TSTP Solution File: NUM453+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 20:34:44 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 110 ( 49 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 45 ~; 39 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f56,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f61,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f65,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f66,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ aInteger0(X0)
| X0 = sdtpldt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f68,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f69,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f229,plain,
aInteger0(xp),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f230,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f234,plain,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(pre_NNF_transformation,[status(esa)],[f49]) ).
fof(f235,plain,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(cnf_transformation,[status(esa)],[f234]) ).
fof(f245,plain,
( spl0_0
<=> sdtpldt0(sz10,xp) = sz10 ),
introduced(split_symbol_definition) ).
fof(f246,plain,
( sdtpldt0(sz10,xp) = sz10
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( spl0_1
<=> sdtpldt0(sz10,smndt0(xp)) = sz10 ),
introduced(split_symbol_definition) ).
fof(f249,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f235,f245,f248]) ).
fof(f255,plain,
aInteger0(smndt0(xp)),
inference(resolution,[status(thm)],[f56,f229]) ).
fof(f256,plain,
aInteger0(smndt0(sz10)),
inference(resolution,[status(thm)],[f56,f54]) ).
fof(f257,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[f66,f229]) ).
fof(f259,plain,
xp = sdtpldt0(sz00,xp),
inference(resolution,[status(thm)],[f67,f229]) ).
fof(f265,plain,
sdtpldt0(xp,smndt0(xp)) = sz00,
inference(resolution,[status(thm)],[f69,f229]) ).
fof(f268,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f70,f54]) ).
fof(f276,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtpldt0(X0,sz10),X1) ),
inference(resolution,[status(thm)],[f62,f54]) ).
fof(f291,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
inference(resolution,[status(thm)],[f276,f229]) ).
fof(f292,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f246,f291]) ).
fof(f299,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp)) ),
inference(resolution,[status(thm)],[f255,f276]) ).
fof(f320,plain,
smndt0(xp) = sdtpldt0(sz00,smndt0(xp)),
inference(resolution,[status(thm)],[f255,f67]) ).
fof(f375,plain,
( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f256,f292]) ).
fof(f376,plain,
( sz00 = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f268,f375]) ).
fof(f377,plain,
( sz00 = sdtpldt0(sz00,xp)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f268,f376]) ).
fof(f401,plain,
( xp = sz00
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f377,f259]) ).
fof(f402,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f230]) ).
fof(f403,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f405,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(xp))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f249,f299]) ).
fof(f409,plain,
( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),smndt0(xp))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f405,f256]) ).
fof(f410,plain,
( sz00 = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),smndt0(xp))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f268,f409]) ).
fof(f411,plain,
( sz00 = sdtpldt0(sz00,smndt0(xp))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f268,f410]) ).
fof(f416,plain,
( smndt0(xp) = sz00
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f411,f320]) ).
fof(f423,plain,
( sdtpldt0(xp,sz00) = sz00
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f416,f265]) ).
fof(f476,plain,
( sz00 = xp
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f423,f257]) ).
fof(f477,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f230]) ).
fof(f478,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f479,plain,
$false,
inference(sat_refutation,[status(thm)],[f251,f403,f478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n025.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 29 21:08:26 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.13/0.31 % Drodi V3.6.0
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.107041 seconds
% 0.13/0.41 % CPU time: 0.746153 seconds
% 0.13/0.41 % Total memory used: 74.451 MB
% 0.13/0.41 % Net memory used: 73.603 MB
%------------------------------------------------------------------------------