%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM018+4 : 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 12:10:18 PM UTC 2026
% Result : Theorem 0.17s 15.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 9 unt; 3 def)
% Number of atoms : 249 ( 17 equ)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 299 ( 85 ~; 97 |; 109 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 40 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [W0] :
( ( isTerminating0(W0)
& aRewritingSystem0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( isTerminating0(xR)
& ! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W0,xR,W1)
| ? [W2] :
( sdtmndtplgtdt0(W2,xR,W1)
& aReductOfIn0(W2,W0,xR)
& aElement0(W2) )
| aReductOfIn0(W1,W0,xR) )
=> iLess0(W1,W0) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1,W2] :
( ( aReductOfIn0(W2,W0,xR)
& aReductOfIn0(W1,W0,xR)
& 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xv,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xu,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f96,plain,
! [W0] :
( ! [W1] :
( ? [W2] : aNormalFormOfIn0(W2,W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f97,plain,
! [W0] :
( ! [W1] :
( aNormalFormOfIn0(sK12_skl(W1,W0),W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(W2,sK12_skl(W1,W0))],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( aNormalFormOfIn0(sK12_skl(X1,X0),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f100,plain,
( isTerminating0(xR)
& ! [W0,W1] :
( iLess0(W1,W0)
| ( ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ sdtmndtplgtdt0(W2,xR,W1)
| ~ aReductOfIn0(W2,W0,xR)
| ~ aElement0(W2) )
& ~ aReductOfIn0(W1,W0,xR) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
& isLocallyConfluent0(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) )
| ~ aReductOfIn0(W2,W0,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f101,plain,
( isTerminating0(xR)
& ! [W0,W1] :
( iLess0(W1,W0)
| ( ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ sdtmndtplgtdt0(W2,xR,W1)
| ~ aReductOfIn0(W2,W0,xR)
| ~ aElement0(W2) )
& ~ aReductOfIn0(W1,W0,xR) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
& isLocallyConfluent0(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 )
& 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] :
( ~ aReductOfIn0(W2,W0,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
( isTerminating0(xR)
& ! [W0,W1] :
( iLess0(W1,W0)
| ( ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ sdtmndtplgtdt0(W2,xR,W1)
| ~ aReductOfIn0(W2,W0,xR)
| ~ aElement0(W2) )
& ~ aReductOfIn0(W1,W0,xR) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
& isLocallyConfluent0(xR)
& ! [W1,W2] :
( ( sdtmndtasgtdt0(W2,xR,sK13_skl(W2,W1))
& ( ( sdtmndtplgtdt0(W2,xR,sK13_skl(W2,W1))
& ( ( sdtmndtplgtdt0(sK15_skl(W2,W1),xR,sK13_skl(W2,W1))
& aReductOfIn0(sK15_skl(W2,W1),W2,xR)
& aElement0(sK15_skl(W2,W1)) )
| aReductOfIn0(sK13_skl(W2,W1),W2,xR) ) )
| W2 = sK13_skl(W2,W1) )
& sdtmndtasgtdt0(W1,xR,sK13_skl(W2,W1))
& ( ( sdtmndtplgtdt0(W1,xR,sK13_skl(W2,W1))
& ( ( sdtmndtplgtdt0(sK14_skl(W2,W1),xR,sK13_skl(W2,W1))
& aReductOfIn0(sK14_skl(W2,W1),W1,xR)
& aElement0(sK14_skl(W2,W1)) )
| aReductOfIn0(sK13_skl(W2,W1),W1,xR) ) )
| W1 = sK13_skl(W2,W1) )
& aElement0(sK13_skl(W2,W1)) )
| ! [W0] :
( ~ aReductOfIn0(W2,W0,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(W3,sK13_skl(W2,W1)),skolemize(W4,sK14_skl(W2,W1)),skolemize(W4,sK15_skl(W2,W1))],[f101]) ).
fof(f118,plain,
isTerminating0(xR),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f206,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK24_skl,xR,xw)
& aReductOfIn0(sK24_skl,xv,xR)
& aElement0(sK24_skl) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK23_skl,xR,xw)
& aReductOfIn0(sK23_skl,xu,xR)
& aElement0(sK23_skl) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(W0,sK23_skl),skolemize(W0,sK24_skl)],[f22]) ).
fof(f207,plain,
aElement0(xw),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f218,plain,
! [W0] :
( ~ aNormalFormOfIn0(W0,xw,xR)
& ( ? [W1] : aReductOfIn0(W1,W0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ! [W1] :
( ~ sdtmndtplgtdt0(W1,xR,W0)
| ~ aReductOfIn0(W1,xw,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(W0,xw,xR)
& xw != W0 )
| ~ aElement0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f219,plain,
( ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR)
& ! [W0] :
( ? [W1] : aReductOfIn0(W1,W0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ! [W1] :
( ~ sdtmndtplgtdt0(W1,xR,W0)
| ~ aReductOfIn0(W1,xw,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(W0,xw,xR)
& xw != W0 )
| ~ aElement0(W0) ) ),
inference(miniscoping,[status(thm)],[f218]) ).
fof(f220,plain,
( ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR)
& ! [W0] :
( aReductOfIn0(sK25_skl(W0),W0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ! [W1] :
( ~ sdtmndtplgtdt0(W1,xR,W0)
| ~ aReductOfIn0(W1,xw,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(W0,xw,xR)
& xw != W0 )
| ~ aElement0(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(W1,sK25_skl(W0))],[f219]) ).
fof(f226,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f385,definition,
( sQ32_spl
<=> aElement0(xw) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( sQ32_spl
| ~ aElement0(xw) ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,definition,
( sQ33_spl
<=> aRewritingSystem0(xR) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( sQ33_spl
| ~ aRewritingSystem0(xR) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f399,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f99]) ).
fof(f400,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f402,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f207]) ).
fof(f403,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f1437,definition,
( sQ181_spl
<=> isTerminating0(xR) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1439,plain,
( sQ181_spl
| ~ isTerminating0(xR) ),
inference(component_clause,[status(thm)],[f1437]) ).
fof(f1467,plain,
( sQ181_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1439,f118]) ).
fof(f1468,plain,
sQ181_spl,
inference(contradiction_clause,[status(thm)],[f1467]) ).
fof(f1657,plain,
( ~ aElement0(xw)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[f98,f226]) ).
fof(f1661,plain,
( ~ sQ32_spl
| ~ sQ181_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1657,f388,f1437,f385]) ).
fof(f1665,plain,
$false,
inference(sat_refutation,[status(thm)],[f400,f403,f1468,f1661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/15.41 % Computer : n008.cluster.edu
% 0.12/15.41 % Model : x86_64 x86_64
% 0.12/15.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.41 % Memory : 8046.5625MB
% 0.12/15.41 % OS : Linux 6.8.0-71-generic
% 0.12/15.41 % CPULimit : 300
% 0.12/15.41 % WCLimit : 300
% 0.12/15.41 % DateTime : Mon Sep 21 14:15:41 UTC 2026
% 0.12/15.41 % CPUTime :
% 0.12/15.43 % Drodi V4.1.1
% 0.17/15.55 % Refutation found
% 0.17/15.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/15.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/15.60 % Elapsed time: 0.171092 seconds
% 0.17/15.60 % CPU time: 0.824944 seconds
% 0.17/15.60 % Total memory used: 94.226 MB
% 0.17/15.60 % Net memory used: 93.507 MB
%------------------------------------------------------------------------------