%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET704+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 : n016.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 02:10:29 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 78 ( 29 ~; 27 |; 14 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 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 : 59 ( 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,X] :
( member(X,A)
=> subset(product(A),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(product(A),X) ),
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(f61,plain,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(X,Y)
| ~ member(Y,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f62,plain,
! [X,A] :
( ( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( ! [X,A] :
( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ! [X,A] :
( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [X,A] :
( ( ~ member(X,sK2_skl(A,X))
& member(sK2_skl(A,X),A) )
| member(X,product(A)) )
& ! [X,A] :
( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(A,X))],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X2,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
? [A,X] :
( ~ subset(product(A),X)
& member(X,A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
( ~ subset(product(sK3_skl),sK4_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(product(sK3_skl),sK4_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [X0,X1,X2] :
( member(sK0_skl(X1,product(X0)),X2)
| ~ member(X2,X0)
| subset(product(X0),X1) ),
inference(resolution,[status(thm)],[f19,f65]) ).
fof(f77,plain,
! [X0] :
( member(sK0_skl(sK4_skl,product(sK3_skl)),X0)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f76,f71]) ).
fof(f99,plain,
member(sK0_skl(sK4_skl,product(sK3_skl)),sK4_skl),
inference(resolution,[status(thm)],[f77,f70]) ).
fof(f100,plain,
subset(product(sK3_skl),sK4_skl),
inference(resolution,[status(thm)],[f99,f20]) ).
fof(f101,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f100,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET704+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n016.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Mon Sep 21 05:38:23 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.46 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.53 % Elapsed time: 0.084266 seconds
% 0.15/0.53 % CPU time: 0.092187 seconds
% 0.15/0.53 % Total memory used: 2.547 MB
% 0.15/0.53 % Net memory used: 2.544 MB
%------------------------------------------------------------------------------