------------------------