TSTP Solution File: RNG105+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG105+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:32:55 EDT 2023
% Result : Theorem 0.14s 0.32s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 73 ( 20 unt; 1 def)
% Number of atoms : 198 ( 30 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 198 ( 73 ~; 78 |; 30 &)
% ( 14 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 51 (; 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( aElement0(xv)
& sdtasdt0(xc,xv) = xy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f49,plain,
aElement0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f50,plain,
aElement0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f53,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| aElement0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| aElement0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f185,plain,
! [W0] :
( ~ aElement0(W0)
| ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f186,plain,
! [W0] :
( ~ aElement0(W0)
| ! [W1] :
( ( W1 != slsdtgt0(W0)
| ( aSet0(W1)
& ! [W2] :
( ( ~ aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) )
& ( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) ) ) ) )
& ( W1 = slsdtgt0(W0)
| ~ aSet0(W1)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) )
& ( aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f185]) ).
fof(f187,plain,
! [W0] :
( ~ aElement0(W0)
| ( ! [W1] :
( W1 != slsdtgt0(W0)
| ( aSet0(W1)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) )
& ! [W2] :
( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) ) ) )
& ! [W1] :
( W1 = slsdtgt0(W0)
| ~ aSet0(W1)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) )
& ( aElementOf0(W2,W1)
| ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f186]) ).
fof(f188,plain,
! [W0] :
( ~ aElement0(W0)
| ( ! [W1] :
( W1 != slsdtgt0(W0)
| ( aSet0(W1)
& ! [W2] :
( ~ aElementOf0(W2,W1)
| ( aElement0(sk0_17(W2,W1,W0))
& sdtasdt0(W0,sk0_17(W2,W1,W0)) = W2 ) )
& ! [W2] :
( aElementOf0(W2,W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != W2 ) ) ) )
& ! [W1] :
( W1 = slsdtgt0(W0)
| ~ aSet0(W1)
| ( ( ~ aElementOf0(sk0_18(W1,W0),W1)
| ! [W3] :
( ~ aElement0(W3)
| sdtasdt0(W0,W3) != sk0_18(W1,W0) ) )
& ( aElementOf0(sk0_18(W1,W0),W1)
| ( aElement0(sk0_19(W1,W0))
& sdtasdt0(W0,sk0_19(W1,W0)) = sk0_18(W1,W0) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f187]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X0)
| X1 != slsdtgt0(X0)
| aElementOf0(X2,X1)
| ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ),
inference(cnf_transformation,[status(esa)],[f188]) ).
fof(f196,plain,
aElement0(xc),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f199,plain,
aElement0(xz),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f200,plain,
aElement0(xu),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f202,plain,
aElement0(xv),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f204,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f205,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f206,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f207,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(cnf_transformation,[status(esa)],[f206]) ).
fof(f221,plain,
( spl0_0
<=> aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
introduced(split_symbol_definition) ).
fof(f224,plain,
( spl0_1
<=> aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
introduced(split_symbol_definition) ).
fof(f227,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f207,f221,f224]) ).
fof(f239,plain,
! [X0,X1] :
( ~ aElement0(X0)
| aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f192]) ).
fof(f241,plain,
( spl0_2
<=> aElement0(xc) ),
introduced(split_symbol_definition) ).
fof(f243,plain,
( ~ aElement0(xc)
| spl0_2 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( spl0_3
<=> aElement0(sdtasdt0(xu,xz)) ),
introduced(split_symbol_definition) ).
fof(f246,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| spl0_3 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ aElement0(xc)
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElement0(sdtasdt0(xu,xz)) ),
inference(paramodulation,[status(thm)],[f205,f239]) ).
fof(f248,plain,
( ~ spl0_2
| spl0_1
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f247,f241,f224,f244]) ).
fof(f279,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f196]) ).
fof(f280,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f279]) ).
fof(f281,plain,
( spl0_10
<=> aElement0(xu) ),
introduced(split_symbol_definition) ).
fof(f283,plain,
( ~ aElement0(xu)
| spl0_10 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f319,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f200]) ).
fof(f320,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f319]) ).
fof(f321,plain,
( spl0_18
<=> aElement0(xv) ),
introduced(split_symbol_definition) ).
fof(f323,plain,
( ~ aElement0(xv)
| spl0_18 ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f359,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f202]) ).
fof(f360,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f369,plain,
( spl0_27
<=> aElement0(xz) ),
introduced(split_symbol_definition) ).
fof(f371,plain,
( ~ aElement0(xz)
| spl0_27 ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( ~ aElement0(xu)
| ~ aElement0(xz)
| spl0_3 ),
inference(resolution,[status(thm)],[f246,f56]) ).
fof(f373,plain,
( ~ spl0_10
| ~ spl0_27
| spl0_3 ),
inference(split_clause,[status(thm)],[f372,f281,f369,f244]) ).
fof(f374,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f199]) ).
fof(f375,plain,
spl0_27,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f564,plain,
( spl0_61
<=> aElement0(sz00) ),
introduced(split_symbol_definition) ).
fof(f566,plain,
( ~ aElement0(sz00)
| spl0_61 ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f572,plain,
( spl0_63
<=> aElement0(sz10) ),
introduced(split_symbol_definition) ).
fof(f574,plain,
( ~ aElement0(sz10)
| spl0_63 ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f624,plain,
( $false
| spl0_63 ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f50]) ).
fof(f625,plain,
spl0_63,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f626,plain,
( $false
| spl0_61 ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f49]) ).
fof(f627,plain,
spl0_61,
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f644,plain,
( spl0_77
<=> aElement0(sdtpldt0(xu,xv)) ),
introduced(split_symbol_definition) ).
fof(f646,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| spl0_77 ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f680,plain,
( ~ aElement0(xc)
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(paramodulation,[status(thm)],[f204,f239]) ).
fof(f681,plain,
( ~ spl0_2
| spl0_0
| ~ spl0_77 ),
inference(split_clause,[status(thm)],[f680,f241,f221,f644]) ).
fof(f801,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| spl0_77 ),
inference(resolution,[status(thm)],[f646,f54]) ).
fof(f802,plain,
( ~ spl0_10
| ~ spl0_18
| spl0_77 ),
inference(split_clause,[status(thm)],[f801,f281,f321,f644]) ).
fof(f803,plain,
$false,
inference(sat_refutation,[status(thm)],[f227,f248,f280,f320,f360,f373,f375,f625,f627,f681,f802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : RNG105+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.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 : Tue May 30 10:39:38 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.32 % Refutation found
% 0.14/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.55 % Elapsed time: 0.040724 seconds
% 0.14/0.55 % CPU time: 0.027473 seconds
% 0.14/0.55 % Memory used: 4.325 MB
%------------------------------------------------------------------------------