%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG087+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:54 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 7 unt; 3 def)
% Number of atoms : 222 ( 23 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 296 ( 117 ~; 109 |; 57 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-5 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 149 ( 123 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
? [W0,W1] :
( xy = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ? [W0,W1] :
( xy = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f81,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f82,definition,
! [W0,W1,W3,W4,W5] :
( sP1_prd(W5,W4,W3,W1,W0)
<=> ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f83,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f81,f82]) ).
fof(f84,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ( ( ! [W3] :
( ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP1_prd(sK6_skl(W2,W1,W0),sK5_skl(W2,W1,W0),sK4_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK4_skl(W2,W1,W0),W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,sK4_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK4_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP1_prd(sK3_skl(W3,W2,W1,W0),sK2_skl(W3,W2,W1,W0),W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(W4,sK2_skl(W3,W2,W1,W0)),skolemize(W5,sK3_skl(W3,W2,W1,W0)),skolemize(W3,sK4_skl(W2,W1,W0)),skolemize(W4,sK5_skl(W2,W1,W0)),skolemize(W5,sK6_skl(W2,W1,W0))],[f85]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( sP1_prd(sK3_skl(X3,X2,X1,X0),sK2_skl(X3,X2,X1,X0),X3,X1,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f103,plain,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f104,plain,
! [W0] :
( ( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(NNF_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
( ! [W0] :
( ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( ! [W0] :
( ( ( ( ~ aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)
& aElement0(sK10_skl(W0)) )
| ( ~ aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0)
& aElementOf0(sK9_skl(W0),W0) ) )
& aElementOf0(sK8_skl(W0),W0) )
| ~ aSet0(W0)
| aIdeal0(W0) )
& ! [W0] :
( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f105]) ).
fof(f107,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f115,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f116,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f118,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f123,plain,
! [W0,W1] :
( xy != sdtpldt0(W0,W1)
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f124,plain,
! [X0,X1] :
( xy != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f130,plain,
! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f82]) ).
fof(f131,plain,
( ! [W0,W1,W3,W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0)
| sP1_prd(W5,W4,W3,W1,W0) )
& ! [W0,W1,W3,W4,W5] :
( ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ sP1_prd(W5,W4,W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X1,X4)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X0,X3)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
! [X0,X1,X2,X3,X4] :
( sdtpldt0(X1,X0) = X2
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f137,plain,
! [X0,X1,X2] :
( sP1_prd(sK3_skl(X2,sdtpldt1(X0,X1),X1,X0),sK2_skl(X2,sdtpldt1(X0,X1),X1,X0),X2,X1,X0)
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f88]) ).
fof(f144,plain,
aSet0(xJ),
inference(resolution,[status(thm)],[f107,f116]) ).
fof(f145,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f107,f115]) ).
fof(f204,plain,
! [X0,X1,X2] :
( sdtpldt0(sK2_skl(X2,sdtpldt1(X0,X1),X1,X0),sK3_skl(X2,sdtpldt1(X0,X1),X1,X0)) = X2
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f137,f134]) ).
fof(f205,plain,
! [X0,X1,X2] :
( aElementOf0(sK3_skl(X2,sdtpldt1(X0,X1),X1,X0),X1)
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f137,f133]) ).
fof(f206,plain,
! [X0,X1,X2] :
( aElementOf0(sK2_skl(X2,sdtpldt1(X0,X1),X1,X0),X0)
| ~ aElementOf0(X2,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f137,f132]) ).
fof(f498,plain,
! [X0,X1] :
( ~ aElementOf0(sK3_skl(xy,sdtpldt1(X0,X1),X1,X0),xJ)
| ~ aElementOf0(sK2_skl(xy,sdtpldt1(X0,X1),X1,X0),xI)
| ~ aElementOf0(xy,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f204,f124]) ).
fof(f499,plain,
! [X0] :
( ~ aElementOf0(xy,sdtpldt1(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0)
| ~ aElementOf0(sK2_skl(xy,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(xy,sdtpldt1(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f498,f205]) ).
fof(f500,plain,
! [X0] :
( ~ aElementOf0(sK2_skl(xy,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(xy,sdtpldt1(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f499]) ).
fof(f501,plain,
! [X0] :
( ~ aElementOf0(sK2_skl(xy,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(xy,sdtpldt1(X0,xJ))
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f144]) ).
fof(f502,plain,
( ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f501,f206]) ).
fof(f503,plain,
( ~ aSet0(xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| ~ aSet0(xI) ),
inference(duplicate_literals_removal,[status(thm)],[f502]) ).
fof(f504,plain,
( ~ aSet0(xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ)) ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f145]) ).
fof(f506,plain,
~ aSet0(xJ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f118]) ).
fof(f507,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f144,f506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG087+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:18:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.093288 seconds
% 0.13/0.45 % CPU time: 0.443063 seconds
% 0.13/0.45 % Total memory used: 110.343 MB
% 0.13/0.45 % Net memory used: 109.558 MB
%------------------------------------------------------------------------------