%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET013-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:08:50 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 93 ( 8 unt; 12 def)
% Number of atoms : 204 ( 14 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 210 ( 99 ~; 99 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Z,X,Y] :
( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
intersection(as,bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
intersection(bs,as) = ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [Z,Y] :
( ~ member(Z,Y)
| ! [X] :
( ~ member(Z,X)
| member(Z,intersection(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
intersection(as,bs) = cs,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
intersection(bs,as) = ds,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
cs != ds,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
( ~ member(f1(cs,ds),ds)
| ~ member(f1(cs,ds),cs) ),
inference(resolution,[status(thm)],[f17,f28]) ).
fof(f30,plain,
( ~ member(f1(ds,cs),cs)
| ~ member(f1(ds,cs),ds) ),
inference(resolution,[status(thm)],[f17,f28]) ).
fof(f31,definition,
( sQ0_spl
<=> member(f1(cs,ds),cs) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( ~ sQ0_spl
| member(f1(cs,ds),cs) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f33,plain,
( sQ0_spl
| ~ member(f1(cs,ds),cs) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ1_spl
<=> member(f1(cs,ds),ds) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( sQ1_spl
| ~ member(f1(cs,ds),ds) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f31,f34]) ).
fof(f38,definition,
( sQ2_spl
<=> member(f1(ds,cs),ds) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( sQ2_spl
| ~ member(f1(ds,cs),ds) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ3_spl
<=> member(f1(ds,cs),cs) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ3_spl
| ~ member(f1(ds,cs),cs) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f30,f38,f41]) ).
fof(f51,plain,
! [X0] :
( ~ member(X0,as)
| ~ member(X0,bs)
| member(X0,ds) ),
inference(paramodulation,[status(thm)],[f27,f23]) ).
fof(f52,plain,
! [X0] :
( ~ member(X0,bs)
| ~ member(X0,as)
| member(X0,cs) ),
inference(paramodulation,[status(thm)],[f26,f23]) ).
fof(f53,plain,
( sQ0_spl
| cs = ds
| member(f1(cs,ds),ds) ),
inference(resolution,[status(thm)],[f16,f33]) ).
fof(f54,plain,
( sQ2_spl
| ds = cs
| member(f1(ds,cs),cs) ),
inference(resolution,[status(thm)],[f16,f40]) ).
fof(f56,definition,
( sQ4_spl
<=> cs = ds ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ4_spl
| cs = ds ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ0_spl
| sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f53,f34,f56,f31]) ).
fof(f60,plain,
( sQ2_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f54,f41,f56,f38]) ).
fof(f61,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f28]) ).
fof(f62,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f67,definition,
! [X0] :
( sQ5_spl
<=> ~ member(f1(cs,ds),X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f68,plain,
! [X0] :
( ~ sQ5_spl
| ~ member(f1(cs,ds),X0) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f89,definition,
! [X1] :
( sQ7_spl
<=> ~ member(f1(cs,ds),intersection(cs,X1)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f90,plain,
! [X0] :
( ~ sQ7_spl
| ~ member(f1(cs,ds),intersection(cs,X0)) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f93,plain,
! [X0] :
( sQ1_spl
| ~ member(f1(cs,ds),intersection(X0,ds)) ),
inference(resolution,[status(thm)],[f36,f21]) ).
fof(f96,plain,
! [X0,X1] :
( sQ1_spl
| ~ member(f1(cs,ds),intersection(X0,intersection(X1,ds))) ),
inference(resolution,[status(thm)],[f93,f21]) ).
fof(f120,plain,
! [X0,X1] :
( sQ1_spl
| ~ member(f1(cs,ds),intersection(X1,ds))
| ~ member(f1(cs,ds),X0) ),
inference(resolution,[status(thm)],[f96,f23]) ).
fof(f123,definition,
! [X1] :
( sQ9_spl
<=> ~ member(f1(cs,ds),intersection(X1,ds)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( sQ1_spl
| sQ9_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f120,f67,f123,f34]) ).
fof(f129,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f68]) ).
fof(f130,plain,
( ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f154,plain,
! [X0] :
( ~ sQ7_spl
| ~ member(f1(cs,ds),X0)
| ~ member(f1(cs,ds),cs) ),
inference(resolution,[status(thm)],[f90,f23]) ).
fof(f157,plain,
( ~ sQ7_spl
| sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f154,f31,f67,f89]) ).
fof(f236,plain,
( sQ2_spl
| ~ member(f1(ds,cs),as)
| ~ member(f1(ds,cs),bs) ),
inference(resolution,[status(thm)],[f51,f40]) ).
fof(f237,definition,
( sQ13_spl
<=> member(f1(ds,cs),bs) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ13_spl
| ~ member(f1(ds,cs),bs) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
( sQ14_spl
<=> member(f1(ds,cs),as) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ14_spl
| ~ member(f1(ds,cs),as) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f236,f237,f240,f38]) ).
