%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM023+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:10:19 PM UTC 2026
% Result : Theorem 10.29s 6.76s
% Output : CNFRefutation 10.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 8 unt; 3 def)
% Number of atoms : 557 ( 56 equ)
% Maximal formula atoms : 33 ( 10 avg)
% Number of connectives : 698 ( 193 ~; 246 |; 253 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 150 ( 105 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,hypothesis,
! [W0,W1,W2] :
( ( ( sdtmndtasgtdt0(W0,xR,W2)
| sdtmndtplgtdt0(W0,xR,W2)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR)
| W0 = W2 )
& ( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
( isConfluent0(xR)
| ! [W0,W1,W2] :
( ( sdtmndtasgtdt0(W0,xR,W2)
& ( ( sdtmndtplgtdt0(W0,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR) ) )
| W0 = W2 )
& sdtmndtasgtdt0(W0,xR,W1)
& ( ( sdtmndtplgtdt0(W0,xR,W1)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR) ) )
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ? [W3] :
( ( sdtmndtasgtdt0(W2,xR,W3)
| sdtmndtplgtdt0(W2,xR,W3)
| ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR)
| W2 = W3 )
& ( sdtmndtasgtdt0(W1,xR,W3)
| sdtmndtplgtdt0(W1,xR,W3)
| ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR)
| W1 = W3 )
& aElement0(W3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ( isConfluent0(xR)
| ! [W0,W1,W2] :
( ( sdtmndtasgtdt0(W0,xR,W2)
& ( ( sdtmndtplgtdt0(W0,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR) ) )
| W0 = W2 )
& sdtmndtasgtdt0(W0,xR,W1)
& ( ( sdtmndtplgtdt0(W0,xR,W1)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR) ) )
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ? [W3] :
( ( sdtmndtasgtdt0(W2,xR,W3)
| sdtmndtplgtdt0(W2,xR,W3)
| ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR)
| W2 = W3 )
& ( sdtmndtasgtdt0(W1,xR,W3)
| sdtmndtplgtdt0(W1,xR,W3)
| ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR)
| W1 = W3 )
& aElement0(W3) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f114,plain,
! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) )
| ( ~ sdtmndtasgtdt0(W0,xR,W2)
& ~ sdtmndtplgtdt0(W0,xR,W2)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W2)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,xR)
& W0 != W2 )
| ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W1)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W1,W0,xR)
& W0 != W1 )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f115,definition,
! [W0,W1] :
( sP0_prd(W1,W0)
<=> ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W1)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W1,W0,xR)
& W0 != W1 ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f116,definition,
! [W0,W2] :
( sP1_prd(W2,W0)
<=> ( ~ sdtmndtasgtdt0(W0,xR,W2)
& ~ sdtmndtplgtdt0(W0,xR,W2)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W2)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,xR)
& W0 != W2 ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f117,plain,
! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) )
| sP1_prd(W2,W0)
| sP0_prd(W1,W0)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(formula_renaming,[status(thm)],[f114,f116,f115]) ).
fof(f118,plain,
! [W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) )
| ! [W0] :
( sP1_prd(W2,W0)
| sP0_prd(W1,W0)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [W1,W2] :
( ( sdtmndtasgtdt0(W2,xR,sK16_skl(W2,W1))
& ( ( sdtmndtplgtdt0(W2,xR,sK16_skl(W2,W1))
& ( ( sdtmndtplgtdt0(sK18_skl(W2,W1),xR,sK16_skl(W2,W1))
& aReductOfIn0(sK18_skl(W2,W1),W2,xR)
& aElement0(sK18_skl(W2,W1)) )
| aReductOfIn0(sK16_skl(W2,W1),W2,xR) ) )
| W2 = sK16_skl(W2,W1) )
& sdtmndtasgtdt0(W1,xR,sK16_skl(W2,W1))
& ( ( sdtmndtplgtdt0(W1,xR,sK16_skl(W2,W1))
& ( ( sdtmndtplgtdt0(sK17_skl(W2,W1),xR,sK16_skl(W2,W1))
& aReductOfIn0(sK17_skl(W2,W1),W1,xR)
& aElement0(sK17_skl(W2,W1)) )
| aReductOfIn0(sK16_skl(W2,W1),W1,xR) ) )
| W1 = sK16_skl(W2,W1) )
& aElement0(sK16_skl(W2,W1)) )
