%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:10:58 PM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 14 unt; 3 def)
% Number of atoms : 181 ( 58 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 221 ( 91 ~; 78 |; 45 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 107 ( 97 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = 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(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C] :
~ ( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ! [A,B,C] :
( ( ( sK0_skl(C,B,A) = B
| sK0_skl(C,B,A) = A
| in(sK0_skl(C,B,A),C) )
& ( ( sK0_skl(C,B,A) != B
& sK0_skl(C,B,A) != A )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,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(f27,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)],[f26]) ).
fof(f28,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))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f43,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)],[f10]) ).
fof(f44,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)],[f43]) ).
fof(f45,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( in(sK4_skl(B,A),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(C,sK4_skl(B,A))],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK4_skl(X1,X0),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
? [A,B,C] :
( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f49,plain,
( ~ disjoint(unordered_pair(sK5_skl,sK7_skl),sK6_skl)
& ~ in(sK7_skl,sK6_skl)
& ~ in(sK5_skl,sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl)],[f48]) ).
fof(f50,plain,
~ in(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
~ in(sK7_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
~ disjoint(unordered_pair(sK5_skl,sK7_skl),sK6_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f56,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f57,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f65,plain,
~ disjoint(unordered_pair(sK7_skl,sK5_skl),sK6_skl),
inference(paramodulation,[status(thm)],[f15,f52]) ).
fof(f92,plain,
in(sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl)),
inference(resolution,[status(thm)],[f46,f65]) ).
fof(f93,plain,
in(sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl)),
inference(resolution,[status(thm)],[f46,f52]) ).
fof(f108,plain,
in(sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK6_skl),
inference(resolution,[status(thm)],[f92,f57]) ).
fof(f119,plain,
in(sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK6_skl),
inference(resolution,[status(thm)],[f93,f57]) ).
fof(f120,plain,
in(sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),unordered_pair(sK5_skl,sK7_skl)),
inference(resolution,[status(thm)],[f93,f56]) ).
fof(f269,definition,
( sQ0_spl
<=> sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ0_spl
| sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) = sK7_skl ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f278,plain,
( ~ sQ0_spl
| in(sK7_skl,sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f270,f108]) ).
fof(f280,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f51]) ).
fof(f281,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = sK7_skl
| sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = sK5_skl ),
inference(resolution,[status(thm)],[f120,f53]) ).
fof(f292,definition,
( sQ2_spl
<=> sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( ~ sQ2_spl
| sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = sK5_skl ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ3_spl
<=> sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( ~ sQ3_spl
| sK4_skl(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = sK7_skl ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f283,f292,f295]) ).
fof(f303,plain,
( ~ sQ2_spl
| in(sK5_skl,sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f293,f119]) ).
fof(f307,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f50]) ).
fof(f308,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f309,plain,
( ~ sQ3_spl
| sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) = sK7_skl ),
inference(paramodulation,[status(thm)],[f15,f296]) ).
fof(f311,plain,
( ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f309,f269,f295]) ).
fof(f313,plain,
$false,
inference(sat_refutation,[status(thm)],[f281,f298,f308,f311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 05:43:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.32 % Refutation found
% 0.03/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.33 % Elapsed time: 0.036761 seconds
% 0.07/0.33 % CPU time: 0.108246 seconds
% 0.07/0.33 % Total memory used: 102.777 MB
% 0.07/0.33 % Net memory used: 102.385 MB
%------------------------------------------------------------------------------