%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:10:38 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 6 unt; 1 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 107 ( 35 ~; 33 |; 26 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 73 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f109,plain,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( apply(R,M,X)
| ~ member(X,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f110,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
( ! [R,E,M] :
( ( ~ apply(R,M,sK9_skl(M,E,R))
& member(sK9_skl(M,E,R),E) )
| lower_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X,sK9_skl(M,E,R))],[f111]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( member(sK9_skl(X0,X2,X1),X2)
| lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ apply(X1,X0,sK9_skl(X0,X2,X1))
| lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f170,plain,
? [R,E] :
( ? [X,Y] :
( ? [M] :
( ~ lower_bound(M,R,X)
& lower_bound(M,R,Y) )
& subset(X,Y)
& subset(Y,E)
& subset(X,E) )
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f171,plain,
( ~ lower_bound(sK20_skl,sK16_skl,sK18_skl)
& lower_bound(sK20_skl,sK16_skl,sK19_skl)
& subset(sK18_skl,sK19_skl)
& subset(sK19_skl,sK17_skl)
& subset(sK18_skl,sK17_skl)
& order(sK16_skl,sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl]),skolemize(R,sK16_skl),skolemize(E,sK17_skl),skolemize(X,sK18_skl),skolemize(Y,sK19_skl),skolemize(M,sK20_skl)],[f170]) ).
fof(f175,plain,
subset(sK18_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
lower_bound(sK20_skl,sK16_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f177,plain,
~ lower_bound(sK20_skl,sK16_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f199,plain,
! [X0] :
( member(X0,sK19_skl)
| ~ member(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f28,f175]) ).
fof(f202,plain,
! [X0] :
( apply(sK16_skl,sK20_skl,X0)
| ~ member(X0,sK19_skl) ),
inference(resolution,[status(thm)],[f113,f176]) ).
fof(f522,plain,
! [X0,X1] :
( member(sK9_skl(X0,sK18_skl,X1),sK19_skl)
| lower_bound(X0,X1,sK18_skl) ),
inference(resolution,[status(thm)],[f114,f199]) ).
fof(f554,plain,
! [X0] :
( ~ member(sK9_skl(sK20_skl,X0,sK16_skl),sK19_skl)
| lower_bound(sK20_skl,sK16_skl,X0) ),
inference(resolution,[status(thm)],[f115,f202]) ).
fof(f581,plain,
( lower_bound(sK20_skl,sK16_skl,sK18_skl)
| lower_bound(sK20_skl,sK16_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f554,f522]) ).
fof(f584,definition,
( sQ15_spl
<=> lower_bound(sK20_skl,sK16_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( ~ sQ15_spl
| lower_bound(sK20_skl,sK16_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,plain,
sQ15_spl,
inference(split_clause,[status(thm)],[f581,f584]) ).
fof(f596,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f177]) ).
fof(f597,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f598,plain,
$false,
inference(sat_refutation,[status(thm)],[f587,f597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:38:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.067235 seconds
% 0.12/0.44 % CPU time: 0.266834 seconds
% 0.12/0.44 % Total memory used: 85.576 MB
% 0.12/0.44 % Net memory used: 85.197 MB
%------------------------------------------------------------------------------