%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:19:16 PM UTC 2026
% Result : Theorem 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 7 unt; 1 def)
% Number of atoms : 93 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 46 ~; 33 |; 23 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 60 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [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(f15,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f19,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f33,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( ! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ! [A,B] :
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f52,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)],[f15]) ).
fof(f53,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f54,plain,
? [A,B] :
( ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
| sP0_prd(B,A) ),
inference(formula_renaming,[status(thm)],[f52,f53]) ).
fof(f55,plain,
( ? [A,B] :
( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
| ? [A,B] : sP0_prd(B,A) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
( ( disjoint(sK7_skl,sK8_skl)
& in(sK9_skl,set_intersection2(sK7_skl,sK8_skl)) )
| sP0_prd(sK6_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f55]) ).
fof(f57,plain,
( in(sK9_skl,set_intersection2(sK7_skl,sK8_skl))
| sP0_prd(sK6_skl,sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
( disjoint(sK7_skl,sK8_skl)
| sP0_prd(sK6_skl,sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [A,B] :
( ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B)
| sP0_prd(B,A) )
& ( ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) )
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f60,plain,
( ! [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B)
| sP0_prd(B,A) )
& ! [A,B] :
( ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) )
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
( ! [A,B] :
( in(sK10_skl(B,A),set_intersection2(A,B))
| disjoint(A,B)
| sP0_prd(B,A) )
& ! [A,B] :
( ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) )
| ~ sP0_prd(B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B,A))],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ disjoint(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ in(X2,set_intersection2(X1,X0))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f89,plain,
! [X0,X1] :
( ~ sP0_prd(X1,X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f23,f63]) ).
fof(f157,plain,
! [X0,X1] :
( ~ sP0_prd(X1,X0)
| set_intersection2(X0,X1) != empty_set ),
inference(resolution,[status(thm)],[f36,f62]) ).
fof(f158,plain,
! [X0,X1] : ~ sP0_prd(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f157,f89]) ).
fof(f159,plain,
disjoint(sK7_skl,sK8_skl),
inference(backward_subsumption_resolution,[status(thm)],[f58,f158]) ).
fof(f161,plain,
in(sK9_skl,set_intersection2(sK7_skl,sK8_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f57,f158]) ).
fof(f162,plain,
set_intersection2(sK7_skl,sK8_skl) = empty_set,
inference(resolution,[status(thm)],[f159,f35]) ).
fof(f175,plain,
in(sK9_skl,empty_set),
inference(forward_demodulation,[status(thm)],[f162,f161]) ).
fof(f176,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f175,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 05:51:25 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.15/5.40 % Refutation found
% 0.15/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.43 % Elapsed time: 0.049324 seconds
% 0.15/5.43 % CPU time: 0.146096 seconds
% 0.15/5.43 % Total memory used: 83.144 MB
% 0.15/5.43 % Net memory used: 82.843 MB
%------------------------------------------------------------------------------