%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:10:35 PM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 23 ~; 19 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 49 !; 8 ?)
% 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,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( apply(R,A,X)
& member(X,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [E,R,A] :
( equivalence(R,E)
=> subset(equivalence_class(A,E,R),E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [E,R,A] :
( equivalence(R,E)
=> subset(equivalence_class(A,E,R),E) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f20,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)],[f19]) ).
fof(f21,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)],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f107,plain,
! [R,E,A,X] :
( ( ~ apply(R,A,X)
| ~ member(X,E)
| member(X,equivalence_class(A,E,R)) )
& ( ( apply(R,A,X)
& member(X,E) )
| ~ member(X,equivalence_class(A,E,R)) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f108,plain,
( ! [R,E,A,X] :
( ~ apply(R,A,X)
| ~ member(X,E)
| member(X,equivalence_class(A,E,R)) )
& ! [R,E,A,X] :
( ( apply(R,A,X)
& member(X,E) )
| ~ member(X,equivalence_class(A,E,R)) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(X0,equivalence_class(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f126,plain,
? [E,R,A] :
( ~ subset(equivalence_class(A,E,R),E)
& equivalence(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f127,plain,
? [E,R] :
( ? [A] : ~ subset(equivalence_class(A,E,R),E)
& equivalence(R,E) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f128,plain,
( ~ subset(equivalence_class(sK16_skl,sK14_skl,sK15_skl),sK14_skl)
& equivalence(sK15_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(E,sK14_skl),skolemize(R,sK15_skl),skolemize(A,sK16_skl)],[f127]) ).
fof(f130,plain,
~ subset(equivalence_class(sK16_skl,sK14_skl,sK15_skl),sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f165,plain,
member(sK0_skl(sK14_skl,equivalence_class(sK16_skl,sK14_skl,sK15_skl)),equivalence_class(sK16_skl,sK14_skl,sK15_skl)),
inference(resolution,[status(thm)],[f24,f130]) ).
fof(f168,plain,
member(sK0_skl(sK14_skl,equivalence_class(sK16_skl,sK14_skl,sK15_skl)),sK14_skl),
inference(resolution,[status(thm)],[f165,f109]) ).
fof(f195,plain,
subset(equivalence_class(sK16_skl,sK14_skl,sK15_skl),sK14_skl),
inference(resolution,[status(thm)],[f168,f25]) ).
fof(f202,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f195,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:38:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.037909 seconds
% 0.11/0.41 % CPU time: 0.071480 seconds
% 0.11/0.41 % Total memory used: 5.250 MB
% 0.11/0.41 % Net memory used: 5.244 MB
%------------------------------------------------------------------------------