TSTP Solution File: NUM845+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM845+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 : Tue Apr 30 20:35:55 EDT 2024
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 21 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 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 : 40 ( 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f12,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& vmul(Vd396,v1) = Vd396 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
? [Vd416] :
( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)
& vmul(vsucc(vd411),vsucc(Vd416)) != vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f18,plain,
( vmul(vsucc(vd411),sk0_0) = vplus(vmul(vd411,sk0_0),sk0_0)
& vmul(vsucc(vd411),vsucc(sk0_0)) != vplus(vmul(vd411,vsucc(sk0_0)),vsucc(sk0_0)) ),
inference(skolemization,[status(esa)],[f17]) ).
fof(f19,plain,
vmul(vsucc(vd411),sk0_0) = vplus(vmul(vd411,sk0_0),sk0_0),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vplus(vmul(vd411,vsucc(sk0_0)),vsucc(sk0_0)),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f38,plain,
( ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& ! [Vd396] : vmul(Vd396,v1) = Vd396 ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f39,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f43,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f44,plain,
( ! [Vd42,Vd43] : vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& ! [Vd42] : vplus(Vd42,v1) = vsucc(Vd42) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f45,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f60,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(vmul(vd411,vsucc(sk0_0)),sk0_0)),
inference(backward_demodulation,[status(thm)],[f45,f20]) ).
fof(f61,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0)))),
inference(forward_demodulation,[status(thm)],[f41,f60]) ).
fof(f67,plain,
vmul(vsucc(vd411),sk0_0) = vplus(sk0_0,vmul(vd411,sk0_0)),
inference(paramodulation,[status(thm)],[f19,f41]) ).
fof(f78,plain,
! [X0,X1] : vmul(vsucc(X0),vsucc(X1)) = vsucc(vplus(vmul(vsucc(X0),X1),X0)),
inference(paramodulation,[status(thm)],[f45,f39]) ).
fof(f79,plain,
! [X0,X1] : vmul(vsucc(X0),vsucc(X1)) = vsucc(vplus(X0,vmul(vsucc(X0),X1))),
inference(forward_demodulation,[status(thm)],[f41,f78]) ).
fof(f104,plain,
! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(X1,vplus(X2,X0)),
inference(paramodulation,[status(thm)],[f41,f43]) ).
fof(f116,plain,
! [X0,X1,X2] : vplus(vmul(X0,vsucc(X1)),X2) = vplus(vmul(X0,X1),vplus(X0,X2)),
inference(paramodulation,[status(thm)],[f39,f43]) ).
fof(f117,plain,
! [X0,X1,X2] : vplus(vmul(X0,vsucc(X1)),X2) = vplus(X0,vplus(X2,vmul(X0,X1))),
inference(forward_demodulation,[status(thm)],[f104,f116]) ).
fof(f654,plain,
vplus(vmul(vd411,vsucc(sk0_0)),sk0_0) = vplus(vd411,vmul(vsucc(vd411),sk0_0)),
inference(paramodulation,[status(thm)],[f67,f117]) ).
fof(f655,plain,
vplus(sk0_0,vmul(vd411,vsucc(sk0_0))) = vplus(vd411,vmul(vsucc(vd411),sk0_0)),
inference(forward_demodulation,[status(thm)],[f41,f654]) ).
fof(f696,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(vd411,vmul(vsucc(vd411),sk0_0))),
inference(backward_demodulation,[status(thm)],[f655,f61]) ).
fof(f697,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vmul(vsucc(vd411),vsucc(sk0_0)),
inference(forward_demodulation,[status(thm)],[f79,f696]) ).
fof(f698,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:46:19 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.20/0.47 % Refutation found
% 0.20/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.49 % Elapsed time: 0.135697 seconds
% 0.20/0.49 % CPU time: 0.940193 seconds
% 0.20/0.49 % Total memory used: 47.951 MB
% 0.20/0.49 % Net memory used: 47.713 MB
%------------------------------------------------------------------------------