TSTP Solution File: RNG108+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG108+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 20:38:01 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 15 unt; 1 def)
% Number of atoms : 180 ( 38 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 193 ( 71 ~; 74 |; 33 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 45 ( 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f48,plain,
aElement0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f49,plain,
aElement0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f70,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f71,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f79,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f80,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f184,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(f185,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)],[f184]) ).
fof(f186,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)],[f185]) ).
fof(f187,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)],[f186]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X0)
| X1 != slsdtgt0(X0)
| aElementOf0(X2,X1)
| ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ),
inference(cnf_transformation,[status(esa)],[f187]) ).
fof(f197,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f198,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f203,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(pre_NNF_transformation,[status(esa)],[f44]) ).
fof(f204,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cnf_transformation,[status(esa)],[f203]) ).
fof(f225,plain,
( spl0_2
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f228,plain,
( spl0_3
<=> aElementOf0(xa,slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f231,plain,
( spl0_4
<=> aElementOf0(sz00,slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( spl0_5
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f237,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f204,f225,f228,f231,f234]) ).
fof(f249,plain,
! [X0,X1] :
( ~ aElement0(X0)
| aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f191]) ).
fof(f257,plain,
sdtasdt0(xb,sz00) = sz00,
inference(resolution,[status(thm)],[f80,f198]) ).
fof(f258,plain,
sdtasdt0(xa,sz00) = sz00,
inference(resolution,[status(thm)],[f80,f197]) ).
fof(f693,plain,
( spl0_61
<=> aElement0(sz10) ),
introduced(split_symbol_definition) ).
fof(f695,plain,
( ~ aElement0(sz10)
| spl0_61 ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f699,plain,
( spl0_63
<=> aElement0(sz00) ),
introduced(split_symbol_definition) ).
fof(f701,plain,
( ~ aElement0(sz00)
| spl0_63 ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f714,plain,
( spl0_66
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f716,plain,
( ~ aElement0(xb)
| spl0_66 ),
inference(component_clause,[status(thm)],[f714]) ).
fof(f721,plain,
( ~ aElement0(xb)
| aElementOf0(sz00,slsdtgt0(xb))
| ~ aElement0(sz00) ),
inference(paramodulation,[status(thm)],[f257,f249]) ).
fof(f722,plain,
( ~ spl0_66
| spl0_4
| ~ spl0_63 ),
inference(split_clause,[status(thm)],[f721,f714,f231,f699]) ).
fof(f725,plain,
( $false
| spl0_63 ),
inference(forward_subsumption_resolution,[status(thm)],[f701,f48]) ).
fof(f726,plain,
spl0_63,
inference(contradiction_clause,[status(thm)],[f725]) ).
fof(f727,plain,
( $false
| spl0_61 ),
inference(forward_subsumption_resolution,[status(thm)],[f695,f49]) ).
fof(f728,plain,
spl0_61,
inference(contradiction_clause,[status(thm)],[f727]) ).
fof(f729,plain,
( $false
| spl0_66 ),
inference(forward_subsumption_resolution,[status(thm)],[f716,f198]) ).
fof(f730,plain,
spl0_66,
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f861,plain,
sdtasdt0(xb,sz10) = xb,
inference(resolution,[status(thm)],[f71,f198]) ).
fof(f868,plain,
( ~ aElement0(xb)
| aElementOf0(xb,slsdtgt0(xb))
| ~ aElement0(sz10) ),
inference(paramodulation,[status(thm)],[f861,f249]) ).
fof(f869,plain,
( ~ spl0_66
| spl0_5
| ~ spl0_61 ),
inference(split_clause,[status(thm)],[f868,f714,f234,f693]) ).
fof(f1030,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolution,[status(thm)],[f197,f71]) ).
fof(f1091,plain,
( spl0_90
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f1093,plain,
( ~ aElement0(xa)
| spl0_90 ),
inference(component_clause,[status(thm)],[f1091]) ).
fof(f1096,plain,
( ~ aElement0(xa)
| aElementOf0(sz00,slsdtgt0(xa))
| ~ aElement0(sz00) ),
inference(paramodulation,[status(thm)],[f258,f249]) ).
fof(f1097,plain,
( ~ spl0_90
| spl0_2
| ~ spl0_63 ),
inference(split_clause,[status(thm)],[f1096,f1091,f225,f699]) ).
fof(f1098,plain,
( $false
| spl0_90 ),
inference(forward_subsumption_resolution,[status(thm)],[f1093,f197]) ).
fof(f1099,plain,
spl0_90,
inference(contradiction_clause,[status(thm)],[f1098]) ).
fof(f1343,plain,
( ~ aElement0(xa)
| aElementOf0(xa,slsdtgt0(xa))
| ~ aElement0(sz10) ),
inference(paramodulation,[status(thm)],[f1030,f249]) ).
fof(f1344,plain,
( ~ spl0_90
| spl0_3
| ~ spl0_61 ),
inference(split_clause,[status(thm)],[f1343,f1091,f228,f693]) ).
fof(f1345,plain,
$false,
inference(sat_refutation,[status(thm)],[f237,f722,f726,f728,f730,f869,f1097,f1099,f1344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG108+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n015.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Apr 29 22:41:47 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.40 % Elapsed time: 0.032308 seconds
% 0.19/0.40 % CPU time: 0.118775 seconds
% 0.19/0.40 % Total memory used: 28.778 MB
% 0.19/0.40 % Net memory used: 28.673 MB
%------------------------------------------------------------------------------