%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU172+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:19:32 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 79 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 91 ( 33 ~; 29 |; 24 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f204,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f205,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f204]) ).
fof(f206,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK15_skl(C,B,A),B)
& in(sK15_skl(C,B,A),A) )
| in(sK15_skl(C,B,A),C) )
& ( in(sK15_skl(C,B,A),B)
| ~ in(sK15_skl(C,B,A),A)
| ~ in(sK15_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(D,sK15_skl(C,B,A))],[f205]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f213,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f214,plain,
! [X0,X1] :
( subset_complement(X1,X0) = set_difference(X1,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f389,plain,
? [A,B,C] :
( in(B,C)
& in(B,subset_complement(A,C))
& element(C,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f390,plain,
? [A,C] :
( ? [B] :
( in(B,C)
& in(B,subset_complement(A,C)) )
& element(C,powerset(A)) ),
inference(miniscoping,[status(thm)],[f389]) ).
fof(f391,plain,
( in(sK27_skl,sK26_skl)
& in(sK27_skl,subset_complement(sK25_skl,sK26_skl))
& element(sK26_skl,powerset(sK25_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl,sK27_skl]),skolemize(A,sK25_skl),skolemize(C,sK26_skl),skolemize(B,sK27_skl)],[f390]) ).
fof(f392,plain,
element(sK26_skl,powerset(sK25_skl)),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f393,plain,
in(sK27_skl,subset_complement(sK25_skl,sK26_skl)),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f394,plain,
in(sK27_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f208]) ).
fof(f516,plain,
subset_complement(sK25_skl,sK26_skl) = set_difference(sK25_skl,sK26_skl),
inference(resolution,[status(thm)],[f214,f392]) ).
fof(f556,plain,
in(sK27_skl,set_difference(sK25_skl,sK26_skl)),
inference(backward_demodulation,[status(thm)],[f516,f393]) ).
fof(f1550,plain,
~ in(sK27_skl,sK26_skl),
inference(resolution,[status(thm)],[f467,f556]) ).
fof(f1556,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1550,f394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:54:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.082157 seconds
% 0.14/0.44 % CPU time: 0.360818 seconds
% 0.14/0.44 % Total memory used: 109.216 MB
% 0.14/0.44 % Net memory used: 108.653 MB
%------------------------------------------------------------------------------