%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 13 unt; 13 def)
% Number of atoms : 250 ( 20 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 267 ( 88 ~; 105 |; 57 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 26 ( 18 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W2,W1,W3)
& sdtmndtplgtdt0(W0,W1,W2) )
=> sdtmndtplgtdt0(W0,W1,W3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f32,plain,
! [W0,W1,W2,W3] :
( sdtmndtplgtdt0(W0,W1,W3)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f40,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f41,plain,
aElement0(xy),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
aElement0(xz),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [W0] :
( ~ sdtmndtplgtdt0(W0,xR,xz)
| ~ aReductOfIn0(W0,xx,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [W0] :
( ~ sdtmndtplgtdt0(W0,xR,xz)
| ~ aReductOfIn0(W0,xx,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(sK2_skl,xR,xz)
& aReductOfIn0(sK2_skl,xy,xR)
& aElement0(sK2_skl) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(sK1_skl,xR,xy)
& aReductOfIn0(sK1_skl,xx,xR)
& aElement0(sK1_skl) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(W0,sK1_skl),skolemize(W0,sK2_skl)],[f43]) ).
fof(f45,plain,
( aElement0(sK1_skl)
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
( aReductOfIn0(sK1_skl,xx,xR)
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
( sdtmndtplgtdt0(sK1_skl,xR,xy)
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f49,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f53,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f56,plain,
~ aReductOfIn0(xz,xx,xR),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f57,plain,
! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ aReductOfIn0(X0,xx,xR)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f58,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f59,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f60,definition,
( sQ0_spl
<=> xx = xy ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| xx = xy ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> aReductOfIn0(xy,xx,xR) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| aReductOfIn0(xy,xx,xR) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ2_spl
<=> aElement0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f60,f63,f66]) ).
fof(f70,definition,
( sQ3_spl
<=> aReductOfIn0(sK1_skl,xx,xR) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ3_spl
| aReductOfIn0(sK1_skl,xx,xR) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( sQ3_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f60,f63,f70]) ).
fof(f74,definition,
( sQ4_spl
<=> sdtmndtplgtdt0(sK1_skl,xR,xy) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ4_spl
| sdtmndtplgtdt0(sK1_skl,xR,xy) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ4_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f60,f63,f74]) ).
fof(f82,definition,
( sQ6_spl
<=> xy = xz ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ6_spl
| xy = xz ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f100,definition,
( sQ11_spl
<=> sdtmndtplgtdt0(xy,xR,xz) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ11_spl
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ11_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f53,f82,f100]) ).
fof(f114,plain,
( ~ sQ6_spl
| ~ sdtmndtasgtdt0(xx,xR,xy) ),
inference(forward_demodulation,[status(thm)],[f83,f59]) ).
fof(f115,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f49]) ).
fof(f116,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f115]) ).
fof(f122,plain,
( ~ sQ0_spl
| ~ sdtmndtplgtdt0(xy,xR,xz) ),
inference(forward_demodulation,[status(thm)],[f61,f58]) ).
fof(f123,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f101]) ).
fof(f124,plain,
( ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ12_spl
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ12_spl
| ~ aElement0(xy) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ13_spl
<=> aRewritingSystem0(xR) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ13_spl
| ~ aRewritingSystem0(xR) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ14_spl
<=> aElement0(xz) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( sQ14_spl
| ~ aElement0(xz) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f145,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f40]) ).
fof(f146,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f154,plain,
( ~ sQ1_spl
| ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[f57,f64]) ).
fof(f159,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f154,f126,f100,f63]) ).
fof(f160,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f41]) ).
fof(f161,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ sQ3_spl
| ~ sdtmndtplgtdt0(sK1_skl,xR,xz)
| ~ aElement0(sK1_skl) ),
inference(resolution,[status(thm)],[f71,f57]) ).
fof(f164,definition,
( sQ17_spl
<=> sdtmndtplgtdt0(sK1_skl,xR,xz) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f162,f66,f164,f70]) ).
fof(f189,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f42]) ).
fof(f190,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f207,definition,
( sQ24_spl
<=> aReductOfIn0(xz,xx,xR) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ24_spl
| aReductOfIn0(xz,xx,xR) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f211,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f56]) ).
fof(f212,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f254,plain,
! [X0] :
( ~ sQ11_spl
| sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtplgtdt0(X0,xR,xy)
| ~ aElement0(xz)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f33,f101]) ).
fof(f269,definition,
! [X0] :
( sQ33_spl
<=> ( sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtplgtdt0(X0,xR,xy)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f270,plain,
! [X0] :
( ~ sQ33_spl
| sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtplgtdt0(X0,xR,xy)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f254,f269,f129,f126,f132,f100]) ).
fof(f290,plain,
( ~ sQ4_spl
| ~ sQ33_spl
| sdtmndtplgtdt0(sK1_skl,xR,xz)
| ~ aElement0(sK1_skl) ),
inference(resolution,[status(thm)],[f270,f75]) ).
fof(f293,plain,
( ~ sQ4_spl
| ~ sQ33_spl
| sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f290,f66,f164,f269,f74]) ).
fof(f299,plain,
$false,
inference(sat_refutation,[status(thm)],[f69,f73,f77,f103,f116,f124,f146,f159,f161,f167,f190,f212,f272,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:16:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.047282 seconds
% 0.14/0.42 % CPU time: 0.139431 seconds
% 0.14/0.42 % Total memory used: 78.717 MB
% 0.14/0.42 % Net memory used: 78.447 MB
%------------------------------------------------------------------------------