TSTP Solution File: RNG123+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:38:05 EDT 2024
% Result : Theorem 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 217 ( 44 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 239 ( 69 ~; 69 |; 87 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 83 ( 57 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,hypothesis,
( aSet0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = smndt0(sdtasdt0(xq,xu)) )
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xb )
& ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xb )
& aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
( ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xr )
| aElementOf0(xr,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ ( ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& sdtpldt0(W0,W1) = xr )
| aElementOf0(xr,xI) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f230,plain,
( aSet0(xI)
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( ! [W1] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f231,plain,
( aSet0(xI)
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( ! [W1] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ~ aElementOf0(W0,slsdtgt0(xa))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xa,W1) != W0 ) ) )
& ! [W0] :
( ( ~ aElementOf0(W0,slsdtgt0(xb))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xb,W1) != W0 ) ) )
& ! [W0] :
( ( ~ aElementOf0(W0,xI)
| ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& ( aElementOf0(W0,xI)
| ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 ) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(NNF_transformation,[status(esa)],[f230]) ).
fof(f232,plain,
( aSet0(xI)
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( ! [W1] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xa,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xa,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xb))
| ? [W1] :
( aElement0(W1)
& sdtasdt0(xb,W1) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xb,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ? [W1,W2] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& sdtpldt0(W1,W2) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
| ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(miniscoping,[status(esa)],[f231]) ).
fof(f233,plain,
( aSet0(xI)
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( ! [W1] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ( aElement0(sk0_23(W0))
& sdtasdt0(xa,sk0_23(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xa,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,slsdtgt0(xb))
| ( aElement0(sk0_24(W0))
& sdtasdt0(xb,sk0_24(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
| ! [W1] :
( ~ aElement0(W1)
| sdtasdt0(xb,W1) != W0 ) )
& ! [W0] :
( ~ aElementOf0(W0,xI)
| ( aElementOf0(sk0_25(W0),slsdtgt0(xa))
& aElementOf0(sk0_26(W0),slsdtgt0(xb))
& sdtpldt0(sk0_25(W0),sk0_26(W0)) = W0 ) )
& ! [W0] :
( aElementOf0(W0,xI)
| ! [W1,W2] :
( ~ aElementOf0(W1,slsdtgt0(xa))
| ~ aElementOf0(W2,slsdtgt0(xb))
| sdtpldt0(W1,W2) != W0 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemization,[status(esa)],[f232]) ).
fof(f235,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(cnf_transformation,[status(esa)],[f233]) ).
fof(f247,plain,
! [X0,X1,X2] :
( aElementOf0(X0,xI)
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 ),
inference(cnf_transformation,[status(esa)],[f233]) ).
fof(f307,plain,
( aElementOf0(sk0_41,slsdtgt0(xa))
& aElementOf0(sk0_42,slsdtgt0(xb))
& sdtpldt0(sk0_41,sk0_42) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f310,plain,
sdtpldt0(sk0_41,sk0_42) = smndt0(sdtasdt0(xq,xu)),
inference(cnf_transformation,[status(esa)],[f307]) ).
fof(f311,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[status(esa)],[f307]) ).
fof(f312,plain,
( aElementOf0(sk0_43,slsdtgt0(xa))
& aElementOf0(sk0_44,slsdtgt0(xb))
& sdtpldt0(sk0_43,sk0_44) = xb
& aElementOf0(sk0_45,slsdtgt0(xa))
& aElementOf0(sk0_46,slsdtgt0(xb))
& sdtpldt0(sk0_45,sk0_46) = xb
& aElementOf0(xb,xI) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f313,plain,
aElementOf0(sk0_43,slsdtgt0(xa)),
inference(cnf_transformation,[status(esa)],[f312]) ).
fof(f314,plain,
aElementOf0(sk0_44,slsdtgt0(xb)),
inference(cnf_transformation,[status(esa)],[f312]) ).
fof(f315,plain,
sdtpldt0(sk0_43,sk0_44) = xb,
inference(cnf_transformation,[status(esa)],[f312]) ).
fof(f320,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f321,plain,
( ! [W0,W1] :
( ~ aElementOf0(W0,slsdtgt0(xa))
| ~ aElementOf0(W1,slsdtgt0(xb))
| sdtpldt0(W0,W1) != xr )
& ~ aElementOf0(xr,xI) ),
inference(pre_NNF_transformation,[status(esa)],[f56]) ).