| ! [W0] :
( sP1_prd(W2,W0)
| sP0_prd(W1,W0)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(W3,sK16_skl(W2,W1)),skolemize(W4,sK17_skl(W2,W1)),skolemize(W4,sK18_skl(W2,W1))],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( aElement0(sK16_skl(X2,X1))
| sP1_prd(X2,X0)
| sP0_prd(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f125,plain,
! [X0,X1,X2] :
( sdtmndtasgtdt0(X1,xR,sK16_skl(X2,X1))
| sP1_prd(X2,X0)
| sP0_prd(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f130,plain,
! [X0,X1,X2] :
( sdtmndtasgtdt0(X2,xR,sK16_skl(X2,X1))
| sP1_prd(X2,X0)
| sP0_prd(X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f131,plain,
( ~ isConfluent0(xR)
& ? [W0,W1,W2] :
( ! [W3] :
( ( ~ sdtmndtasgtdt0(W2,xR,W3)
& ~ sdtmndtplgtdt0(W2,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W2,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W2,xR)
& W2 != W3 )
| ( ~ sdtmndtasgtdt0(W1,xR,W3)
& ~ sdtmndtplgtdt0(W1,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W1,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W1,xR)
& W1 != W3 )
| ~ aElement0(W3) )
& sdtmndtasgtdt0(W0,xR,W2)
& ( ( sdtmndtplgtdt0(W0,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR) ) )
| W0 = W2 )
& sdtmndtasgtdt0(W0,xR,W1)
& ( ( sdtmndtplgtdt0(W0,xR,W1)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR) ) )
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f132,definition,
! [W1,W3] :
( sP2_prd(W3,W1)
<=> ( ~ sdtmndtasgtdt0(W1,xR,W3)
& ~ sdtmndtplgtdt0(W1,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W1,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W1,xR)
& W1 != W3 ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f133,plain,
( ~ isConfluent0(xR)
& ? [W0,W1,W2] :
( ! [W3] :
( ( ~ sdtmndtasgtdt0(W2,xR,W3)
& ~ sdtmndtplgtdt0(W2,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W2,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W2,xR)
& W2 != W3 )
| sP2_prd(W3,W1)
| ~ aElement0(W3) )
& sdtmndtasgtdt0(W0,xR,W2)
& ( ( sdtmndtplgtdt0(W0,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR) ) )
| W0 = W2 )
& sdtmndtasgtdt0(W0,xR,W1)
& ( ( sdtmndtplgtdt0(W0,xR,W1)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR) ) )
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) ) ),
inference(formula_renaming,[status(thm)],[f131,f132]) ).
fof(f134,plain,
( ~ isConfluent0(xR)
& ? [W1,W2] :
( ! [W3] :
( ( ~ sdtmndtasgtdt0(W2,xR,W3)
& ~ sdtmndtplgtdt0(W2,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W2,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W2,xR)
& W2 != W3 )
| sP2_prd(W3,W1)
| ~ aElement0(W3) )
& ? [W0] :
( sdtmndtasgtdt0(W0,xR,W2)
& ( ( sdtmndtplgtdt0(W0,xR,W2)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR) ) )
| W0 = W2 )
& sdtmndtasgtdt0(W0,xR,W1)
& ( ( sdtmndtplgtdt0(W0,xR,W1)
& ( ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR) ) )
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) ) ) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ isConfluent0(xR)
& ! [W3] :
( ( ~ sdtmndtasgtdt0(sK20_skl,xR,W3)
& ~ sdtmndtplgtdt0(sK20_skl,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,sK20_skl,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,sK20_skl,xR)
& sK20_skl != W3 )
| sP2_prd(W3,sK19_skl)
| ~ aElement0(W3) )
& sdtmndtasgtdt0(sK21_skl,xR,sK20_skl)
& ( ( sdtmndtplgtdt0(sK21_skl,xR,sK20_skl)
& ( ( sdtmndtplgtdt0(sK23_skl,xR,sK20_skl)
& aReductOfIn0(sK23_skl,sK21_skl,xR)
& aElement0(sK23_skl) )
| aReductOfIn0(sK20_skl,sK21_skl,xR) ) )
| sK21_skl = sK20_skl )
& sdtmndtasgtdt0(sK21_skl,xR,sK19_skl)
& ( ( sdtmndtplgtdt0(sK21_skl,xR,sK19_skl)
& ( ( sdtmndtplgtdt0(sK22_skl,xR,sK19_skl)
& aReductOfIn0(sK22_skl,sK21_skl,xR)
& aElement0(sK22_skl) )
| aReductOfIn0(sK19_skl,sK21_skl,xR) ) )
| sK21_skl = sK19_skl )
& aElement0(sK20_skl)
& aElement0(sK19_skl)
& aElement0(sK21_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(W1,sK19_skl),skolemize(W2,sK20_skl),skolemize(W0,sK21_skl),skolemize(W3,sK22_skl),skolemize(W3,sK23_skl)],[f134]) ).
