%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET918+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 : n026.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 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 13 unt; 4 def)
% Number of atoms : 208 ( 82 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 253 ( 98 ~; 95 |; 50 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 106 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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(f10,conjecture,
! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,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)],[f5]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
( ! [A,B,C] :
( ( ( sK1_skl(C,B,A) = B
| sK1_skl(C,B,A) = A
| in(sK1_skl(C,B,A),C) )
& ( ( sK1_skl(C,B,A) != B
& sK1_skl(C,B,A) != A )
| ~ in(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f24]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f32,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)],[f6]) ).
fof(f33,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)],[f32]) ).
fof(f34,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_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,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f47,plain,
? [A,B,C] :
( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f48,plain,
? [A,B] :
( A != B
& ? [C] :
( in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( sK5_skl != sK6_skl
& in(sK6_skl,sK7_skl)
& set_intersection2(unordered_pair(sK5_skl,sK6_skl),sK7_skl) = singleton(sK5_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,
set_intersection2(unordered_pair(sK5_skl,sK6_skl),sK7_skl) = singleton(sK5_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
in(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
sK5_skl != sK6_skl,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f58,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f69,plain,
singleton(sK5_skl) = set_intersection2(sK7_skl,unordered_pair(sK5_skl,sK6_skl)),
inference(paramodulation,[status(thm)],[f50,f15]) ).
fof(f78,plain,
~ in(sK6_skl,singleton(sK5_skl)),
inference(resolution,[status(thm)],[f53,f52]) ).
fof(f111,plain,
! [X0] : ~ in(sK6_skl,set_intersection2(singleton(sK5_skl),X0)),
inference(resolution,[status(thm)],[f58,f78]) ).
fof(f359,plain,
! [X0] :
( ~ in(sK6_skl,X0)
| ~ in(sK6_skl,singleton(sK5_skl)) ),
inference(resolution,[status(thm)],[f60,f111]) ).
fof(f386,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK5_skl,sK6_skl))
| ~ in(X0,sK7_skl)
| in(X0,singleton(sK5_skl)) ),
inference(paramodulation,[status(thm)],[f69,f60]) ).
fof(f394,definition,
! [X2] :
( sQ1_spl
<=> ~ in(sK6_skl,X2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f395,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f418,definition,
( sQ7_spl
<=> in(sK6_skl,singleton(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ7_spl
| ~ in(sK6_skl,singleton(sK5_skl)) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f359,f418,f394]) ).
fof(f486,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f395]) ).
fof(f487,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f531,plain,
( sQ7_spl
| ~ in(sK6_skl,unordered_pair(sK5_skl,sK6_skl))
| ~ in(sK6_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f386,f420]) ).
fof(f538,definition,
( sQ22_spl
<=> in(sK6_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ22_spl
| ~ in(sK6_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ23_spl
<=> in(sK6_skl,unordered_pair(sK5_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( sQ23_spl
| ~ in(sK6_skl,unordered_pair(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( sQ7_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f531,f538,f541,f418]) ).
fof(f560,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f51]) ).
fof(f561,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f562,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f57]) ).
fof(f563,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f564,plain,
$false,
inference(sat_refutation,[status(thm)],[f421,f487,f544,f561,f563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n026.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 05:46:21 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.57 % Elapsed time: 0.099773 seconds
% 0.19/0.57 % CPU time: 0.248142 seconds
% 0.19/0.57 % Total memory used: 59.088 MB
% 0.19/0.57 % Net memory used: 58.955 MB
%------------------------------------------------------------------------------