%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET944+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:11:01 PM UTC 2026
% Result : Theorem 1.30s 0.62s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 7 unt; 3 def)
% Number of atoms : 216 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 264 ( 106 ~; 110 |; 38 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 143 ( 130 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B] : subset(union(set_intersection2(A,B)),set_intersection2(union(A),union(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B] : subset(union(set_intersection2(A,B)),set_intersection2(union(A),union(B))),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,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)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f24,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))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f31,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ( ( ( in(sK4_skl(B,A),A)
& in(sK3_skl(B,A),sK4_skl(B,A)) )
| in(sK3_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK3_skl(B,A),D) )
| ~ in(sK3_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK2_skl(C,B,A),A)
& in(C,sK2_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(D,sK2_skl(C,B,A)),skolemize(C,sK3_skl(B,A)),skolemize(D,sK4_skl(B,A))],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( in(X2,sK2_skl(X2,X0,X1))
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( in(sK2_skl(X2,X0,X1),X1)
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f48,plain,
? [A,B] : ~ subset(union(set_intersection2(A,B)),set_intersection2(union(A),union(B))),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f49,plain,
~ subset(union(set_intersection2(sK7_skl,sK8_skl)),set_intersection2(union(sK7_skl),union(sK8_skl))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f48]) ).
fof(f50,plain,
~ subset(union(set_intersection2(sK7_skl,sK8_skl)),set_intersection2(union(sK7_skl),union(sK8_skl))),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f25]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,sK2_skl(X0,union(X1),X1))
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f34]) ).
fof(f55,plain,
! [X0,X1] :
( in(sK2_skl(X0,union(X1),X1),X1)
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(set_intersection2(X1,X2),X0),X2)
| ~ in(sK0_skl(set_intersection2(X1,X2),X0),X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(resolution,[status(thm)],[f21,f53]) ).
fof(f129,plain,
( ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(sK8_skl))
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(sK7_skl)) ),
inference(resolution,[status(thm)],[f78,f50]) ).
fof(f134,definition,
( sQ0_spl
<=> in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(sK7_skl)) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,definition,
( sQ1_spl
<=> in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ1_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(sK8_skl)) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f134,f137]) ).
fof(f205,plain,
! [X0,X1,X2] :
( in(sK2_skl(X0,union(set_intersection2(X1,X2)),set_intersection2(X1,X2)),X2)
| ~ in(X0,union(set_intersection2(X1,X2))) ),
inference(resolution,[status(thm)],[f55,f52]) ).
fof(f206,plain,
! [X0,X1,X2] :
( in(sK2_skl(X0,union(set_intersection2(X1,X2)),set_intersection2(X1,X2)),X1)
| ~ in(X0,union(set_intersection2(X1,X2))) ),
inference(resolution,[status(thm)],[f55,f51]) ).
fof(f221,plain,
! [X0] :
( sQ0_spl
| ~ in(X0,sK7_skl)
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),X0) ),
inference(resolution,[status(thm)],[f136,f56]) ).
fof(f223,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(X0))
| ~ in(sK2_skl(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(X0),X0),sK7_skl) ),
inference(resolution,[status(thm)],[f221,f54]) ).
fof(f229,definition,
( sQ3_spl
<=> subset(union(set_intersection2(sK7_skl,sK8_skl)),set_intersection2(union(sK7_skl),union(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( ~ sQ3_spl
| subset(union(set_intersection2(sK7_skl,sK8_skl)),set_intersection2(union(sK7_skl),union(sK8_skl))) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f233,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f50]) ).
fof(f234,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0] :
( sQ1_spl
| ~ in(X0,sK8_skl)
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),X0) ),
inference(resolution,[status(thm)],[f139,f56]) ).
fof(f458,plain,
! [X0] :
( sQ1_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(X0))
| ~ in(sK2_skl(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(X0),X0),sK8_skl) ),
inference(resolution,[status(thm)],[f235,f54]) ).
fof(f706,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(set_intersection2(sK7_skl,X0)))
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(set_intersection2(sK7_skl,X0))) ),
inference(resolution,[status(thm)],[f206,f223]) ).
fof(f719,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(set_intersection2(sK7_skl,X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f706]) ).
fof(f747,plain,
( sQ0_spl
| subset(union(set_intersection2(sK7_skl,sK8_skl)),set_intersection2(union(sK7_skl),union(sK8_skl))) ),
inference(resolution,[status(thm)],[f719,f20]) ).
fof(f752,plain,
( sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f747,f229,f134]) ).
fof(f930,plain,
! [X0] :
( sQ1_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(set_intersection2(X0,sK8_skl)))
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(set_intersection2(X0,sK8_skl))) ),
inference(resolution,[status(thm)],[f458,f205]) ).
fof(f933,plain,
! [X0] :
( sQ1_spl
| ~ in(sK0_skl(set_intersection2(union(sK7_skl),union(sK8_skl)),union(set_intersection2(sK7_skl,sK8_skl))),union(set_intersection2(X0,sK8_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f930]) ).
fof(f2285,plain,
( sQ1_spl
| subset(union(set_intersection2(sK7_skl,sK8_skl)),set_intersection2(union(sK7_skl),union(sK8_skl))) ),
inference(resolution,[status(thm)],[f933,f20]) ).
fof(f2291,plain,
( sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f2285,f229,f137]) ).
fof(f2292,plain,
$false,
inference(sat_refutation,[status(thm)],[f140,f234,f752,f2291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET944+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:44:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 1.30/0.62 % Refutation found
% 1.30/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.30/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.30/0.65 % Elapsed time: 0.277150 seconds
% 1.30/0.65 % CPU time: 2.007300 seconds
% 1.30/0.65 % Total memory used: 127.773 MB
% 1.30/0.65 % Net memory used: 122.495 MB
%------------------------------------------------------------------------------