fof(f136,plain,
aElement0(sK21_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
aElement0(sK19_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
aElement0(sK20_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f143,plain,
sdtmndtasgtdt0(sK21_skl,xR,sK19_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f148,plain,
sdtmndtasgtdt0(sK21_skl,xR,sK20_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f153,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK20_skl,xR,X0)
| sP2_prd(X0,sK19_skl)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f155,plain,
! [W0,W1] :
( ( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1
| sP0_prd(W1,W0) )
& ( ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W1)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W1,W0,xR)
& W0 != W1 )
| ~ sP0_prd(W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f115]) ).
fof(f156,plain,
( ! [W0,W1] :
( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1
| sP0_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W1)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W1,W0,xR)
& W0 != W1 )
| ~ sP0_prd(W1,W0) ) ),
inference(miniscoping,[status(thm)],[f155]) ).
fof(f157,plain,
( ! [W0,W1] :
( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ( sdtmndtplgtdt0(sK24_skl(W1,W0),xR,W1)
& aReductOfIn0(sK24_skl(W1,W0),W0,xR)
& aElement0(sK24_skl(W1,W0)) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1
| sP0_prd(W1,W0) )
& ! [W0,W1] :
( ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W1)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W1,W0,xR)
& W0 != W1 )
| ~ sP0_prd(W1,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(W3,sK24_skl(W1,W0))],[f156]) ).
fof(f162,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f166,plain,
! [W0,W2] :
( ( sdtmndtasgtdt0(W0,xR,W2)
| sdtmndtplgtdt0(W0,xR,W2)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR)
| W0 = W2
| sP1_prd(W2,W0) )
& ( ( ~ sdtmndtasgtdt0(W0,xR,W2)
& ~ sdtmndtplgtdt0(W0,xR,W2)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W2)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,xR)
& W0 != W2 )
| ~ sP1_prd(W2,W0) ) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f167,plain,
( ! [W0,W2] :
( sdtmndtasgtdt0(W0,xR,W2)
| sdtmndtplgtdt0(W0,xR,W2)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR)
| W0 = W2
| sP1_prd(W2,W0) )
& ! [W0,W2] :
( ( ~ sdtmndtasgtdt0(W0,xR,W2)
& ~ sdtmndtplgtdt0(W0,xR,W2)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W2)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,xR)
& W0 != W2 )
| ~ sP1_prd(W2,W0) ) ),
inference(miniscoping,[status(thm)],[f166]) ).
fof(f168,plain,
( ! [W0,W2] :
( sdtmndtasgtdt0(W0,xR,W2)
| sdtmndtplgtdt0(W0,xR,W2)
| ( sdtmndtplgtdt0(sK25_skl(W2,W0),xR,W2)
& aReductOfIn0(sK25_skl(W2,W0),W0,xR)
& aElement0(sK25_skl(W2,W0)) )
| aReductOfIn0(W2,W0,xR)
| W0 = W2
| sP1_prd(W2,W0) )
& ! [W0,W2] :
( ( ~ sdtmndtasgtdt0(W0,xR,W2)
& ~ sdtmndtplgtdt0(W0,xR,W2)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W2)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,xR)
& W0 != W2 )
| ~ sP1_prd(W2,W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(W3,sK25_skl(W2,W0))],[f167]) ).
fof(f173,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f177,plain,
! [W1,W3] :
( ( sdtmndtasgtdt0(W1,xR,W3)
| sdtmndtplgtdt0(W1,xR,W3)
| ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR)
| W1 = W3
| sP2_prd(W3,W1) )
& ( ( ~ sdtmndtasgtdt0(W1,xR,W3)
& ~ sdtmndtplgtdt0(W1,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W1,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W1,xR)
& W1 != W3 )
| ~ sP2_prd(W3,W1) ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f178,plain,
( ! [W1,W3] :
( sdtmndtasgtdt0(W1,xR,W3)
| sdtmndtplgtdt0(W1,xR,W3)
| ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR)
| W1 = W3
| sP2_prd(W3,W1) )
& ! [W1,W3] :
( ( ~ sdtmndtasgtdt0(W1,xR,W3)
& ~ sdtmndtplgtdt0(W1,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W1,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W1,xR)
& W1 != W3 )
| ~ sP2_prd(W3,W1) ) ),
inference(miniscoping,[status(thm)],[f177]) ).
