TSTP Solution File: RNG076+2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG076+2 : 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 : Wed May 31 12:32:48 EDT 2023
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 32
% Syntax : Number of formulae : 107 ( 23 unt; 0 def)
% Number of atoms : 250 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 241 ( 98 ~; 106 |; 14 &)
% ( 18 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 30 (; 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,hypothesis,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,conjecture,
sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f81,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| aScalar0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f83,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| aScalar0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f119,plain,
! [W0,W1,W2,W3] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| ~ aScalar0(W2)
| ~ aScalar0(W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W2,W3)
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f120,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f123,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| sdtlseqdt0(W0,W1)
| sdtlseqdt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f178,plain,
aScalar0(xC),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f180,plain,
aScalar0(xD),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f182,plain,
aScalar0(xE),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f188,plain,
aScalar0(xH),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f190,plain,
aScalar0(xR),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f193,plain,
xP = sdtasdt0(xE,xH),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f194,plain,
aScalar0(xS),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f198,plain,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f199,plain,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f200,plain,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f219,plain,
( spl0_4
<=> aScalar0(xE) ),
introduced(split_symbol_definition) ).
fof(f221,plain,
( ~ aScalar0(xE)
| spl0_4 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( spl0_5
<=> aScalar0(xH) ),
introduced(split_symbol_definition) ).
fof(f224,plain,
( ~ aScalar0(xH)
| spl0_5 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( spl0_6
<=> aScalar0(xP) ),
introduced(split_symbol_definition) ).
fof(f228,plain,
( ~ aScalar0(xE)
| ~ aScalar0(xH)
| aScalar0(xP) ),
inference(paramodulation,[status(thm)],[f193,f84]) ).
fof(f229,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f228,f219,f222,f225]) ).
fof(f230,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f188]) ).
fof(f231,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f182]) ).
fof(f233,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f263,plain,
( spl0_14
<=> aScalar0(sdtasdt0(xE,xE)) ),
introduced(split_symbol_definition) ).
fof(f265,plain,
( ~ aScalar0(sdtasdt0(xE,xE))
| spl0_14 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( spl0_15
<=> aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))) ),
introduced(split_symbol_definition) ).
fof(f268,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| spl0_15 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f271,plain,
( ~ aScalar0(xE)
| ~ aScalar0(xE)
| spl0_14 ),
inference(resolution,[status(thm)],[f265,f84]) ).
fof(f272,plain,
( ~ spl0_4
| spl0_14 ),
inference(split_clause,[status(thm)],[f271,f219,f263]) ).
fof(f273,plain,
( spl0_16
<=> aScalar0(sdtpldt0(xP,xP)) ),
introduced(split_symbol_definition) ).
fof(f275,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| spl0_16 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( spl0_17
<=> aScalar0(sdtasdt0(xH,xH)) ),
introduced(split_symbol_definition) ).
fof(f278,plain,
( ~ aScalar0(sdtasdt0(xH,xH))
| spl0_17 ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtasdt0(xH,xH))
| spl0_15 ),
inference(resolution,[status(thm)],[f268,f82]) ).
fof(f280,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_15 ),
inference(split_clause,[status(thm)],[f279,f273,f276,f266]) ).
fof(f281,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| spl0_16 ),
inference(resolution,[status(thm)],[f275,f82]) ).
fof(f282,plain,
( ~ spl0_6
| spl0_16 ),
inference(split_clause,[status(thm)],[f281,f225,f273]) ).
fof(f283,plain,
( spl0_18
<=> aScalar0(sdtasdt0(xC,xD)) ),
introduced(split_symbol_definition) ).
fof(f285,plain,
( ~ aScalar0(sdtasdt0(xC,xD))
| spl0_18 ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( spl0_19
<=> aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) ),
introduced(split_symbol_definition) ).
fof(f288,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| spl0_19 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f291,plain,
( ~ aScalar0(xH)
| ~ aScalar0(xH)
| spl0_17 ),
inference(resolution,[status(thm)],[f278,f84]) ).
fof(f292,plain,
( ~ spl0_5
| spl0_17 ),
inference(split_clause,[status(thm)],[f291,f222,f276]) ).
fof(f293,plain,
( spl0_20
<=> aScalar0(sdtpldt0(xR,xS)) ),
introduced(split_symbol_definition) ).
fof(f295,plain,
( ~ aScalar0(sdtpldt0(xR,xS))
| spl0_20 ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtasdt0(xH,xH))
| spl0_19 ),
inference(resolution,[status(thm)],[f288,f82]) ).
