TSTP Solution File: NUM848+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM848+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 : Tue Apr 30 20:35:56 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 27 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 4 &)
% ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,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(f10,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& vmul(Vd396,v1) = Vd396 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f20,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
( ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& ! [Vd396] : vmul(Vd396,v1) = Vd396 ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f27,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f31,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f32,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f35,plain,
( ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f36,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f51,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vplus(vsucc(X0),X1),
inference(forward_demodulation,[status(thm)],[f32,f36]) ).
fof(f52,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
inference(backward_demodulation,[status(thm)],[f51,f32]) ).
fof(f90,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(X0,vmul(X0,X1)),
inference(forward_demodulation,[status(thm)],[f31,f27]) ).
fof(f132,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(forward_demodulation,[status(thm)],[f31,f20]) ).
fof(f133,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(forward_demodulation,[status(thm)],[f90,f132]) ).
fof(f134,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(forward_demodulation,[status(thm)],[f52,f133]) ).
fof(f135,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(forward_demodulation,[status(thm)],[f34,f134]) ).
fof(f136,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))),
inference(forward_demodulation,[status(thm)],[f31,f135]) ).
fof(f137,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(forward_demodulation,[status(thm)],[f90,f136]) ).
fof(f138,plain,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vmul(vd436,vplus(vd437,vsucc(vd439))),
inference(backward_demodulation,[status(thm)],[f137,f18]) ).
fof(f139,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) != vmul(vd436,vplus(vd437,vsucc(vd439))),
inference(forward_demodulation,[status(thm)],[f31,f138]) ).
fof(f140,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vmul(vd436,vplus(vd437,vsucc(vd439))),
inference(forward_demodulation,[status(thm)],[f90,f139]) ).
fof(f141,plain,
vmul(vd436,vplus(vd437,vsucc(vd439))) != vmul(vd436,vplus(vd437,vsucc(vd439))),
inference(forward_demodulation,[status(thm)],[f137,f140]) ).
fof(f142,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM848+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:00:13 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.019579 seconds
% 0.13/0.38 % CPU time: 0.034554 seconds
% 0.13/0.38 % Total memory used: 12.948 MB
% 0.13/0.38 % Net memory used: 12.915 MB
%------------------------------------------------------------------------------