fof(f179,plain,
( ! [W1,W3] :
( sdtmndtasgtdt0(W1,xR,W3)
| sdtmndtplgtdt0(W1,xR,W3)
| ( sdtmndtplgtdt0(sK26_skl(W3,W1),xR,W3)
& aReductOfIn0(sK26_skl(W3,W1),W1,xR)
& aElement0(sK26_skl(W3,W1)) )
| aReductOfIn0(W3,W1,xR)
| W1 = W3
| sP2_prd(W3,W1) )
& ! [W1,W3] :
( ( ~ sdtmndtasgtdt0(W1,xR,W3)
& ~ sdtmndtplgtdt0(W1,xR,W3)
& ! [W4] :
( ~ sdtmndtplgtdt0(W4,xR,W3)
| ~ aReductOfIn0(W4,W1,xR)
| ~ aElement0(W4) )
& ~ aReductOfIn0(W3,W1,xR)
& W1 != W3 )
| ~ sP2_prd(W3,W1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl]),skolemize(W4,sK26_skl(W3,W1))],[f178]) ).
fof(f184,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f469,plain,
! [X0,X1] :
( aElement0(sK16_skl(X1,sK20_skl))
| sP1_prd(X1,X0)
| sP0_prd(sK20_skl,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f120,f138]) ).
fof(f577,plain,
! [X0] :
( aElement0(sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,X0)
| sP0_prd(sK20_skl,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f469,f137]) ).
fof(f696,plain,
( aElement0(sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f577,f136]) ).
fof(f1463,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK16_skl(sK19_skl,X1))
| sP1_prd(sK19_skl,X0)
| sP0_prd(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f125,f137]) ).
fof(f1774,plain,
! [X0] :
( sdtmndtasgtdt0(sK20_skl,xR,sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,X0)
| sP0_prd(sK20_skl,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f1463,f138]) ).
fof(f2325,plain,
( sdtmndtasgtdt0(sK20_skl,xR,sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f1774,f136]) ).
fof(f2721,plain,
( sP2_prd(sK16_skl(sK19_skl,sK20_skl),sK19_skl)
| ~ aElement0(sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f2325,f153]) ).
fof(f2723,plain,
( sP2_prd(sK16_skl(sK19_skl,sK20_skl),sK19_skl)
| sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2721,f696]) ).
fof(f2726,plain,
( ~ sdtmndtasgtdt0(sK19_skl,xR,sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f2723,f184]) ).
fof(f3234,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK16_skl(X1,sK20_skl))
| sP1_prd(X1,X0)
| sP0_prd(sK20_skl,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f130,f138]) ).
fof(f3432,plain,
! [X0] :
( sdtmndtasgtdt0(sK19_skl,xR,sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,X0)
| sP0_prd(sK20_skl,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f3234,f137]) ).
fof(f3605,plain,
( sdtmndtasgtdt0(sK19_skl,xR,sK16_skl(sK19_skl,sK20_skl))
| sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f3432,f136]) ).
fof(f3615,plain,
( sP1_prd(sK19_skl,sK21_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3605,f2726]) ).
fof(f3658,plain,
( ~ sdtmndtasgtdt0(sK21_skl,xR,sK19_skl)
| sP0_prd(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f3615,f173]) ).
fof(f3661,plain,
sP0_prd(sK20_skl,sK21_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3658,f143]) ).
fof(f3663,plain,
~ sdtmndtasgtdt0(sK21_skl,xR,sK20_skl),
inference(resolution,[status(thm)],[f3661,f162]) ).
fof(f3666,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3663,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM023+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 14:18:09 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 10.29/6.76 % Refutation found
% 10.29/6.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.29/6.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.29/6.79 % Elapsed time: 1.405345 seconds
% 10.29/6.79 % CPU time: 10.951942 seconds
% 10.29/6.79 % Total memory used: 177.980 MB
% 10.29/6.79 % Net memory used: 168.389 MB
%------------------------------------------------------------------------------