fof(f323,plain,
~ aElementOf0(xr,xI),
inference(cnf_transformation,[status(esa)],[f321]) ).
fof(f406,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(destructive_equality_resolution,[status(esa)],[f247]) ).
fof(f494,plain,
( spl0_28
<=> aElementOf0(xb,xI) ),
introduced(split_symbol_definition) ).
fof(f815,plain,
( spl0_91
<=> aElementOf0(sk0_43,slsdtgt0(xa)) ),
introduced(split_symbol_definition) ).
fof(f817,plain,
( ~ aElementOf0(sk0_43,slsdtgt0(xa))
| spl0_91 ),
inference(component_clause,[status(thm)],[f815]) ).
fof(f818,plain,
( spl0_92
<=> aElementOf0(sk0_44,slsdtgt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f820,plain,
( ~ aElementOf0(sk0_44,slsdtgt0(xb))
| spl0_92 ),
inference(component_clause,[status(thm)],[f818]) ).
fof(f821,plain,
( aElementOf0(xb,xI)
| ~ aElementOf0(sk0_43,slsdtgt0(xa))
| ~ aElementOf0(sk0_44,slsdtgt0(xb)) ),
inference(paramodulation,[status(thm)],[f315,f406]) ).
fof(f822,plain,
( spl0_28
| ~ spl0_91
| ~ spl0_92 ),
inference(split_clause,[status(thm)],[f821,f494,f815,f818]) ).
fof(f849,plain,
( $false
| spl0_92 ),
inference(forward_subsumption_resolution,[status(thm)],[f820,f314]) ).
fof(f850,plain,
spl0_92,
inference(contradiction_clause,[status(thm)],[f849]) ).
fof(f851,plain,
( $false
| spl0_91 ),
inference(forward_subsumption_resolution,[status(thm)],[f817,f313]) ).
fof(f852,plain,
spl0_91,
inference(contradiction_clause,[status(thm)],[f851]) ).
fof(f1524,plain,
( spl0_202
<=> aElementOf0(xr,xI) ),
introduced(split_symbol_definition) ).
fof(f1525,plain,
( aElementOf0(xr,xI)
| ~ spl0_202 ),
inference(component_clause,[status(thm)],[f1524]) ).
fof(f2343,plain,
aElementOf0(sdtpldt0(sk0_41,sk0_42),xI),
inference(backward_demodulation,[status(thm)],[f310,f311]) ).
fof(f2823,plain,
xr = sdtpldt0(sdtpldt0(sk0_41,sk0_42),xb),
inference(forward_demodulation,[status(thm)],[f310,f320]) ).
fof(f2855,plain,
( spl0_322
<=> aElementOf0(sdtpldt0(sk0_41,sk0_42),xI) ),
introduced(split_symbol_definition) ).
fof(f2857,plain,
( ~ aElementOf0(sdtpldt0(sk0_41,sk0_42),xI)
| spl0_322 ),
inference(component_clause,[status(thm)],[f2855]) ).
fof(f2858,plain,
( ~ aElementOf0(sdtpldt0(sk0_41,sk0_42),xI)
| ~ aElementOf0(xb,xI)
| aElementOf0(xr,xI) ),
inference(paramodulation,[status(thm)],[f2823,f235]) ).
fof(f2859,plain,
( ~ spl0_322
| ~ spl0_28
| spl0_202 ),
inference(split_clause,[status(thm)],[f2858,f2855,f494,f1524]) ).
fof(f2874,plain,
( $false
| spl0_322 ),
inference(forward_subsumption_resolution,[status(thm)],[f2857,f2343]) ).
fof(f2875,plain,
spl0_322,
inference(contradiction_clause,[status(thm)],[f2874]) ).
fof(f2876,plain,
( $false
| ~ spl0_202 ),
inference(forward_subsumption_resolution,[status(thm)],[f1525,f323]) ).
fof(f2877,plain,
~ spl0_202,
inference(contradiction_clause,[status(thm)],[f2876]) ).
fof(f2878,plain,
$false,
inference(sat_refutation,[status(thm)],[f822,f850,f852,f2859,f2875,f2877]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n029.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 : Mon Apr 29 22:38:19 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.48/0.55 % Elapsed time: 0.219500 seconds
% 1.48/0.55 % CPU time: 1.504718 seconds
% 1.48/0.55 % Total memory used: 87.939 MB
% 1.48/0.55 % Net memory used: 87.009 MB
%------------------------------------------------------------------------------