TSTP Solution File: NUM623+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM623+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:29:59 EDT 2023
% Result : Theorem 2.22s 0.78s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 137 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 122 ( 39 ~; 38 |; 32 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 26 (; 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
( aElementOf0(xp,xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,hypothesis,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,hypothesis,
( aElement0(xx)
& aElementOf0(xx,xQ)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,hypothesis,
( aElementOf0(xx,szNzAzT0)
& ? [W0] :
( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,W0) = xx ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,hypothesis,
! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,hypothesis,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
& aElementOf0(xx,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,conjecture,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f121,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f120]) ).
fof(f226,plain,
! [W0,W1] :
( ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f227,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f226]) ).
fof(f437,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| aElementOf0(W1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f82]) ).
fof(f439,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f437]) ).
fof(f553,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f91]) ).
fof(f556,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[status(esa)],[f553]) ).
fof(f629,plain,
( aElementOf0(xp,xQ)
& ! [W0] :
( ~ aElementOf0(W0,xQ)
| sdtlseqdt0(xp,W0) )
& xp = szmzizndt0(xQ) ),
inference(pre_NNF_transformation,[status(esa)],[f103]) ).
fof(f631,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[status(esa)],[f629]) ).
fof(f658,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f659,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f662,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f665,plain,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(sk0_38,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,sk0_38) = xx ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f666,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f665]) ).
fof(f671,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f116]) ).
fof(f672,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[status(esa)],[f671]) ).
fof(f681,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f683,plain,
xp != xx,
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f849,plain,
sdtlseqdt0(xp,xx),
inference(resolution,[status(thm)],[f631,f662]) ).
fof(f1024,plain,
sdtlseqdt0(xx,xp),
inference(resolution,[status(thm)],[f672,f681]) ).
fof(f1368,plain,
( spl0_60
<=> aElementOf0(xn,szNzAzT0) ),
introduced(split_symbol_definition) ).
fof(f1370,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl0_60 ),
inference(component_clause,[status(thm)],[f1368]) ).
fof(f1376,plain,
( $false
| spl0_60 ),
inference(forward_subsumption_resolution,[status(thm)],[f1370,f658]) ).
fof(f1377,plain,
spl0_60,
inference(contradiction_clause,[status(thm)],[f1376]) ).
fof(f1430,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f439,f556]) ).
fof(f1431,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X0),szNzAzT0) ),
inference(duplicate_literals_removal,[status(esa)],[f1430]) ).
fof(f1439,plain,
( spl0_65
<=> aElementOf0(xp,szNzAzT0) ),
introduced(split_symbol_definition) ).
fof(f1452,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aElementOf0(xp,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f659,f1431]) ).
fof(f1453,plain,
( ~ spl0_60
| spl0_65 ),
inference(split_clause,[status(thm)],[f1452,f1368,f1439]) ).
fof(f1958,plain,
( spl0_124
<=> aElementOf0(xx,szNzAzT0) ),
introduced(split_symbol_definition) ).
fof(f1960,plain,
( ~ aElementOf0(xx,szNzAzT0)
| spl0_124 ),
inference(component_clause,[status(thm)],[f1958]) ).
fof(f2007,plain,
( spl0_135
<=> xx = xp ),
introduced(split_symbol_definition) ).
fof(f2008,plain,
( xx = xp
| ~ spl0_135 ),
inference(component_clause,[status(thm)],[f2007]) ).
fof(f2058,plain,
( spl0_146
<=> sdtlseqdt0(xx,xp) ),
introduced(split_symbol_definition) ).
fof(f2060,plain,
( ~ sdtlseqdt0(xx,xp)
| spl0_146 ),
inference(component_clause,[status(thm)],[f2058]) ).
fof(f2061,plain,
( ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0)
| ~ sdtlseqdt0(xx,xp)
| xp = xx ),
inference(resolution,[status(thm)],[f227,f849]) ).
fof(f2062,plain,
( ~ spl0_65
| ~ spl0_124
| ~ spl0_146
| spl0_135 ),
inference(split_clause,[status(thm)],[f2061,f1439,f1958,f2058,f2007]) ).
fof(f2108,plain,
( $false
| spl0_146 ),
inference(forward_subsumption_resolution,[status(thm)],[f2060,f1024]) ).
fof(f2109,plain,
spl0_146,
inference(contradiction_clause,[status(thm)],[f2108]) ).
fof(f2112,plain,
( $false
| spl0_124 ),
inference(forward_subsumption_resolution,[status(thm)],[f1960,f666]) ).
fof(f2113,plain,
spl0_124,
inference(contradiction_clause,[status(thm)],[f2112]) ).
fof(f2115,plain,
( $false
| ~ spl0_135 ),
inference(forward_subsumption_resolution,[status(thm)],[f2008,f683]) ).
fof(f2116,plain,
~ spl0_135,
inference(contradiction_clause,[status(thm)],[f2115]) ).
fof(f2117,plain,
$false,
inference(sat_refutation,[status(thm)],[f1377,f1453,f2062,f2109,f2113,f2116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM623+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 09:53:38 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.34 % Drodi V3.5.1
% 2.22/0.78 % Refutation found
% 2.22/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.22/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.22/0.80 % Elapsed time: 0.482451 seconds
% 2.22/0.80 % CPU time: 2.509889 seconds
% 2.22/0.80 % Memory used: 95.477 MB
%------------------------------------------------------------------------------