%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET945+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 : 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 02:11:02 PM UTC 2026
% Result : Theorem 1.19s 0.64s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 3 unt; 0 def)
% Number of atoms : 177 ( 19 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 227 ( 91 ~; 88 |; 40 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 136 ( 122 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,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(f9,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> disjoint(C,B) )
=> disjoint(union(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> disjoint(C,B) )
=> disjoint(union(A),B) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,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)],[f3]) ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
( ! [A,B,C] :
( ( ( ( in(sK0_skl(C,B,A),B)
& in(sK0_skl(C,B,A),A) )
| in(sK0_skl(C,B,A),C) )
& ( ~ in(sK0_skl(C,B,A),B)
| ~ in(sK0_skl(C,B,A),A)
| ~ in(sK0_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,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f24,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)],[f4]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
( ! [A,B] :
( ( ( ( in(sK3_skl(B,A),A)
& in(sK2_skl(B,A),sK3_skl(B,A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK2_skl(B,A),D) )
| ~ in(sK2_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK1_skl(C,B,A),A)
& in(C,sK1_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( in(X2,sK1_skl(X2,X0,X1))
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,X0,X1),X1)
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f41,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( in(sK6_skl(B,A),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(C,sK6_skl(B,A))],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( in(sK6_skl(X1,X0),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
? [A,B] :
( ~ disjoint(union(A),B)
& ! [C] :
( disjoint(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f47,plain,
( ~ disjoint(union(sK7_skl),sK8_skl)
& ! [C] :
( disjoint(C,sK8_skl)
| ~ in(C,sK7_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f46]) ).
fof(f48,plain,
! [X0] :
( disjoint(X0,sK8_skl)
| ~ in(X0,sK7_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
~ disjoint(union(sK7_skl),sK8_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f51,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,sK1_skl(X0,union(X1),X1))
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( in(sK1_skl(X0,union(X1),X1),X1)
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f103,plain,
! [X0,X1] :
( in(sK6_skl(X1,X0),X1)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f44,f51]) ).
fof(f104,plain,
! [X0,X1] :
( in(sK6_skl(X1,X0),X0)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f44,f50]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f52,f45]) ).
fof(f346,plain,
! [X0] :
( disjoint(sK1_skl(X0,union(sK7_skl),sK7_skl),sK8_skl)
| ~ in(X0,union(sK7_skl)) ),
inference(resolution,[status(thm)],[f54,f48]) ).
fof(f362,plain,
! [X0,X1] :
( ~ in(X1,sK8_skl)
| ~ in(X1,sK1_skl(X0,union(sK7_skl),sK7_skl))
| ~ in(X0,union(sK7_skl)) ),
inference(resolution,[status(thm)],[f346,f166]) ).
fof(f597,plain,
! [X0] :
( ~ in(X0,union(sK7_skl))
| ~ in(X0,sK8_skl)
| ~ in(X0,union(sK7_skl)) ),
inference(resolution,[status(thm)],[f362,f53]) ).
fof(f598,plain,
! [X0] :
( ~ in(X0,sK8_skl)
| ~ in(X0,union(sK7_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f597]) ).
fof(f603,plain,
! [X0] :
( disjoint(union(sK7_skl),X0)
| ~ in(sK6_skl(X0,union(sK7_skl)),sK8_skl) ),
inference(resolution,[status(thm)],[f598,f104]) ).
fof(f612,plain,
( disjoint(union(sK7_skl),sK8_skl)
| disjoint(union(sK7_skl),sK8_skl) ),
inference(resolution,[status(thm)],[f603,f103]) ).
fof(f613,plain,
disjoint(union(sK7_skl),sK8_skl),
inference(duplicate_literals_removal,[status(thm)],[f612]) ).
fof(f614,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f613,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:44:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 1.19/0.64 % Refutation found
% 1.19/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.19/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.19/0.67 % Elapsed time: 0.300094 seconds
% 1.19/0.67 % CPU time: 2.146386 seconds
% 1.19/0.67 % Total memory used: 130.807 MB
% 1.19/0.67 % Net memory used: 124.932 MB
%------------------------------------------------------------------------------