TSTP Solution File: NUM849+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 7 unt; 0 def)
% Number of atoms : 73 ( 46 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 25 ~; 22 |; 4 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
=> vmul(vmul(vd448,vd449),vsucc(Vd454)) = vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) = vmul(vd448,vmul(vd449,Vd451))
=> vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Vd396,Vd397] :
( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& vmul(Vd396,v1) = Vd396 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,plain,
? [Vd454] :
( vmul(vmul(vd448,vd449),Vd454) = vmul(vd448,vmul(vd449,Vd454))
& vmul(vmul(vd448,vd449),vsucc(Vd454)) != vmul(vd448,vmul(vd449,vsucc(Vd454))) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f59,plain,
( vmul(vmul(vd448,vd449),sk0_0) = vmul(vd448,vmul(vd449,sk0_0))
& vmul(vmul(vd448,vd449),vsucc(sk0_0)) != vmul(vd448,vmul(vd449,vsucc(sk0_0))) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
vmul(vmul(vd448,vd449),sk0_0) = vmul(vd448,vmul(vd449,sk0_0)),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
vmul(vmul(vd448,vd449),vsucc(sk0_0)) != vmul(vd448,vmul(vd449,vsucc(sk0_0))),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f64,plain,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) != vmul(vd448,vmul(vd449,Vd451))
| vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,Vd451),vd449)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f65,plain,
! [X0] :
( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
| vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X0),vd449)) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [Vd451] :
( vmul(vmul(vd448,vd449),Vd451) != vmul(vd448,vmul(vd449,Vd451))
| vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f67,plain,
! [X0] :
( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
| vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f76,plain,
( ! [Vd396,Vd397] : vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& ! [Vd396] : vmul(Vd396,v1) = Vd396 ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f77,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f78,plain,
! [X0] : vmul(X0,v1) = X0,
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f200,plain,
( spl0_0
<=> vmul(vd448,vmul(vd449,sk0_0)) = vmul(vd448,vmul(vd449,sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( vmul(vd448,vmul(vd449,sk0_0)) != vmul(vd448,vmul(vd449,sk0_0))
| spl0_0 ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f210,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f202]) ).
fof(f211,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f260,plain,
! [X0] :
( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
| vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(X0))) ),
inference(forward_demodulation,[status(thm)],[f77,f65]) ).
fof(f262,plain,
( spl0_2
<=> vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(sk0_0))) ),
introduced(split_symbol_definition) ).
fof(f263,plain,
( vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(sk0_0)))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( vmul(vd448,vmul(vd449,sk0_0)) != vmul(vd448,vmul(vd449,sk0_0))
| vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) = vmul(vd448,vmul(vd449,vsucc(sk0_0))) ),
inference(paramodulation,[status(thm)],[f60,f260]) ).
fof(f266,plain,
( ~ spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f265,f200,f262]) ).
fof(f269,plain,
! [X0] :
( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
| vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) ),
inference(forward_demodulation,[status(thm)],[f77,f67]) ).
fof(f271,plain,
( spl0_3
<=> vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) ),
introduced(split_symbol_definition) ).
fof(f272,plain,
( vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( vmul(vd448,vmul(vd449,sk0_0)) != vmul(vd448,vmul(vd449,sk0_0))
| vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vplus(vmul(vd448,vmul(vd449,sk0_0)),vmul(vd448,vd449)) ),
inference(paramodulation,[status(thm)],[f60,f269]) ).
fof(f275,plain,
( ~ spl0_0
| spl0_3 ),
inference(split_clause,[status(thm)],[f274,f200,f271]) ).
fof(f300,plain,
( spl0_4
<=> vmul(vd448,vd449) = vmul(vd448,vmul(vd449,v1)) ),
introduced(split_symbol_definition) ).
fof(f302,plain,
( vmul(vd448,vd449) != vmul(vd448,vmul(vd449,v1))
| spl0_4 ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f318,plain,
( vmul(vd448,vd449) != vmul(vd448,vd449)
| spl0_4 ),
inference(forward_demodulation,[status(thm)],[f78,f302]) ).
fof(f319,plain,
( $false
| spl0_4 ),
inference(trivial_equality_resolution,[status(esa)],[f318]) ).
fof(f320,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f319]) ).
fof(f325,plain,
( vmul(vmul(vd448,vd449),vsucc(sk0_0)) = vmul(vd448,vmul(vd449,vsucc(sk0_0)))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f263,f272]) ).
fof(f326,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f61]) ).
fof(f327,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
$false,
inference(sat_refutation,[status(thm)],[f211,f266,f275,f320,f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 29 21:08:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.6.0
% 0.12/0.34 % Refutation found
% 0.12/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.35 % Elapsed time: 0.021633 seconds
% 0.17/0.35 % CPU time: 0.038938 seconds
% 0.17/0.35 % Total memory used: 13.556 MB
% 0.17/0.35 % Net memory used: 13.548 MB
%------------------------------------------------------------------------------