%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET800+4 : 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 02:10:38 PM UTC 2026
% Result : Theorem 0.10s 0.61s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 166 ( 53 ~; 48 |; 50 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 119 ( 107 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( ! [M] :
( ( lower_bound(M,R,X)
& member(M,E) )
=> apply(R,M,A) )
& lower_bound(A,R,X)
& member(A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M2,X2,R,E)
& greatest_lower_bound(M1,X1,R,E) )
=> apply(R,M2,M1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M2,X2,R,E)
& greatest_lower_bound(M1,X1,R,E) )
=> apply(R,M2,M1) ) ) ),
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(f160,plain,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f161,plain,
! [A,X,R,E] :
( ( ? [M] :
( ~ apply(R,M,A)
& lower_bound(M,R,X)
& member(M,E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X)
| greatest_lower_bound(A,X,R,E) )
& ( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
( ! [A,X,R,E] :
( ? [M] :
( ~ apply(R,M,A)
& lower_bound(M,R,X)
& member(M,E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X)
| greatest_lower_bound(A,X,R,E) )
& ! [A,X,R,E] :
( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f163,plain,
( ! [A,X,R,E] :
( ( ~ apply(R,sK15_skl(E,R,X,A),A)
& lower_bound(sK15_skl(E,R,X,A),R,X)
& member(sK15_skl(E,R,X,A),E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X)
| greatest_lower_bound(A,X,R,E) )
& ! [A,X,R,E] :
( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(M,sK15_skl(E,R,X,A))],[f162]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( lower_bound(X0,X2,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f170,plain,
? [R,E] :
( ? [X1,X2] :
( ? [M1,M2] :
( ~ apply(R,M2,M1)
& greatest_lower_bound(M2,X2,R,E)
& greatest_lower_bound(M1,X1,R,E) )
& subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f171,plain,
( ~ apply(sK16_skl,sK21_skl,sK20_skl)
& greatest_lower_bound(sK21_skl,sK19_skl,sK16_skl,sK17_skl)
& greatest_lower_bound(sK20_skl,sK18_skl,sK16_skl,sK17_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,sK21_skl]),skolemize(R,sK16_skl),skolemize(E,sK17_skl),skolemize(X1,sK18_skl),skolemize(X2,sK19_skl),skolemize(M1,sK20_skl),skolemize(M2,sK21_skl)],[f170]) ).
fof(f175,plain,
subset(sK18_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
greatest_lower_bound(sK20_skl,sK18_skl,sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f177,plain,
greatest_lower_bound(sK21_skl,sK19_skl,sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f178,plain,
~ apply(sK16_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f201,plain,
member(sK20_skl,sK18_skl),
inference(resolution,[status(thm)],[f164,f176]) ).
fof(f202,plain,
lower_bound(sK21_skl,sK16_skl,sK19_skl),
inference(resolution,[status(thm)],[f165,f177]) ).
fof(f205,plain,
! [X0] :
( member(X0,sK19_skl)
| ~ member(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f28,f175]) ).
fof(f208,plain,
member(sK20_skl,sK19_skl),
inference(resolution,[status(thm)],[f205,f201]) ).
fof(f545,plain,
! [X0] :
( apply(sK16_skl,sK21_skl,X0)
| ~ member(X0,sK19_skl) ),
inference(resolution,[status(thm)],[f113,f202]) ).
fof(f596,plain,
~ member(sK20_skl,sK19_skl),
inference(resolution,[status(thm)],[f545,f178]) ).
fof(f599,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f596,f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET800+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n026.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 05:41:38 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.59 % Drodi V4.1.1
% 0.10/0.61 % Refutation found
% 0.10/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.64 % Elapsed time: 0.057534 seconds
% 0.14/0.64 % CPU time: 0.195690 seconds
% 0.14/0.64 % Total memory used: 80.014 MB
% 0.14/0.64 % Net memory used: 79.773 MB
%------------------------------------------------------------------------------