%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM017+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 : n003.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 0.15s 15.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 12 unt; 1 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 317 ( 136 ~; 131 |; 44 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 79 ( 67 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
=> ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f30,plain,
! [W0,W1] :
( ! [W2] :
( aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
! [X0,X1,X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f66,plain,
! [W0] :
( ( isLocallyConfluent0(W0)
<=> ! [W1,W2,W3] :
( ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) )
| ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) ) )
| ~ aRewritingSystem0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f67,plain,
! [W0] :
( ( ( ? [W1,W2,W3] :
( ! [W4] :
( ~ sdtmndtasgtdt0(W3,W0,W4)
| ~ sdtmndtasgtdt0(W2,W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
| isLocallyConfluent0(W0) )
& ( ! [W1,W2,W3] :
( ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) )
| ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [W0] :
( ( ( ? [W2,W3] :
( ! [W4] :
( ~ sdtmndtasgtdt0(W3,W0,W4)
| ~ sdtmndtasgtdt0(W2,W0,W4)
| ~ aElement0(W4) )
& ? [W1] :
( aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) ) )
| isLocallyConfluent0(W0) )
& ( ! [W2,W3] :
( ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) )
| ! [W1] :
( ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) ) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [W0] :
( ( ( ( ! [W4] :
( ~ sdtmndtasgtdt0(sK7_skl(W0),W0,W4)
| ~ sdtmndtasgtdt0(sK6_skl(W0),W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(sK7_skl(W0),sK8_skl(W0),W0)
& aReductOfIn0(sK6_skl(W0),sK8_skl(W0),W0)
& aElement0(sK7_skl(W0))
& aElement0(sK6_skl(W0))
& aElement0(sK8_skl(W0)) )
| isLocallyConfluent0(W0) )
& ( ! [W2,W3] :
( ( sdtmndtasgtdt0(W3,W0,sK5_skl(W3,W2,W0))
& sdtmndtasgtdt0(W2,W0,sK5_skl(W3,W2,W0))
& aElement0(sK5_skl(W3,W2,W0)) )
| ! [W1] :
( ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) ) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(W4,sK5_skl(W3,W2,W0)),skolemize(W2,sK6_skl(W0)),skolemize(W3,sK7_skl(W0)),skolemize(W1,sK8_skl(W0))],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( aElement0(sK5_skl(X3,X2,X0))
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X2,X0,sK5_skl(X3,X2,X0))
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X3,X0,sK5_skl(X3,X2,X0))
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f98,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f99,plain,
isLocallyConfluent0(xR),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f101,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f111,plain,
aElement0(xu),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f112,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f115,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f117,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xv,xR,W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f118,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( aElement0(sK5_skl(X2,X3,X0))
| ~ aReductOfIn0(X2,X1,X0)
| ~ aReductOfIn0(X3,X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f31]) ).
fof(f301,plain,
! [X0] :
( aElement0(sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ isLocallyConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[f300,f115]) ).
fof(f303,plain,
! [X0] :
( aElement0(sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ isLocallyConfluent0(xR) ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f98]) ).
fof(f305,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X3,X0,sK5_skl(X2,X3,X0))
| ~ aReductOfIn0(X2,X1,X0)
| ~ aReductOfIn0(X3,X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f31]) ).
fof(f306,plain,
! [X0] :
( sdtmndtasgtdt0(xv,xR,sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ isLocallyConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[f305,f115]) ).
fof(f308,plain,
! [X0] :
( sdtmndtasgtdt0(xv,xR,sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ isLocallyConfluent0(xR) ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f98]) ).
fof(f310,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X2,X0,sK5_skl(X2,X3,X0))
| ~ aReductOfIn0(X2,X1,X0)
| ~ aReductOfIn0(X3,X1,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f31]) ).
fof(f311,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ isLocallyConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[f310,f115]) ).
fof(f313,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ isLocallyConfluent0(xR) ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f98]) ).
fof(f416,plain,
! [X0] :
( aElement0(sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa) ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f99]) ).
fof(f418,plain,
( aElement0(sK5_skl(xu,xv,xR))
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f416,f112]) ).
fof(f420,plain,
( aElement0(sK5_skl(xu,xv,xR))
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f101]) ).
fof(f426,plain,
! [X0] :
( sdtmndtasgtdt0(xv,xR,sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa) ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f99]) ).
fof(f428,plain,
( sdtmndtasgtdt0(xv,xR,sK5_skl(xu,xv,xR))
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f426,f112]) ).
fof(f430,plain,
( sdtmndtasgtdt0(xv,xR,sK5_skl(xu,xv,xR))
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f101]) ).
fof(f438,plain,
aElement0(sK5_skl(xu,xv,xR)),
inference(forward_subsumption_resolution,[status(thm)],[f420,f111]) ).
fof(f563,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,sK5_skl(X0,xv,xR))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0)
| ~ aElement0(xa) ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f99]) ).
fof(f565,plain,
( sdtmndtasgtdt0(xu,xR,sK5_skl(xu,xv,xR))
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f563,f112]) ).
fof(f567,plain,
( sdtmndtasgtdt0(xu,xR,sK5_skl(xu,xv,xR))
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f101]) ).
fof(f798,plain,
sdtmndtasgtdt0(xv,xR,sK5_skl(xu,xv,xR)),
inference(forward_subsumption_resolution,[status(thm)],[f430,f111]) ).
fof(f805,plain,
( ~ sdtmndtasgtdt0(xu,xR,sK5_skl(xu,xv,xR))
| ~ aElement0(sK5_skl(xu,xv,xR)) ),
inference(resolution,[status(thm)],[f798,f118]) ).
fof(f821,plain,
~ sdtmndtasgtdt0(xu,xR,sK5_skl(xu,xv,xR)),
inference(forward_subsumption_resolution,[status(thm)],[f805,f438]) ).
fof(f1078,plain,
sdtmndtasgtdt0(xu,xR,sK5_skl(xu,xv,xR)),
inference(forward_subsumption_resolution,[status(thm)],[f567,f111]) ).
fof(f1079,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f821,f1078]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/15.56 % Computer : n003.cluster.edu
% 0.12/15.56 % Model : x86_64 x86_64
% 0.12/15.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.56 % Memory : 8046.5625MB
% 0.12/15.56 % OS : Linux 6.8.0-71-generic
% 0.12/15.56 % CPULimit : 300
% 0.12/15.56 % WCLimit : 300
% 0.12/15.56 % DateTime : Mon Sep 21 14:16:17 UTC 2026
% 0.12/15.57 % CPUTime :
% 0.12/15.58 % Drodi V4.1.1
% 0.15/15.64 % Refutation found
% 0.15/15.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/15.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/15.71 % Elapsed time: 0.136962 seconds
% 0.15/15.71 % CPU time: 0.283439 seconds
% 0.15/15.71 % Total memory used: 33.237 MB
% 0.15/15.71 % Net memory used: 33.063 MB
%------------------------------------------------------------------------------