%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG095+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 : n008.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 02:04:56 PM UTC 2026
% Result : Theorem 0.21s 0.78s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 10 unt; 8 def)
% Number of atoms : 265 ( 23 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 336 ( 133 ~; 129 |; 55 &)
% ( 14 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-5 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-4 aty)
% Number of variables : 153 ( 127 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f28,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
! [W0] :
( aElement0(W0)
=> aElementOf0(W0,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f37,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f84,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(f85,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(f86,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)],[f84,f85]) ).
fof(f87,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)],[f86]) ).
fof(f88,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)],[f87]) ).
fof(f89,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))],[f88]) ).
fof(f91,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)],[f89]) ).
fof(f106,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(f107,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)],[f106]) ).
fof(f108,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)],[f107]) ).
fof(f109,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))],[f108]) ).
fof(f110,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f126,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f127,plain,
aIdeal0(xJ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f128,plain,
! [W0] :
( aElementOf0(W0,sdtpldt1(xI,xJ))
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f129,plain,
! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f132,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) != sz10
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f133,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != sz10
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f139,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)],[f85]) ).
fof(f140,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)],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X1,X4)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4] :
( aElementOf0(X0,X3)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4] :
( sdtpldt0(X1,X0) = X2
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f145,plain,
aSet0(xJ),
inference(resolution,[status(thm)],[f110,f127]) ).
fof(f146,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f110,f126]) ).
fof(f156,definition,
( sQ2_spl
<=> aElement0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( sQ2_spl
| ~ aElement0(sz10) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f174,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f37]) ).
fof(f175,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f240,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(equality_resolution,[status(thm)],[f91]) ).
fof(f286,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)],[f240,f143]) ).
fof(f287,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)],[f240,f142]) ).
fof(f288,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)],[f240,f141]) ).
fof(f308,definition,
( sQ14_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( sQ14_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,definition,
( sQ15_spl
<=> aSet0(xJ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( sQ15_spl
| ~ aSet0(xJ) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f326,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f145]) ).
fof(f327,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f146]) ).
fof(f329,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f449,plain,
! [X0,X1] :
( ~ aElementOf0(sK3_skl(sz10,sdtpldt1(X0,X1),X1,X0),xJ)
| ~ aElementOf0(sK2_skl(sz10,sdtpldt1(X0,X1),X1,X0),xI)
| ~ aElementOf0(sz10,sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f286,f133]) ).
fof(f457,plain,
! [X0] :
( ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0)
| ~ aElementOf0(sK2_skl(sz10,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(xJ)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f449,f287]) ).
fof(f458,definition,
! [X0] :
( sQ19_spl
<=> ( ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(X0)
| ~ aElementOf0(sK2_skl(sz10,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f459,plain,
! [X0] :
( ~ sQ19_spl
| ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(X0)
| ~ aElementOf0(sK2_skl(sz10,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( ~ sQ15_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f457,f458,f311]) ).
fof(f462,plain,
! [X0] :
( ~ sQ19_spl
| ~ aElementOf0(sK2_skl(sz10,sdtpldt1(X0,xJ),xJ,X0),xI)
| ~ aElementOf0(sz10,sdtpldt1(X0,xJ))
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f459]) ).
fof(f463,plain,
( ~ sQ19_spl
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f462,f288]) ).
fof(f464,definition,
( sQ20_spl
<=> aElementOf0(sz10,sdtpldt1(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ20_spl
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ)) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f463,f308,f464,f311,f458]) ).
fof(f522,plain,
( sQ20_spl
| ~ aElement0(sz10) ),
inference(resolution,[status(thm)],[f466,f129]) ).
fof(f523,plain,
( sQ20_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f522,f156,f464]) ).
fof(f524,plain,
$false,
inference(sat_refutation,[status(thm)],[f175,f327,f329,f461,f467,f523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG095+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % Computer : n008.cluster.edu
% 0.17/0.48 % Model : x86_64 x86_64
% 0.17/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.48 % Memory : 8046.5625MB
% 0.17/0.48 % OS : Linux 6.8.0-71-generic
% 0.17/0.49 % CPULimit : 300
% 0.17/0.49 % WCLimit : 300
% 0.17/0.49 % DateTime : Mon Sep 21 04:19:57 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.17/0.53 % Drodi V4.1.1
% 0.21/0.78 % Refutation found
% 0.21/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.84 % Elapsed time: 0.319826 seconds
% 0.21/0.84 % CPU time: 1.755566 seconds
% 0.21/0.84 % Total memory used: 104.222 MB
% 0.21/0.84 % Net memory used: 102.267 MB
%------------------------------------------------------------------------------