%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET637+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 : n016.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 02:10:19 PM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 7 unt; 5 def)
% Number of atoms : 213 ( 31 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 227 ( 86 ~; 103 |; 25 &)
% ( 12 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 97 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( not_equal(B,C)
<=> 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] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ( member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
( ! [B,C] :
( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [B,C] :
( ( ( member(sK1_skl(C,B),C)
| member(sK1_skl(C,B),B) )
& ( ~ member(sK1_skl(C,B),C)
| ~ member(sK1_skl(C,B),B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
( ! [B,C] :
( B = C
| not_equal(B,C) )
& ! [B,C] :
( B != C
| ~ not_equal(B,C) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f42,plain,
? [B,C] :
( intersect(B,C)
<~> not_equal(intersection(B,C),empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
? [B,C] :
( ( ~ not_equal(intersection(B,C),empty_set)
| ~ intersect(B,C) )
& ( not_equal(intersection(B,C),empty_set)
| intersect(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( ( ~ not_equal(intersection(sK3_skl,sK4_skl),empty_set)
| ~ intersect(sK3_skl,sK4_skl) )
& ( not_equal(intersection(sK3_skl,sK4_skl),empty_set)
| intersect(sK3_skl,sK4_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f43]) ).
fof(f45,plain,
( not_equal(intersection(sK3_skl,sK4_skl),empty_set)
| intersect(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
( ~ not_equal(intersection(sK3_skl,sK4_skl),empty_set)
| ~ intersect(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ0_spl
<=> intersect(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ0_spl
| intersect(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f49,plain,
( sQ0_spl
| ~ intersect(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ1_spl
<=> not_equal(intersection(sK3_skl,sK4_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ1_spl
| not_equal(intersection(sK3_skl,sK4_skl),empty_set) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( sQ1_spl
| ~ not_equal(intersection(sK3_skl,sK4_skl),empty_set) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f47,f50]) ).
fof(f54,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f47,f50]) ).
fof(f55,plain,
! [X0] : ~ not_equal(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f67,plain,
! [X0,X1,X2] :
( member(sK1_skl(intersection(X1,X2),X0),X2)
| member(sK1_skl(intersection(X1,X2),X0),X0)
| X0 = intersection(X1,X2) ),
inference(resolution,[status(thm)],[f29,f14]) ).
fof(f88,plain,
( ~ sQ0_spl
| member(sK0_skl(sK4_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f48,f20]) ).
fof(f89,plain,
( ~ sQ0_spl
| member(sK0_skl(sK4_skl,sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f48,f19]) ).
fof(f93,plain,
( sQ1_spl
| intersection(sK3_skl,sK4_skl) = empty_set ),
inference(resolution,[status(thm)],[f52,f33]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ~ member(sK1_skl(intersection(X1,X2),X0),X3)
| intersect(X3,X2)
| member(sK1_skl(intersection(X1,X2),X0),X0)
| X0 = intersection(X1,X2) ),
inference(resolution,[status(thm)],[f67,f21]) ).
fof(f100,plain,
! [X0,X1,X2] :
( member(sK1_skl(intersection(X2,X1),X0),X2)
| member(sK1_skl(intersection(X1,X2),X0),X0)
| X0 = intersection(X1,X2) ),
inference(paramodulation,[status(thm)],[f34,f67]) ).
fof(f121,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(sK0_skl(sK4_skl,sK3_skl),X0)
| member(sK0_skl(sK4_skl,sK3_skl),intersection(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f88,f15]) ).
fof(f171,definition,
( sQ4_spl
<=> intersection(sK3_skl,sK4_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ4_spl
| intersection(sK3_skl,sK4_skl) = empty_set ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f320,plain,
! [X0,X1] :
( sQ0_spl
| ~ member(sK1_skl(intersection(X1,sK4_skl),X0),sK3_skl)
| member(sK1_skl(intersection(X1,sK4_skl),X0),X0)
| X0 = intersection(X1,sK4_skl) ),
inference(resolution,[status(thm)],[f98,f49]) ).
fof(f372,plain,
! [X0] :
( sQ0_spl
| member(sK1_skl(intersection(sK4_skl,sK3_skl),X0),X0)
| X0 = intersection(sK4_skl,sK3_skl)
| member(sK1_skl(intersection(sK3_skl,sK4_skl),X0),X0)
| X0 = intersection(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f320,f100]) ).
fof(f385,plain,
( sQ0_spl
| empty_set = intersection(sK4_skl,sK3_skl)
| member(sK1_skl(intersection(sK3_skl,sK4_skl),empty_set),empty_set)
| empty_set = intersection(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f372,f22]) ).
fof(f406,definition,
( sQ12_spl
<=> member(sK1_skl(intersection(sK3_skl,sK4_skl),empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ12_spl
| member(sK1_skl(intersection(sK3_skl,sK4_skl),empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,definition,
( sQ13_spl
<=> empty_set = intersection(sK4_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ13_spl
| empty_set = intersection(sK4_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( sQ0_spl
| sQ13_spl
| sQ12_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f385,f171,f406,f409,f47]) ).
fof(f656,plain,
( ~ sQ0_spl
| member(sK0_skl(sK4_skl,sK3_skl),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f121,f89]) ).
fof(f659,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| member(sK0_skl(sK4_skl,sK3_skl),empty_set) ),
inference(forward_demodulation,[status(thm)],[f172,f656]) ).
fof(f660,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f22]) ).
fof(f661,plain,
( ~ sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f662,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f22]) ).
fof(f663,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f677,plain,
( ~ sQ13_spl
| empty_set = intersection(sK3_skl,sK4_skl) ),
inference(paramodulation,[status(thm)],[f34,f410]) ).
fof(f695,plain,
( ~ sQ13_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f677,f171,f409]) ).
fof(f731,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| not_equal(empty_set,empty_set) ),
inference(backward_demodulation,[status(thm)],[f172,f51]) ).
fof(f746,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f731,f55]) ).
fof(f747,plain,
( ~ sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f752,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f93,f171,f50]) ).
fof(f753,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f54,f412,f661,f663,f695,f747,f752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n016.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 05:35:38 UTC 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.084779 seconds
% 0.15/0.45 % CPU time: 0.373455 seconds
% 0.15/0.45 % Total memory used: 106.451 MB
% 0.15/0.45 % Net memory used: 105.399 MB
%------------------------------------------------------------------------------