%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU155+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:19:26 PM UTC 2026
% Result : Theorem 0.22s 0.46s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 99 ( 8 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 117 ( 42 ~; 44 |; 24 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 71 ( 60 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f10,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,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)],[f3]) ).
fof(f18,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)],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,plain,
? [A,B] :
( ~ subset(A,union(B))
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
( ~ subset(sK4_skl,union(sK5_skl))
& in(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f26]) ).
fof(f28,plain,
in(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
~ subset(sK4_skl,union(sK5_skl)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f37,plain,
! [X0] :
( ~ in(X0,sK4_skl)
| in(X0,union(sK5_skl)) ),
inference(resolution,[status(thm)],[f34,f28]) ).
fof(f38,plain,
! [X0] :
( in(sK0_skl(X0,sK4_skl),union(sK5_skl))
| subset(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f15,f37]) ).
fof(f66,plain,
( subset(sK4_skl,union(sK5_skl))
| subset(sK4_skl,union(sK5_skl)) ),
inference(resolution,[status(thm)],[f38,f16]) ).
fof(f71,plain,
subset(sK4_skl,union(sK5_skl)),
inference(duplicate_literals_removal,[status(thm)],[f66]) ).
fof(f72,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f71,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU155+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:54:32 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.22/0.46 % Refutation found
% 0.22/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.48 % Elapsed time: 0.032252 seconds
% 0.22/0.48 % CPU time: 0.071220 seconds
% 0.22/0.48 % Total memory used: 7.589 MB
% 0.22/0.48 % Net memory used: 7.558 MB
%------------------------------------------------------------------------------