%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 7 unt; 2 def)
% Number of atoms : 129 ( 9 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 147 ( 56 ~; 56 |; 24 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 83 ( 72 !; 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(f7,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),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(f33,plain,
? [A,B] :
( ~ subset(union(A),B)
& ! [C] :
( subset(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
( ~ subset(union(sK6_skl),sK7_skl)
& ! [C] :
( subset(C,sK7_skl)
| ~ in(C,sK6_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f33]) ).
fof(f35,plain,
! [X0] :
( subset(X0,sK7_skl)
| ~ in(X0,sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
~ subset(union(sK6_skl),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(f40,plain,
in(sK0_skl(sK7_skl,union(sK6_skl)),union(sK6_skl)),
inference(resolution,[status(thm)],[f16,f36]) ).
fof(f63,definition,
( sQ2_spl
<=> in(sK0_skl(sK7_skl,union(sK6_skl)),union(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ2_spl
| ~ in(sK0_skl(sK7_skl,union(sK6_skl)),union(sK6_skl)) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f68,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ subset(sK1_skl(X0,union(X1),X1),X2)
| ~ in(X0,union(X1)) ),
inference(resolution,[status(thm)],[f37,f15]) ).
fof(f70,plain,
in(sK1_skl(sK0_skl(sK7_skl,union(sK6_skl)),union(sK6_skl),sK6_skl),sK6_skl),
inference(resolution,[status(thm)],[f38,f40]) ).
fof(f82,plain,
subset(sK1_skl(sK0_skl(sK7_skl,union(sK6_skl)),union(sK6_skl),sK6_skl),sK7_skl),
inference(resolution,[status(thm)],[f70,f35]) ).
fof(f86,plain,
( in(sK0_skl(sK7_skl,union(sK6_skl)),sK7_skl)
| ~ in(sK0_skl(sK7_skl,union(sK6_skl)),union(sK6_skl)) ),
inference(resolution,[status(thm)],[f82,f68]) ).
fof(f87,definition,
( sQ3_spl
<=> in(sK0_skl(sK7_skl,union(sK6_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ3_spl
| in(sK0_skl(sK7_skl,union(sK6_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f86,f63,f87]) ).
fof(f91,plain,
( ~ sQ3_spl
| subset(union(sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f88,f17]) ).
fof(f95,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f36]) ).
fof(f96,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f40]) ).
fof(f98,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f99,plain,
$false,
inference(sat_refutation,[status(thm)],[f90,f96,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:45:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.067381 seconds
% 0.13/0.43 % CPU time: 0.213726 seconds
% 0.13/0.43 % Total memory used: 66.068 MB
% 0.13/0.43 % Net memory used: 65.640 MB
%------------------------------------------------------------------------------