TSTP Solution File: NUM454+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM454+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 0.20s 0.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 47 unt; 0 def)
% Number of atoms : 184 ( 99 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 147 ( 60 ~; 59 |; 17 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W0 = sz00
| W1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f55,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f56,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f57,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f62,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(f63,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)],[f62]) ).
fof(f64,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f68,plain,
! [X0] :
( ~ aInteger0(X0)
| X0 = sdtpldt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f69,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f70,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f76,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f77,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f79,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f88,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| sdtasdt0(W0,W1) != sz00
| W0 = sz00
| W1 = sz00 ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,X1) != sz00
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f230,plain,
aInteger0(xp),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f231,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f237,plain,
( sdtpldt0(sz10,xp) = smndt0(sz10)
& sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
inference(pre_NNF_transformation,[status(esa)],[f50]) ).
fof(f238,plain,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(cnf_transformation,[status(esa)],[f237]) ).
fof(f239,plain,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(cnf_transformation,[status(esa)],[f237]) ).
fof(f255,plain,
aInteger0(smndt0(sz10)),
inference(resolution,[status(thm)],[f57,f55]) ).
fof(f256,plain,
aInteger0(smndt0(xp)),
inference(resolution,[status(thm)],[f230,f57]) ).
fof(f259,plain,
xp = sdtpldt0(sz00,xp),
inference(resolution,[status(thm)],[f68,f230]) ).
fof(f260,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[status(thm)],[f68,f55]) ).
fof(f261,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[f77,f230]) ).
fof(f266,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolution,[status(thm)],[f70,f55]) ).
fof(f270,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(xp,X1)) = sdtpldt0(sdtpldt0(X0,xp),X1) ),
inference(resolution,[status(thm)],[f63,f230]) ).
fof(f272,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtpldt0(X0,sz10),X1) ),
inference(resolution,[status(thm)],[f63,f55]) ).
fof(f275,plain,
sz00 = sdtpldt0(smndt0(xp),xp),
inference(resolution,[status(thm)],[f71,f230]) ).
fof(f276,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f71,f55]) ).
fof(f279,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,xp) = sdtpldt0(xp,X0) ),
inference(resolution,[status(thm)],[f65,f230]) ).
fof(f280,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[f65,f55]) ).
fof(f281,plain,
sdtpldt0(sz10,xp) = sdtpldt0(xp,sz10),
inference(resolution,[status(thm)],[f279,f55]) ).
fof(f282,plain,
smndt0(sz10) = sdtpldt0(xp,sz10),
inference(forward_demodulation,[status(thm)],[f238,f281]) ).
fof(f286,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(xp,sz10)) = sdtpldt0(sdtpldt0(X0,xp),sz10) ),
inference(resolution,[status(thm)],[f270,f55]) ).
fof(f287,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(sz10)) = sdtpldt0(sdtpldt0(X0,xp),sz10) ),
inference(forward_demodulation,[status(thm)],[f282,f286]) ).
fof(f292,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
inference(resolution,[status(thm)],[f272,f230]) ).
fof(f293,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(sz10)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
inference(forward_demodulation,[status(thm)],[f238,f292]) ).
fof(f295,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(sdtpldt0(xp,sz10),xp),
inference(resolution,[status(thm)],[f293,f230]) ).
fof(f296,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(smndt0(sz10),xp),
inference(forward_demodulation,[status(thm)],[f282,f295]) ).
fof(f299,plain,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp),
inference(resolution,[status(thm)],[f255,f293]) ).
fof(f300,plain,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = sdtpldt0(sz00,xp),
inference(forward_demodulation,[status(thm)],[f276,f299]) ).
fof(f301,plain,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = xp,
inference(forward_demodulation,[status(thm)],[f259,f300]) ).
fof(f304,plain,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = sdtpldt0(sdtpldt0(smndt0(sz10),xp),sz10),
inference(resolution,[status(thm)],[f255,f287]) ).
fof(f305,plain,
xp = sdtpldt0(sdtpldt0(smndt0(sz10),xp),sz10),
inference(forward_demodulation,[status(thm)],[f301,f304]) ).
fof(f306,plain,
xp = sdtpldt0(sdtpldt0(xp,smndt0(sz10)),sz10),
inference(forward_demodulation,[status(thm)],[f296,f305]) ).
fof(f311,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(sz10)) = sdtpldt0(smndt0(sz10),X0) ),
inference(resolution,[status(thm)],[f255,f65]) ).
fof(f314,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(smndt0(sz10),smndt0(sz10))) = sdtpldt0(sdtpldt0(X0,smndt0(sz10)),smndt0(sz10)) ),
inference(resolution,[status(thm)],[f255,f63]) ).
fof(f315,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,xp) = sdtpldt0(sdtpldt0(X0,smndt0(sz10)),smndt0(sz10)) ),
inference(forward_demodulation,[status(thm)],[f301,f314]) ).
fof(f329,plain,
sdtpldt0(xp,xp) = sdtpldt0(sdtpldt0(xp,smndt0(sz10)),smndt0(sz10)),
inference(resolution,[status(thm)],[f315,f230]) ).
fof(f336,plain,
sdtpldt0(smndt0(xp),smndt0(sz10)) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(resolution,[status(thm)],[f256,f311]) ).
