%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM016+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 : n020.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 12:10:17 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 10 unt; 10 def)
% Number of atoms : 283 ( 5 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 378 ( 163 ~; 173 |; 26 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 75 ( 70 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
? [W0] :
( sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f28,plain,
! [W0,W1] :
( ! [W2] :
( aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f34,plain,
! [W0,W1,W2] :
( ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [W0,W1,W2] :
( ( ( ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [W0,W1,W2] :
( ( ( ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ( sdtmndtplgtdt0(sK0_skl(W2,W1,W0),W1,W2)
& aReductOfIn0(sK0_skl(W2,W1,W0),W0,W1)
& aElement0(sK0_skl(W2,W1,W0)) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W3,sK0_skl(W2,W1,W0))],[f35]) ).
fof(f38,plain,
! [X0,X1,X2] :
( aReductOfIn0(sK0_skl(X2,X1,X0),X0,X1)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( sdtmndtplgtdt0(sK0_skl(X2,X1,X0),X1,X2)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f44,plain,
! [W0,W1,W2] :
( ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2 ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f45,plain,
! [W0,W1,W2] :
( ( ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
& W0 != W2 )
| sdtmndtasgtdt0(W0,W1,W2) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2
| ~ sdtmndtasgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1,X2] :
( X0 != X2
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f96,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f99,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f100,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f107,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f109,plain,
! [W0] :
( ~ sdtmndtasgtdt0(W0,xR,xb)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f110,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f112,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f96,f112]) ).
fof(f114,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f96,f29]) ).
fof(f115,plain,
( ~ aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f113,f110]) ).
fof(f117,definition,
( sQ0_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ0_spl
| ~ aElement0(xb) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
( sQ1_spl
<=> aReductOfIn0(xb,xa,xR) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f115,f117,f120]) ).
fof(f127,definition,
( sQ3_spl
<=> aRewritingSystem0(xR) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( sQ3_spl
| ~ aRewritingSystem0(xR) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f131,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f100]) ).
fof(f132,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( aReductOfIn0(sK0_skl(X1,xR,X0),X0,xR)
| aReductOfIn0(X1,X0,xR)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f38,f96]) ).
fof(f136,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(sK0_skl(X0,xR,xa))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f133,f110]) ).
fof(f137,definition,
( sQ4_spl
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ4_spl
| ~ aElement0(xa) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,definition,
! [X0] :
( sQ5_spl
<=> ( ~ sdtmndtasgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(sK0_skl(X0,xR,xa))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f141,plain,
! [X0] :
( ~ sQ5_spl
| ~ sdtmndtasgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(sK0_skl(X0,xR,xa))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f136,f137,f140]) ).
fof(f144,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f99]) ).
fof(f145,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ sdtmndtplgtdt0(X0,xR,X1)
| sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f48,f96]) ).
fof(f147,plain,
! [X0] :
( ~ sQ5_spl
| ~ aElement0(sK0_skl(X0,xR,xa))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(xb)
| ~ aElement0(sK0_skl(X0,xR,xa)) ),
inference(resolution,[status(thm)],[f146,f141]) ).
fof(f150,definition,
! [X0] :
( sQ6_spl
<=> ( ~ aElement0(sK0_skl(X0,xR,xa))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(sK0_skl(X0,xR,xa)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0] :
( ~ sQ6_spl
| ~ aElement0(sK0_skl(X0,xR,xa))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(sK0_skl(X0,xR,xa)) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f147,f150,f117,f140]) ).
fof(f162,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f96]) ).
fof(f163,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0] :
( ~ sQ6_spl
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb)
| ~ aElement0(sK0_skl(X0,xR,xa)) ),
inference(duplicate_literals_removal,[status(thm)],[f151]) ).
fof(f187,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ aReductOfIn0(sK0_skl(X0,xR,xa),X1,xR)
| ~ aElement0(X1)
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb) ),
inference(resolution,[status(thm)],[f165,f114]) ).
fof(f189,definition,
! [X0] :
( sQ12_spl
<=> ( aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f190,plain,
! [X0] :
( ~ sQ12_spl
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f193,plain,
! [X0] :
( ~ sQ12_spl
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb) ),
inference(duplicate_literals_removal,[status(thm)],[f190]) ).
fof(f194,plain,
! [X0] :
( ~ sQ6_spl
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ aElement0(xa)
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(sK0_skl(X0,xR,xa),xR,xb) ),
inference(resolution,[status(thm)],[f187,f133]) ).
fof(f195,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f194,f189,f137,f150]) ).
fof(f350,plain,
( ~ sQ12_spl
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f193,f39]) ).
fof(f355,definition,
( sQ38_spl
<=> sdtmndtplgtdt0(xa,xR,xb) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( sQ38_spl
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ1_spl
| ~ sQ38_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f350,f117,f355,f120,f137,f127,f189]) ).
fof(f375,plain,
( sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f107]) ).
fof(f376,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
$false,
inference(sat_refutation,[status(thm)],[f123,f132,f143,f145,f153,f163,f195,f358,f376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM016+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n020.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 14:15:33 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.064787 seconds
% 0.13/0.44 % CPU time: 0.204821 seconds
% 0.13/0.44 % Total memory used: 83.828 MB
% 0.13/0.44 % Net memory used: 83.629 MB
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