fof(f244,plain,
! [X0] :
( sQ13_spl
| ~ member(f1(ds,cs),intersection(X0,bs)) ),
inference(resolution,[status(thm)],[f239,f21]) ).
fof(f245,plain,
! [X0] :
( sQ13_spl
| ~ member(f1(ds,cs),intersection(bs,X0)) ),
inference(resolution,[status(thm)],[f239,f19]) ).
fof(f246,plain,
( sQ0_spl
| ~ member(f1(cs,ds),bs)
| ~ member(f1(cs,ds),as) ),
inference(resolution,[status(thm)],[f52,f33]) ).
fof(f247,definition,
( sQ15_spl
<=> member(f1(cs,ds),as) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ15_spl
| ~ member(f1(cs,ds),as) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
( sQ16_spl
<=> member(f1(cs,ds),bs) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( sQ16_spl
| ~ member(f1(cs,ds),bs) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( sQ0_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f246,f247,f250,f31]) ).
fof(f254,plain,
! [X0] :
( sQ15_spl
| ~ member(f1(cs,ds),intersection(X0,as)) ),
inference(resolution,[status(thm)],[f249,f21]) ).
fof(f314,plain,
( sQ13_spl
| ~ member(f1(ds,cs),cs) ),
inference(paramodulation,[status(thm)],[f26,f244]) ).
fof(f316,plain,
( sQ13_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f314,f41,f237]) ).
fof(f317,plain,
! [X0] :
( sQ14_spl
| ~ member(f1(ds,cs),intersection(X0,as)) ),
inference(resolution,[status(thm)],[f242,f21]) ).
fof(f318,plain,
! [X0] :
( sQ14_spl
| ~ member(f1(ds,cs),intersection(as,X0)) ),
inference(resolution,[status(thm)],[f242,f19]) ).
fof(f323,plain,
( sQ15_spl
| ~ member(f1(cs,ds),ds) ),
inference(paramodulation,[status(thm)],[f27,f254]) ).
fof(f325,plain,
( sQ15_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f323,f34,f247]) ).
fof(f326,plain,
! [X0] :
( sQ16_spl
| ~ member(f1(cs,ds),intersection(X0,bs)) ),
inference(resolution,[status(thm)],[f252,f21]) ).
fof(f327,plain,
! [X0] :
( sQ16_spl
| ~ member(f1(cs,ds),intersection(bs,X0)) ),
inference(resolution,[status(thm)],[f252,f19]) ).
fof(f332,plain,
( sQ14_spl
| ~ member(f1(ds,cs),ds) ),
inference(paramodulation,[status(thm)],[f27,f317]) ).
fof(f337,plain,
( sQ14_spl
| ~ member(f1(ds,cs),cs) ),
inference(paramodulation,[status(thm)],[f26,f318]) ).
fof(f340,plain,
( sQ14_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f337,f41,f240]) ).
fof(f341,plain,
( sQ3_spl
| ~ member(f1(ds,cs),bs)
| ~ member(f1(ds,cs),as) ),
inference(resolution,[status(thm)],[f43,f52]) ).
fof(f344,plain,
( sQ3_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f341,f240,f237,f41]) ).
fof(f345,plain,
( sQ14_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f332,f38,f240]) ).
fof(f352,plain,
( sQ16_spl
| ~ member(f1(cs,ds),cs) ),
inference(paramodulation,[status(thm)],[f26,f326]) ).
fof(f357,plain,
( sQ16_spl
| ~ member(f1(cs,ds),ds) ),
inference(paramodulation,[status(thm)],[f27,f327]) ).
fof(f360,plain,
( sQ16_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f357,f34,f250]) ).
fof(f361,plain,
( sQ1_spl
| ~ member(f1(cs,ds),as)
| ~ member(f1(cs,ds),bs) ),
inference(resolution,[status(thm)],[f36,f51]) ).
fof(f364,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f361,f250,f247,f34]) ).
fof(f365,plain,
( sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f352,f31,f250]) ).
fof(f422,plain,
( sQ13_spl
| ~ member(f1(ds,cs),ds) ),
inference(paramodulation,[status(thm)],[f27,f245]) ).
fof(f425,plain,
( sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f422,f38,f237]) ).
fof(f426,plain,
$false,
inference(sat_refutation,[status(thm)],[f37,f44,f59,f60,f62,f126,f130,f157,f243,f253,f316,f325,f340,f344,f345,f360,f364,f365,f425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:41:27 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.072468 seconds
% 0.10/0.44 % CPU time: 0.196916 seconds
% 0.10/0.44 % Total memory used: 102.826 MB
% 0.10/0.44 % Net memory used: 102.360 MB
%------------------------------------------------------------------------------