fof(f340,plain,
sdtpldt0(smndt0(xp),smndt0(sz10)) = sdtpldt0(sdtpldt0(smndt0(xp),sz10),xp),
inference(resolution,[status(thm)],[f256,f293]) ).
fof(f341,plain,
sdtpldt0(smndt0(sz10),smndt0(xp)) = sdtpldt0(sdtpldt0(smndt0(xp),sz10),xp),
inference(forward_demodulation,[status(thm)],[f336,f340]) ).
fof(f344,plain,
sdtpldt0(smndt0(xp),smndt0(sz10)) = sdtpldt0(sdtpldt0(smndt0(xp),xp),sz10),
inference(resolution,[status(thm)],[f256,f287]) ).
fof(f345,plain,
sdtpldt0(smndt0(sz10),smndt0(xp)) = sdtpldt0(sdtpldt0(smndt0(xp),xp),sz10),
inference(forward_demodulation,[status(thm)],[f336,f344]) ).
fof(f346,plain,
sdtpldt0(smndt0(sz10),smndt0(xp)) = sdtpldt0(sz00,sz10),
inference(forward_demodulation,[status(thm)],[f275,f345]) ).
fof(f347,plain,
sdtpldt0(smndt0(sz10),smndt0(xp)) = sz10,
inference(forward_demodulation,[status(thm)],[f260,f346]) ).
fof(f350,plain,
sdtpldt0(smndt0(xp),sz10) = sdtpldt0(sz10,smndt0(xp)),
inference(resolution,[status(thm)],[f256,f280]) ).
fof(f351,plain,
sdtpldt0(smndt0(xp),sz10) = smndt0(sz10),
inference(forward_demodulation,[status(thm)],[f239,f350]) ).
fof(f368,plain,
sz10 = sdtpldt0(sdtpldt0(smndt0(xp),sz10),xp),
inference(backward_demodulation,[status(thm)],[f347,f341]) ).
fof(f369,plain,
sz10 = sdtpldt0(smndt0(sz10),xp),
inference(forward_demodulation,[status(thm)],[f351,f368]) ).
fof(f372,plain,
sdtpldt0(xp,smndt0(sz10)) = sz10,
inference(backward_demodulation,[status(thm)],[f369,f296]) ).
fof(f373,plain,
sdtpldt0(xp,xp) = sdtpldt0(sz10,smndt0(sz10)),
inference(backward_demodulation,[status(thm)],[f372,f329]) ).
fof(f374,plain,
sdtpldt0(xp,xp) = sz00,
inference(forward_demodulation,[status(thm)],[f266,f373]) ).
fof(f375,plain,
xp = sdtpldt0(sz10,sz10),
inference(backward_demodulation,[status(thm)],[f372,f306]) ).
fof(f544,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sdtpldt0(sz10,sz10)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz10)) ),
inference(resolution,[status(thm)],[f80,f55]) ).
fof(f545,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,xp) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,sz10)) ),
inference(forward_demodulation,[status(thm)],[f375,f544]) ).
fof(f563,plain,
sdtasdt0(xp,xp) = sdtpldt0(sdtasdt0(xp,sz10),sdtasdt0(xp,sz10)),
inference(resolution,[status(thm)],[f545,f230]) ).
fof(f564,plain,
sdtasdt0(xp,xp) = sdtpldt0(xp,sdtasdt0(xp,sz10)),
inference(forward_demodulation,[status(thm)],[f261,f563]) ).
fof(f565,plain,
sdtasdt0(xp,xp) = sdtpldt0(xp,xp),
inference(forward_demodulation,[status(thm)],[f261,f564]) ).
fof(f566,plain,
sdtasdt0(xp,xp) = sz00,
inference(forward_demodulation,[status(thm)],[f374,f565]) ).
fof(f1198,plain,
( spl0_10
<=> xp = sz00 ),
introduced(split_symbol_definition) ).
fof(f1199,plain,
( xp = sz00
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f1198]) ).
fof(f1252,plain,
( spl0_16
<=> aInteger0(xp) ),
introduced(split_symbol_definition) ).
fof(f1254,plain,
( ~ aInteger0(xp)
| spl0_16 ),
inference(component_clause,[status(thm)],[f1252]) ).
fof(f1263,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xp)
| xp = sz00
| xp = sz00 ),
inference(resolution,[status(thm)],[f89,f566]) ).
fof(f1264,plain,
( ~ spl0_16
| spl0_10 ),
inference(split_clause,[status(thm)],[f1263,f1252,f1198]) ).
fof(f1299,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f1254,f230]) ).
fof(f1300,plain,
spl0_16,
inference(contradiction_clause,[status(thm)],[f1299]) ).
fof(f1303,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f1199,f231]) ).
fof(f1304,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f1303]) ).
fof(f1305,plain,
$false,
inference(sat_refutation,[status(thm)],[f1264,f1300,f1304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM454+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 20:39:34 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.36 % Drodi V3.6.0
% 0.20/0.54 % Refutation found
% 0.20/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.56 % Elapsed time: 0.199231 seconds
% 1.44/0.56 % CPU time: 1.449307 seconds
% 1.44/0.56 % Total memory used: 84.151 MB
% 1.44/0.56 % Net memory used: 82.783 MB
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