%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM018+1 : 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 12:10:18 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 11 unt; 2 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 23 ~; 19 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [W0] :
( ( isTerminating0(W0)
& aRewritingSystem0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
? [W0] : aNormalFormOfIn0(W0,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ? [W0] : aNormalFormOfIn0(W0,xw,xR),
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(f101,plain,
isTerminating0(xR),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f118,plain,
aElement0(xw),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f121,plain,
! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f122,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f145,plain,
! [X0] :
( aNormalFormOfIn0(sK12_skl(X0,xR),X0,xR)
| ~ aElement0(X0)
| ~ isTerminating0(xR) ),
inference(resolution,[status(thm)],[f98,f99]) ).
fof(f146,definition,
( sQ3_spl
<=> isTerminating0(xR) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ3_spl
| ~ isTerminating0(xR) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
! [X0] :
( sQ4_spl
<=> ( aNormalFormOfIn0(sK12_skl(X0,xR),X0,xR)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f150,plain,
! [X0] :
( ~ sQ4_spl
| aNormalFormOfIn0(sK12_skl(X0,xR),X0,xR)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f145,f146,f149]) ).
fof(f153,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f101]) ).
fof(f154,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f155,plain,
( ~ sQ4_spl
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[f150,f122]) ).
fof(f157,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f118]) ).
fof(f158,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f154,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:17:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.048407 seconds
% 0.09/0.42 % CPU time: 0.122515 seconds
% 0.09/0.42 % Total memory used: 64.472 MB
% 0.09/0.42 % Net memory used: 64.418 MB
%------------------------------------------------------------------------------