%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET355+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 : n017.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 02:09:50 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 74 ( 27 ~; 26 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 47 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(X,sum(A)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f55,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
( ! [X,A] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ! [X,A] :
( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
( ! [X,A] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ! [X,A] :
( ( member(X,sK1_skl(A,X))
& member(sK1_skl(A,X),A) )
| ~ member(X,sum(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(A,X))],[f56]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f68,plain,
? [A,X] :
( ~ subset(X,sum(A))
& member(X,A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
( ~ subset(sK4_skl,sum(sK3_skl))
& member(sK4_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(X,sK4_skl)],[f68]) ).
fof(f70,plain,
member(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
~ subset(sK4_skl,sum(sK3_skl)),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,plain,
! [X0] :
( ~ member(X0,sK4_skl)
| member(X0,sum(sK3_skl)) ),
inference(resolution,[status(thm)],[f60,f70]) ).
fof(f76,plain,
! [X0] :
( member(sK0_skl(X0,sK4_skl),sum(sK3_skl))
| subset(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f19,f75]) ).
fof(f85,plain,
( subset(sK4_skl,sum(sK3_skl))
| subset(sK4_skl,sum(sK3_skl)) ),
inference(resolution,[status(thm)],[f20,f76]) ).
fof(f88,plain,
subset(sK4_skl,sum(sK3_skl)),
inference(duplicate_literals_removal,[status(thm)],[f85]) ).
fof(f89,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f88,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:06:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.051634 seconds
% 0.10/0.43 % CPU time: 0.148509 seconds
% 0.10/0.43 % Total memory used: 80.621 MB
% 0.10/0.43 % Net memory used: 80.344 MB
%------------------------------------------------------------------------------