%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM012+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 : n015.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 0.09s 0.54s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 15 unt; 12 def)
% Number of atoms : 197 ( 11 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 221 ( 92 ~; 96 |; 15 &)
% ( 13 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% 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/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(f9,hypothesis,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,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(f34,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(f35,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)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
aElement0(xx),
inference(cnf_transformation,[status(thm)],[f9]) ).
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)
& sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f49,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[f36,f45]) ).
fof(f50,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f36,f44]) ).
fof(f51,definition,
( sQ0_spl
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ0_spl
| ~ aElement0(xy) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> aRewritingSystem0(xR) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ1_spl
| ~ aRewritingSystem0(xR) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ2_spl
<=> aElement0(xz) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ2_spl
| ~ aElement0(xz) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ3_spl
<=> xy = xz ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ3_spl
| xy = xz ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ4_spl
<=> sdtmndtplgtdt0(xy,xR,xz) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ4_spl
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ4_spl
| sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f51,f54,f57,f60,f63]) ).
fof(f67,definition,
( sQ5_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( sQ5_spl
| ~ aElement0(xx) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ6_spl
<=> xx = xy ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ6_spl
| xx = xy ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ7_spl
<=> sdtmndtplgtdt0(xx,xR,xy) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ7_spl
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ7_spl
| sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f50,f67,f54,f51,f70,f73]) ).
fof(f77,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f41]) ).
fof(f78,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f40]) ).
fof(f80,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f39]) ).
fof(f82,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( ~ sQ6_spl
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(backward_demodulation,[status(thm)],[f71,f45]) ).
fof(f86,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f46]) ).
fof(f87,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f103,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f42]) ).
fof(f104,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f107,plain,
( ~ sQ3_spl
| ~ sdtmndtasgtdt0(xx,xR,xy) ),
inference(backward_demodulation,[status(thm)],[f61,f46]) ).
fof(f108,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f44]) ).
fof(f109,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f116,plain,
! [X0] :
( ~ sQ4_spl
| sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtplgtdt0(X0,xR,xy)
| ~ aElement0(xz)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[f33,f64]) ).
fof(f118,definition,
! [X0] :
( sQ10_spl
<=> ( sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtplgtdt0(X0,xR,xy)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ10_spl
| sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtplgtdt0(X0,xR,xy)
| ~ aElement0(X0) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f116,f118,f54,f51,f57,f63]) ).
fof(f126,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f119,f74]) ).
fof(f127,definition,
( sQ12_spl
<=> sdtmndtplgtdt0(xx,xR,xz) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ12_spl
| sdtmndtplgtdt0(xx,xR,xz) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sQ12_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f126,f67,f127,f118,f73]) ).
fof(f132,plain,
( ~ sQ12_spl
| sdtmndtasgtdt0(xx,xR,xz)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[f128,f38]) ).
fof(f137,definition,
( sQ14_spl
<=> sdtmndtasgtdt0(xx,xR,xz) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ14_spl
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( ~ sQ12_spl
| sQ14_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f132,f67,f54,f57,f137,f127]) ).
fof(f141,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f46]) ).
fof(f142,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f143,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f76,f78,f80,f82,f87,f104,f109,f121,f130,f140,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.50 % Computer : n015.cluster.edu
% 0.09/0.50 % Model : x86_64 x86_64
% 0.09/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.50 % Memory : 8046.5625MB
% 0.09/0.50 % OS : Linux 6.8.0-71-generic
% 0.09/0.50 % CPULimit : 300
% 0.09/0.50 % WCLimit : 300
% 0.09/0.50 % DateTime : Mon Sep 21 14:17:37 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.52 % Drodi V4.1.1
% 0.09/0.54 % Refutation found
% 0.09/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.56 % Elapsed time: 0.048791 seconds
% 0.09/0.56 % CPU time: 0.132455 seconds
% 0.09/0.56 % Total memory used: 70.363 MB
% 0.09/0.56 % Net memory used: 70.048 MB
%------------------------------------------------------------------------------