%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET983+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 : n010.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 02:11:05 PM UTC 2026
% Result : Theorem 0.15s 0.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 2 def)
% Number of atoms : 90 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 100 ( 37 ~; 35 |; 22 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 49 !; 7 ?)
% 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(f7,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f13,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(f14,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)],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
? [A,B,C,D,E] :
( ~ in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E)))
& in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
( ~ in(sK3_skl,cartesian_product2(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK7_skl)))
& in(sK3_skl,cartesian_product2(sK6_skl,sK7_skl))
& in(sK3_skl,cartesian_product2(sK4_skl,sK5_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl),skolemize(D,sK6_skl),skolemize(E,sK7_skl)],[f29]) ).
fof(f31,plain,
in(sK3_skl,cartesian_product2(sK4_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
in(sK3_skl,cartesian_product2(sK6_skl,sK7_skl)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
~ in(sK3_skl,cartesian_product2(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK7_skl))),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f37,plain,
~ in(sK3_skl,set_intersection2(cartesian_product2(sK4_skl,sK5_skl),cartesian_product2(sK6_skl,sK7_skl))),
inference(forward_demodulation,[status(thm)],[f28,f33]) ).
fof(f79,plain,
( ~ in(sK3_skl,cartesian_product2(sK6_skl,sK7_skl))
| ~ in(sK3_skl,cartesian_product2(sK4_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f37,f36]) ).
fof(f82,definition,
( sQ0_spl
<=> in(sK3_skl,cartesian_product2(sK4_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ0_spl
| ~ in(sK3_skl,cartesian_product2(sK4_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> in(sK3_skl,cartesian_product2(sK6_skl,sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( sQ1_spl
| ~ in(sK3_skl,cartesian_product2(sK6_skl,sK7_skl)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f82,f85]) ).
fof(f89,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f31]) ).
fof(f90,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f32]) ).
fof(f92,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f93,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f90,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.57 % Computer : n010.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Mon Sep 21 05:46:26 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.15/0.59 % Drodi V4.1.1
% 0.15/0.61 % Refutation found
% 0.15/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.64 % Elapsed time: 0.055758 seconds
% 0.15/0.64 % CPU time: 0.160846 seconds
% 0.15/0.64 % Total memory used: 101.650 MB
% 0.15/0.64 % Net memory used: 101.256 MB
%------------------------------------------------------------------------------