%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:10:22 PM UTC 2026
% Result : Theorem 0.14s 10.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 10 unt; 3 def)
% Number of atoms : 264 ( 16 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 318 ( 128 ~; 128 |; 25 &)
% ( 11 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 125 ( 120 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
=> intersection(B,C) = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> intersection(D,cross_product(B,C)) = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> intersection(D,cross_product(B,C)) = D ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
! [B] :
( ! [C] :
( intersection(B,C) = B
| ~ subset(B,C)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f53,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f79,plain,
! [B] :
( ! [C] :
( ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f80,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f90,plain,
! [B] :
( ! [C] :
( ( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f91,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK7_skl(C,B),C)
& member(sK7_skl(C,B),B)
& ilf_type(sK7_skl(C,B),set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(D,sK7_skl(C,B))],[f91]) ).
fof(f95,plain,
! [X0,X1] :
( member(sK7_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f96,plain,
! [X0,X1] :
( ~ member(sK7_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f99,plain,
! [B] :
( ! [C] :
( ( member(B,power_set(C))
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f100,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK8_skl(C,B),C)
& member(sK8_skl(C,B),B)
& ilf_type(sK8_skl(C,B),set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(D,sK8_skl(C,B))],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f106,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f107,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
! [B] :
( ! [C] :
( ( ilf_type(B,member_type(C))
<=> member(B,C) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f110,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f147,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f148,plain,
? [B] :
( ? [C] :
( ? [D] :
( intersection(D,cross_product(B,C)) != D
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f149,plain,
( intersection(sK17_skl,cross_product(sK15_skl,sK16_skl)) != sK17_skl
& ilf_type(sK17_skl,relation_type(sK15_skl,sK16_skl))
& ilf_type(sK16_skl,set_type)
& ilf_type(sK15_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl]),skolemize(B,sK15_skl),skolemize(C,sK16_skl),skolemize(D,sK17_skl)],[f148]) ).
fof(f152,plain,
ilf_type(sK17_skl,relation_type(sK15_skl,sK16_skl)),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f153,plain,
intersection(sK17_skl,cross_product(sK15_skl,sK16_skl)) != sK17_skl,
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f166,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f107,f147]) ).
fof(f172,plain,
! [X0,X1] :
( intersection(X1,X0) = X1
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f147]) ).
fof(f173,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f172,f147]) ).
fof(f187,plain,
! [X0,X1] :
( member(sK7_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f147]) ).
fof(f188,plain,
! [X0,X1] :
( ~ member(sK7_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f147]) ).
fof(f189,plain,
! [X0,X1] :
( ~ member(sK7_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f188,f147]) ).
fof(f190,plain,
! [X0,X1] :
( intersection(X1,X0) = X1
| ~ member(sK7_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f189,f173]) ).
fof(f201,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f147]) ).
fof(f370,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f147]) ).
fof(f562,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f147]) ).
fof(f563,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f562,f147]) ).
fof(f564,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f147]) ).
fof(f757,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f147]) ).
fof(f758,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f757,f147]) ).
fof(f764,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X0))
| empty(power_set(X0)) ),
inference(resolution,[status(thm)],[f758,f370]) ).
fof(f766,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f764,f166]) ).
fof(f812,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f147]) ).
fof(f814,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f812,f201]) ).
fof(f816,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f814,f147]) ).
fof(f868,plain,
member(sK17_skl,power_set(cross_product(sK15_skl,sK16_skl))),
inference(resolution,[status(thm)],[f816,f152]) ).
fof(f877,plain,
! [X0] :
( member(X0,cross_product(sK15_skl,sK16_skl))
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f868,f564]) ).
fof(f881,plain,
! [X0] :
( intersection(X0,cross_product(sK15_skl,sK16_skl)) = X0
| ~ member(sK7_skl(cross_product(sK15_skl,sK16_skl),X0),sK17_skl) ),
inference(resolution,[status(thm)],[f877,f190]) ).
fof(f1322,plain,
( subset(sK17_skl,cross_product(sK15_skl,sK16_skl))
| ~ ilf_type(cross_product(sK15_skl,sK16_skl),set_type)
| intersection(sK17_skl,cross_product(sK15_skl,sK16_skl)) = sK17_skl ),
inference(resolution,[status(thm)],[f881,f187]) ).
fof(f1329,definition,
( sQ31_spl
<=> intersection(sK17_skl,cross_product(sK15_skl,sK16_skl)) = sK17_skl ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1330,plain,
( ~ sQ31_spl
| intersection(sK17_skl,cross_product(sK15_skl,sK16_skl)) = sK17_skl ),
inference(component_clause,[status(thm)],[f1329]) ).
fof(f1332,definition,
( sQ32_spl
<=> ilf_type(cross_product(sK15_skl,sK16_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1334,plain,
( sQ32_spl
| ~ ilf_type(cross_product(sK15_skl,sK16_skl),set_type) ),
inference(component_clause,[status(thm)],[f1332]) ).
fof(f1335,definition,
( sQ33_spl
<=> subset(sK17_skl,cross_product(sK15_skl,sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1336,plain,
( ~ sQ33_spl
| subset(sK17_skl,cross_product(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f1335]) ).
fof(f1338,plain,
( sQ33_spl
| ~ sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f1322,f1329,f1332,f1335]) ).
fof(f1353,plain,
( ~ sQ33_spl
| intersection(sK17_skl,cross_product(sK15_skl,sK16_skl)) = sK17_skl ),
inference(resolution,[status(thm)],[f1336,f173]) ).
fof(f1354,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1353,f153]) ).
fof(f1355,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f1354]) ).
fof(f1356,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1330,f153]) ).
fof(f1357,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1356]) ).
fof(f1358,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1334,f147]) ).
fof(f1359,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1358]) ).
fof(f1360,plain,
$false,
inference(sat_refutation,[status(thm)],[f1338,f1355,f1357,f1359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n005.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Mon Sep 21 05:31:13 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Drodi V4.1.1
% 0.14/10.46 % Refutation found
% 0.14/10.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.49 % Elapsed time: 0.096758 seconds
% 0.14/10.49 % CPU time: 0.532657 seconds
% 0.14/10.49 % Total memory used: 92.589 MB
% 0.14/10.49 % Net memory used: 91.627 MB
%------------------------------------------------------------------------------