TSTP Solution File: NUM845+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% 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 : n010.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 12:30:48 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 25 unt; 0 def)
% Number of atoms : 117 ( 88 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 85 ( 39 ~; 32 |; 6 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 (; 61 !; 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(f3,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) = vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)
=> vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f14,axiom,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59),
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(f21,plain,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413)
| vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) = vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413)) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f35,plain,
! [Vd413] :
( vmul(vsucc(vd411),Vd413) != vplus(vmul(vd411,Vd413),Vd413)
| vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f36,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
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(f40,plain,
! [X0] : vmul(X0,v1) = 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(f42,plain,
! [X0] : vplus(v1,X0) = vsucc(X0),
inference(cnf_transformation,[status(esa)],[f14]) ).
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(f47,plain,
vmul(vsucc(vd411),sk0_0) = vplus(sk0_0,vmul(vd411,sk0_0)),
inference(paramodulation,[status(thm)],[f19,f41]) ).
fof(f51,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vplus(vsucc(sk0_0),vmul(vd411,vsucc(sk0_0))),
inference(paramodulation,[status(thm)],[f41,f20]) ).
fof(f55,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f45]) ).
fof(f80,plain,
! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(X1,vplus(X2,X0)),
inference(paramodulation,[status(thm)],[f41,f43]) ).
fof(f96,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X1,vplus(X0,X2)),
inference(paramodulation,[status(thm)],[f41,f43]) ).
fof(f97,plain,
! [X0,X1,X2] : vplus(X0,vplus(X1,X2)) = vplus(X1,vplus(X0,X2)),
inference(forward_demodulation,[status(thm)],[f43,f96]) ).
fof(f285,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f22]) ).
fof(f286,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0))) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(forward_demodulation,[status(thm)],[f43,f285]) ).
fof(f287,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vd411,vplus(vmul(vd411,X0),vsucc(X0))) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(forward_demodulation,[status(thm)],[f97,f286]) ).
fof(f288,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vplus(vd411,vsucc(vplus(vmul(vd411,X0),X0))) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(forward_demodulation,[status(thm)],[f45,f287]) ).
fof(f289,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vsucc(vplus(vd411,vplus(vmul(vd411,X0),X0))) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(forward_demodulation,[status(thm)],[f45,f288]) ).
fof(f290,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vsucc(vplus(vd411,vplus(X0,vmul(vd411,X0)))) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f289]) ).
fof(f291,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vsucc(vplus(vd411,vplus(X0,vmul(vd411,X0)))) = vsucc(vplus(vmul(vd411,vsucc(X0)),X0)) ),
inference(forward_demodulation,[status(thm)],[f45,f290]) ).
fof(f292,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vsucc(vplus(vd411,vplus(X0,vmul(vd411,X0)))) = vsucc(vplus(X0,vmul(vd411,vsucc(X0)))) ),
inference(forward_demodulation,[status(thm)],[f41,f291]) ).
fof(f305,plain,
( spl0_0
<=> vmul(vsucc(vd411),sk0_0) = vmul(vsucc(vd411),sk0_0) ),
introduced(split_symbol_definition) ).
fof(f307,plain,
( vmul(vsucc(vd411),sk0_0) != vmul(vsucc(vd411),sk0_0)
| spl0_0 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( spl0_1
<=> vsucc(vplus(vd411,vplus(sk0_0,vmul(vd411,sk0_0)))) = vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0)))) ),
introduced(split_symbol_definition) ).
fof(f309,plain,
( vsucc(vplus(vd411,vplus(sk0_0,vmul(vd411,sk0_0)))) = vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0))))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,plain,
( vmul(vsucc(vd411),sk0_0) != vmul(vsucc(vd411),sk0_0)
| vsucc(vplus(vd411,vplus(sk0_0,vmul(vd411,sk0_0)))) = vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0)))) ),
inference(paramodulation,[status(thm)],[f47,f292]) ).
fof(f312,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f311,f305,f308]) ).
fof(f321,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f307]) ).
fof(f322,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f323,plain,
( vsucc(vplus(vd411,vmul(vsucc(vd411),sk0_0))) = vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0))))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f47,f309]) ).
