%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU138+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:19:20 PM UTC 2026
% Result : Theorem 0.27s 0.90s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 10 unt; 7 def)
% Number of atoms : 235 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 272 ( 108 ~; 120 |; 32 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 114 ( 108 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f23,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f39,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [A,B,C] :
( ( ( ( in(sK1_skl(C,B,A),B)
& in(sK1_skl(C,B,A),A) )
| in(sK1_skl(C,B,A),C) )
& ( ~ in(sK1_skl(C,B,A),B)
| ~ in(sK1_skl(C,B,A),A)
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f39]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X0,X2,X1),X2)
| ~ in(sK1_skl(X0,X2,X1),X1)
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X2)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f47,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK2_skl(C,B,A),B)
& in(sK2_skl(C,B,A),A) )
| in(sK2_skl(C,B,A),C) )
& ( in(sK2_skl(C,B,A),B)
| ~ in(sK2_skl(C,B,A),A)
| ~ in(sK2_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f67,plain,
? [A,B] : set_difference(A,set_difference(A,B)) != set_intersection2(A,B),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f68,plain,
set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) != set_intersection2(sK5_skl,sK6_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f67]) ).
fof(f69,plain,
set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) != set_intersection2(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f84,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f86,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ in(X1,X0)
| ~ in(X0,set_difference(X1,X2)) ),
inference(resolution,[status(thm)],[f84,f24]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(set_difference(X0,X1),X2,X3),X2)
| set_difference(X0,X1) = set_intersection2(X3,X2)
| ~ in(sK1_skl(set_difference(X0,X1),X2,X3),X1) ),
inference(resolution,[status(thm)],[f85,f46]) ).
fof(f518,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(set_difference(X0,X1),X2,X3),X2)
| set_difference(X0,X1) = set_intersection2(X3,X2)
| ~ in(X0,sK1_skl(set_difference(X0,X1),X2,X3)) ),
inference(resolution,[status(thm)],[f184,f46]) ).
fof(f519,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(set_difference(X0,X1),X2,X3),X3)
| set_difference(X0,X1) = set_intersection2(X3,X2)
| ~ in(X0,sK1_skl(set_difference(X0,X1),X2,X3)) ),
inference(resolution,[status(thm)],[f184,f45]) ).
fof(f617,plain,
( ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK6_skl)
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK5_skl)
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f44,f69]) ).
fof(f621,definition,
( sQ5_spl
<=> in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ5_spl
| in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl))) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f623,plain,
( sQ5_spl
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl))) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,definition,
( sQ6_spl
<=> in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( sQ6_spl
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,definition,
( sQ7_spl
<=> in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( sQ7_spl
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f617,f621,f624,f627]) ).
fof(f735,plain,
( sQ7_spl
| set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) = set_intersection2(sK5_skl,sK6_skl)
| ~ in(sK5_skl,sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f629,f518]) ).
fof(f736,plain,
( sQ7_spl
| set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) = set_intersection2(sK5_skl,sK6_skl)
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f629,f193]) ).
fof(f743,definition,
( sQ10_spl
<=> in(sK5_skl,sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f746,definition,
( sQ11_spl
<=> set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) = set_intersection2(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f747,plain,
( ~ sQ11_spl
| set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) = set_intersection2(sK5_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f746]) ).
fof(f749,plain,
( sQ7_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f735,f743,f746,f627]) ).
fof(f750,definition,
( sQ12_spl
<=> in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( ~ sQ12_spl
| in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f750]) ).
fof(f752,plain,
( sQ12_spl
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f750]) ).
fof(f753,plain,
( sQ7_spl
| sQ11_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f736,f750,f746,f627]) ).
fof(f758,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f747,f69]) ).
fof(f759,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f758]) ).
fof(f760,plain,
( sQ6_spl
| set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) = set_intersection2(sK5_skl,sK6_skl)
| ~ in(sK5_skl,sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f626,f519]) ).
fof(f764,plain,
! [X0] :
( sQ6_spl
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,X0)) ),
inference(resolution,[status(thm)],[f626,f84]) ).
fof(f768,plain,
( sQ6_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f760,f743,f746,f624]) ).
fof(f772,plain,
( sQ5_spl
| in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK5_skl)
| set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) = set_intersection2(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f623,f45]) ).
fof(f773,plain,
( sQ5_spl
| in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,sK6_skl))
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f623,f86]) ).
fof(f780,plain,
( sQ5_spl
| sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f772,f746,f624,f621]) ).
fof(f781,plain,
( sQ5_spl
| sQ12_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f773,f624,f750,f621]) ).
fof(f797,definition,
( sQ15_spl
<=> set_intersection2(sK6_skl,sK5_skl) = set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f798,plain,
( ~ sQ15_spl
| set_intersection2(sK6_skl,sK5_skl) = set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f874,plain,
( ~ sQ15_spl
| set_intersection2(sK6_skl,sK5_skl) != set_intersection2(sK5_skl,sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f798,f69]) ).
fof(f900,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f874,f25]) ).
fof(f901,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f1062,plain,
( ~ sQ12_spl
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f751,f85]) ).
fof(f1065,plain,
( ~ sQ12_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1062,f627,f750]) ).
fof(f1066,plain,
( ~ sQ5_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f764]) ).
fof(f1067,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1066]) ).
fof(f1105,plain,
( sQ12_spl
| in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK6_skl)
| ~ in(sK1_skl(set_difference(sK5_skl,set_difference(sK5_skl,sK6_skl)),sK6_skl,sK5_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f752,f86]) ).
fof(f1111,plain,
( sQ12_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1105,f624,f627,f750]) ).
fof(f1112,plain,
$false,
inference(sat_refutation,[status(thm)],[f630,f749,f753,f759,f768,f780,f781,f901,f1065,f1067,f1111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU138+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n009.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:52:27 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.27/0.90 % Refutation found
% 0.27/0.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.27/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.94 % Elapsed time: 0.474757 seconds
% 0.27/0.94 % CPU time: 3.209142 seconds
% 0.27/0.94 % Total memory used: 126.610 MB
% 0.27/0.94 % Net memory used: 122.693 MB
%------------------------------------------------------------------------------