%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET942+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 02:11:01 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 5 unt; 1 def)
% Number of atoms : 130 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 154 ( 61 ~; 61 |; 24 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 92 ( 81 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,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)],[f11]) ).
fof(f13,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)],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
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) )
& ( ! [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(f19,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)],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( in(X2,sK1_skl(X2,X0,X1))
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,X0,X1),X1)
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f33,plain,
? [A,B] :
( ~ subset(union(A),union(B))
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
( ~ subset(union(sK6_skl),union(sK7_skl))
& subset(sK6_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f33]) ).
fof(f35,plain,
subset(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
~ subset(union(sK6_skl),union(sK7_skl)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( in(X0,sK1_skl(X0,union(X1),X1))
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( in(sK1_skl(X0,union(X1),X1),X1)
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f40,plain,
! [X0] :
( in(X0,sK7_skl)
| ~ in(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f15,f35]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(sK0_skl(union(X1),X0),X2)
| subset(X0,union(X1)) ),
inference(resolution,[status(thm)],[f17,f39]) ).
fof(f57,plain,
! [X0] :
( in(sK1_skl(X0,union(sK6_skl),sK6_skl),sK7_skl)
| ~ in(X0,union(sK6_skl)) ),
inference(resolution,[status(thm)],[f38,f40]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(union(X1),X0),union(X2))
| ~ in(sK1_skl(sK0_skl(union(X1),X0),union(X2),X2),X1)
| subset(X0,union(X1)) ),
inference(resolution,[status(thm)],[f47,f37]) ).
fof(f137,plain,
! [X0] :
( ~ in(sK0_skl(union(sK7_skl),X0),union(sK6_skl))
| ~ in(sK0_skl(union(sK7_skl),X0),union(sK6_skl))
| subset(X0,union(sK7_skl)) ),
inference(resolution,[status(thm)],[f72,f57]) ).
fof(f141,plain,
! [X0] :
( ~ in(sK0_skl(union(sK7_skl),X0),union(sK6_skl))
| subset(X0,union(sK7_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f137]) ).
fof(f150,plain,
( subset(union(sK6_skl),union(sK7_skl))
| subset(union(sK6_skl),union(sK7_skl)) ),
inference(resolution,[status(thm)],[f141,f16]) ).
fof(f153,definition,
( sQ4_spl
<=> subset(union(sK6_skl),union(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ4_spl
| subset(union(sK6_skl),union(sK7_skl)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
sQ4_spl,
inference(split_clause,[status(thm)],[f150,f153]) ).
fof(f161,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f36]) ).
fof(f162,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET942+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:47:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.077872 seconds
% 0.13/0.43 % CPU time: 0.367799 seconds
% 0.13/0.43 % Total memory used: 84.199 MB
% 0.13/0.43 % Net memory used: 82.854 MB
%------------------------------------------------------------------------------