fof(f348,plain,
! [X0,X1] : vplus(X0,vplus(v1,X1)) = vsucc(vplus(X1,X0)),
inference(paramodulation,[status(thm)],[f80,f42]) ).
fof(f349,plain,
! [X0,X1] : vplus(X0,vsucc(X1)) = vsucc(vplus(X1,X0)),
inference(forward_demodulation,[status(thm)],[f42,f348]) ).
fof(f350,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vsucc(vplus(X1,X0)),
inference(forward_demodulation,[status(thm)],[f45,f349]) ).
fof(f887,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(vmul(vd411,vsucc(sk0_0)),sk0_0)),
inference(forward_demodulation,[status(thm)],[f55,f51]) ).
fof(f888,plain,
vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(sk0_0,vmul(vd411,vsucc(sk0_0)))),
inference(forward_demodulation,[status(thm)],[f350,f887]) ).
fof(f889,plain,
( vmul(vsucc(vd411),vsucc(sk0_0)) != vsucc(vplus(vd411,vmul(vsucc(vd411),sk0_0)))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f323,f888]) ).
fof(f1363,plain,
( spl0_9
<=> vmul(vsucc(vd411),v1) = vplus(v1,vmul(vd411,v1)) ),
introduced(split_symbol_definition) ).
fof(f1365,plain,
( vmul(vsucc(vd411),v1) != vplus(v1,vmul(vd411,v1))
| spl0_9 ),
inference(component_clause,[status(thm)],[f1363]) ).
fof(f1378,plain,
( spl0_11
<=> vmul(vsucc(vd411),sk0_0) = vplus(sk0_0,vmul(vd411,sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f1380,plain,
( vmul(vsucc(vd411),sk0_0) != vplus(sk0_0,vmul(vd411,sk0_0))
| spl0_11 ),
inference(component_clause,[status(thm)],[f1378]) ).
fof(f1410,plain,
( vmul(vsucc(vd411),sk0_0) != vmul(vsucc(vd411),sk0_0)
| spl0_11 ),
inference(forward_demodulation,[status(thm)],[f47,f1380]) ).
fof(f1411,plain,
( $false
| spl0_11 ),
inference(trivial_equality_resolution,[status(esa)],[f1410]) ).
fof(f1412,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f1411]) ).
fof(f1413,plain,
( vsucc(vd411) != vplus(v1,vmul(vd411,v1))
| spl0_9 ),
inference(forward_demodulation,[status(thm)],[f40,f1365]) ).
fof(f1414,plain,
( vsucc(vd411) != vsucc(vmul(vd411,v1))
| spl0_9 ),
inference(forward_demodulation,[status(thm)],[f42,f1413]) ).
fof(f1415,plain,
( vsucc(vd411) != vsucc(vd411)
| spl0_9 ),
inference(forward_demodulation,[status(thm)],[f40,f1414]) ).
fof(f1416,plain,
( $false
| spl0_9 ),
inference(trivial_equality_resolution,[status(esa)],[f1415]) ).
fof(f1417,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f1416]) ).
fof(f1429,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) ),
inference(forward_demodulation,[status(thm)],[f41,f36]) ).
fof(f1430,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vmul(vsucc(vd411),vsucc(X0)) = vsucc(vplus(vmul(vsucc(vd411),X0),vd411)) ),
inference(forward_demodulation,[status(thm)],[f45,f1429]) ).
fof(f1431,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(X0,vmul(vd411,X0))
| vmul(vsucc(vd411),vsucc(X0)) = vsucc(vplus(vd411,vmul(vsucc(vd411),X0))) ),
inference(forward_demodulation,[status(thm)],[f350,f1430]) ).
fof(f1432,plain,
( vmul(vsucc(vd411),sk0_0) != vplus(sk0_0,vmul(vd411,sk0_0))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f1431,f889]) ).
fof(f1433,plain,
( ~ spl0_11
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f1432,f1378,f308]) ).
fof(f1439,plain,
$false,
inference(sat_refutation,[status(thm)],[f312,f322,f1412,f1417,f1433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n010.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 : Tue May 30 09:47:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.42 % Refutation found
% 0.19/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.47 % Elapsed time: 0.117710 seconds
% 0.19/0.47 % CPU time: 0.174859 seconds
% 0.19/0.47 % Memory used: 11.521 MB
%------------------------------------------------------------------------------