%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET598+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:10:11 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 9 unt; 11 def)
% Number of atoms : 214 ( 25 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 236 ( 94 ~; 100 |; 24 &)
% ( 14 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 47 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( ( subset(B,D)
& subset(B,C) )
=> subset(B,intersection(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C,D] :
( B = intersection(C,D)
<=> ( ! [E] :
( ( subset(E,D)
& subset(E,C) )
=> subset(E,B) )
& subset(B,D)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C,D] :
( B = intersection(C,D)
<=> ( ! [E] :
( ( subset(E,D)
& subset(E,C) )
=> subset(E,B) )
& subset(B,D)
& subset(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [B,C,D] :
( subset(B,intersection(C,D))
| ~ subset(B,D)
| ~ subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f26,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f40,plain,
? [B,C,D] :
( B = intersection(C,D)
<~> ( ! [E] :
( subset(E,B)
| ~ subset(E,D)
| ~ subset(E,C) )
& subset(B,D)
& subset(B,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
? [B,C,D] :
( ( ? [E] :
( ~ subset(E,B)
& subset(E,D)
& subset(E,C) )
| ~ subset(B,D)
| ~ subset(B,C)
| B != intersection(C,D) )
& ( ( ! [E] :
( subset(E,B)
| ~ subset(E,D)
| ~ subset(E,C) )
& subset(B,D)
& subset(B,C) )
| B = intersection(C,D) ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( ( ( ~ subset(sK5_skl,sK2_skl)
& subset(sK5_skl,sK4_skl)
& subset(sK5_skl,sK3_skl) )
| ~ subset(sK2_skl,sK4_skl)
| ~ subset(sK2_skl,sK3_skl)
| sK2_skl != intersection(sK3_skl,sK4_skl) )
& ( ( ! [E] :
( subset(E,sK2_skl)
| ~ subset(E,sK4_skl)
| ~ subset(E,sK3_skl) )
& subset(sK2_skl,sK4_skl)
& subset(sK2_skl,sK3_skl) )
| sK2_skl = intersection(sK3_skl,sK4_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl),skolemize(E,sK5_skl)],[f41]) ).
fof(f43,plain,
( subset(sK2_skl,sK3_skl)
| sK2_skl = intersection(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( subset(sK2_skl,sK4_skl)
| sK2_skl = intersection(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0] :
( subset(X0,sK2_skl)
| ~ subset(X0,sK4_skl)
| ~ subset(X0,sK3_skl)
| sK2_skl = intersection(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
( subset(sK5_skl,sK3_skl)
| ~ subset(sK2_skl,sK4_skl)
| ~ subset(sK2_skl,sK3_skl)
| sK2_skl != intersection(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
( subset(sK5_skl,sK4_skl)
| ~ subset(sK2_skl,sK4_skl)
| ~ subset(sK2_skl,sK3_skl)
| sK2_skl != intersection(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f48,plain,
( ~ subset(sK5_skl,sK2_skl)
| ~ subset(sK2_skl,sK4_skl)
| ~ subset(sK2_skl,sK3_skl)
| sK2_skl != intersection(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f49,definition,
( sQ0_spl
<=> sK2_skl = intersection(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ0_spl
| sK2_skl = intersection(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f51,plain,
( sQ0_spl
| sK2_skl != intersection(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ1_spl
<=> subset(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f49,f52]) ).
fof(f56,definition,
( sQ2_spl
<=> subset(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f49,f56]) ).
fof(f60,definition,
! [X0] :
( sQ3_spl
<=> ( subset(X0,sK2_skl)
| ~ subset(X0,sK4_skl)
| ~ subset(X0,sK3_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f61,plain,
! [X0] :
( ~ sQ3_spl
| subset(X0,sK2_skl)
| ~ subset(X0,sK4_skl)
| ~ subset(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f49,f60]) ).
fof(f64,definition,
( sQ4_spl
<=> subset(sK5_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f49,f52,f56,f64]) ).
fof(f68,definition,
( sQ5_spl
<=> subset(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f49,f52,f56,f68]) ).
fof(f72,definition,
( sQ6_spl
<=> subset(sK5_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( sQ6_spl
| ~ subset(sK5_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f49,f52,f56,f72]) ).
fof(f76,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f78,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ subset(sK5_skl,sK4_skl)
| ~ subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f74,f61]) ).
fof(f79,plain,
( ~ sQ3_spl
| sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f78,f64,f68,f72,f60]) ).
fof(f82,plain,
( ~ sQ0_spl
| subset(sK2_skl,sK3_skl) ),
inference(paramodulation,[status(thm)],[f50,f11]) ).
fof(f83,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f82,f52,f49]) ).
fof(f84,plain,
( sQ0_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK2_skl)
| ~ subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f30,f51]) ).
fof(f86,definition,
( sQ7_spl
<=> subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ7_spl
| ~ subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,definition,
( sQ8_spl
<=> subset(intersection(sK3_skl,sK4_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( sQ8_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f84,f86,f89,f49]) ).
fof(f94,plain,
( sQ7_spl
| ~ subset(sK2_skl,sK4_skl)
| ~ subset(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f88,f13]) ).
fof(f95,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f94,f52,f56,f86]) ).
fof(f96,plain,
( sQ8_spl
| ~ sQ0_spl
| ~ subset(sK2_skl,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f50,f91]) ).
fof(f98,plain,
( sQ8_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f76]) ).
fof(f99,plain,
( sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f107,plain,
! [X0] :
( ~ sQ0_spl
| subset(X0,sK2_skl)
| ~ subset(X0,sK4_skl)
| ~ subset(X0,sK3_skl) ),
inference(paramodulation,[status(thm)],[f50,f13]) ).
fof(f115,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(paramodulation,[status(thm)],[f31,f11]) ).
fof(f119,plain,
( ~ sQ0_spl
| subset(sK2_skl,sK4_skl) ),
inference(paramodulation,[status(thm)],[f50,f115]) ).
fof(f122,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f119,f56,f49]) ).
fof(f123,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f107,f60,f49]) ).
fof(f129,plain,
( ~ sQ3_spl
| sQ8_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK4_skl)
| ~ subset(intersection(sK3_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f91,f61]) ).
fof(f130,definition,
( sQ9_spl
<=> subset(intersection(sK3_skl,sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( sQ9_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ10_spl
<=> subset(intersection(sK3_skl,sK4_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ10_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( ~ sQ3_spl
| sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f129,f130,f133,f89,f60]) ).
fof(f137,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f11]) ).
fof(f138,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f115]) ).
fof(f140,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f59,f63,f67,f71,f75,f79,f83,f92,f95,f99,f122,f123,f136,f138,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET598+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:28:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.064400 seconds
% 0.08/0.43 % CPU time: 0.153812 seconds
% 0.08/0.43 % Total memory used: 57.371 MB
% 0.08/0.43 % Net memory used: 57.196 MB
%------------------------------------------------------------------------------