fof(f297,plain,
( ~ spl0_20
| ~ spl0_17
| spl0_19 ),
inference(split_clause,[status(thm)],[f296,f293,f276,f286]) ).
fof(f298,plain,
( spl0_21
<=> aScalar0(xR) ),
introduced(split_symbol_definition) ).
fof(f300,plain,
( ~ aScalar0(xR)
| spl0_21 ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,plain,
( spl0_22
<=> aScalar0(xS) ),
introduced(split_symbol_definition) ).
fof(f303,plain,
( ~ aScalar0(xS)
| spl0_22 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xS)
| spl0_20 ),
inference(resolution,[status(thm)],[f295,f82]) ).
fof(f305,plain,
( ~ spl0_21
| ~ spl0_22
| spl0_20 ),
inference(split_clause,[status(thm)],[f304,f298,f301,f293]) ).
fof(f306,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f190]) ).
fof(f307,plain,
spl0_21,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f308,plain,
( $false
| spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f194]) ).
fof(f309,plain,
spl0_22,
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f310,plain,
( spl0_23
<=> aScalar0(xC) ),
introduced(split_symbol_definition) ).
fof(f312,plain,
( ~ aScalar0(xC)
| spl0_23 ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,plain,
( spl0_24
<=> aScalar0(xD) ),
introduced(split_symbol_definition) ).
fof(f315,plain,
( ~ aScalar0(xD)
| spl0_24 ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,plain,
( ~ aScalar0(xC)
| ~ aScalar0(xD)
| spl0_18 ),
inference(resolution,[status(thm)],[f285,f84]) ).
fof(f317,plain,
( ~ spl0_23
| ~ spl0_24
| spl0_18 ),
inference(split_clause,[status(thm)],[f316,f310,f313,f283]) ).
fof(f318,plain,
( $false
| spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f178]) ).
fof(f319,plain,
spl0_23,
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f320,plain,
( $false
| spl0_24 ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f180]) ).
fof(f321,plain,
spl0_24,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f411,plain,
( spl0_42
<=> sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
introduced(split_symbol_definition) ).
fof(f413,plain,
( ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| spl0_42 ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f414,plain,
( spl0_43
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) ),
introduced(split_symbol_definition) ).
fof(f416,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| spl0_43 ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,plain,
( ~ aScalar0(sdtasdt0(xE,xE))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)))
| ~ aScalar0(sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))
| ~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))) ),
inference(resolution,[status(thm)],[f120,f200]) ).
fof(f418,plain,
( ~ spl0_14
| ~ spl0_18
| ~ spl0_15
| ~ spl0_19
| ~ spl0_42
| ~ spl0_43 ),
inference(split_clause,[status(thm)],[f417,f263,f283,f266,f286,f411,f414]) ).
fof(f423,plain,
( $false
| spl0_42 ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f198]) ).
fof(f424,plain,
spl0_42,
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f722,plain,
( spl0_101
<=> sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ),
introduced(split_symbol_definition) ).
fof(f724,plain,
( ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS))
| spl0_101 ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( spl0_102
<=> sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH)) ),
introduced(split_symbol_definition) ).
fof(f727,plain,
( ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| spl0_102 ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f728,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| spl0_43 ),
inference(resolution,[status(thm)],[f416,f120]) ).
fof(f729,plain,
( ~ spl0_16
| ~ spl0_20
| ~ spl0_17
| ~ spl0_101
| ~ spl0_102
| spl0_43 ),
inference(split_clause,[status(thm)],[f728,f273,f293,f276,f722,f725,f414]) ).
fof(f735,plain,
( $false
| spl0_101 ),
inference(forward_subsumption_resolution,[status(thm)],[f724,f199]) ).
fof(f736,plain,
spl0_101,
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f737,plain,
( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| spl0_102 ),
inference(resolution,[status(thm)],[f727,f124]) ).
fof(f738,plain,
( ~ spl0_17
| spl0_102 ),
inference(split_clause,[status(thm)],[f737,f276,f725]) ).
fof(f741,plain,
$false,
inference(sat_refutation,[status(thm)],[f229,f231,f233,f272,f280,f282,f292,f297,f305,f307,f309,f317,f319,f321,f418,f424,f729,f736,f738]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : RNG076+2 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n029.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 10:51:21 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.5.1
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.56 % Elapsed time: 0.040804 seconds
% 0.15/0.56 % CPU time: 0.023311 seconds
% 0.15/0.56 % Memory used: 4.229 MB
%------------------------------------------------------------------------------