%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 8 unt; 1 def)
% Number of atoms : 135 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 156 ( 58 ~; 57 |; 25 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f139,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f140,plain,
( ! [A,B] :
( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(miniscoping,[status(thm)],[f139]) ).
fof(f141,plain,
( ! [A,B] :
( ( ( subset(sK2_skl(B,A),A)
| in(sK2_skl(B,A),B) )
& ( ~ subset(sK2_skl(B,A),A)
| ~ in(sK2_skl(B,A),B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f140]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f147,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(NNF_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
( ! [A] :
( ( ! [B] :
( ~ empty(B)
| element(B,A) )
& ! [B] :
( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ! [A] :
( ( ! [B] :
( ~ in(B,A)
| element(B,A) )
& ! [B] :
( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f150,plain,
! [X0,X1] :
( ~ in(X1,X0)
| element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f180,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f181,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f181]) ).
fof(f183,plain,
( ! [A,B] :
( ( ~ in(sK10_skl(B,A),B)
& in(sK10_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B,A))],[f182]) ).
fof(f185,plain,
! [X0,X1] :
( in(sK10_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f186,plain,
! [X0,X1] :
( ~ in(sK10_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f230,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f279,plain,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f280,plain,
( ~ element(sK17_skl,powerset(sK18_skl))
& ! [C] :
( in(C,sK18_skl)
| ~ in(C,sK17_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl)],[f279]) ).
fof(f281,plain,
! [X0] :
( in(X0,sK18_skl)
| ~ in(X0,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
fof(f282,plain,
~ element(sK17_skl,powerset(sK18_skl)),
inference(cnf_transformation,[status(thm)],[f280]) ).
fof(f453,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f515,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f150,f230]) ).
fof(f615,plain,
~ in(sK17_skl,powerset(sK18_skl)),
inference(resolution,[status(thm)],[f515,f282]) ).
fof(f620,plain,
~ subset(sK17_skl,sK18_skl),
inference(resolution,[status(thm)],[f615,f453]) ).
fof(f1028,plain,
! [X0] :
( ~ in(sK10_skl(sK18_skl,X0),sK17_skl)
| subset(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f186,f281]) ).
fof(f1030,plain,
( subset(sK17_skl,sK18_skl)
| subset(sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f1028,f185]) ).
fof(f1031,definition,
( sQ10_spl
<=> subset(sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1032,plain,
( ~ sQ10_spl
| subset(sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f1031]) ).
fof(f1034,plain,
sQ10_spl,
inference(split_clause,[status(thm)],[f1030,f1031]) ).
fof(f1035,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1032,f620]) ).
fof(f1036,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f1035]) ).
fof(f1037,plain,
$false,
inference(sat_refutation,[status(thm)],[f1034,f1036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:55:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.47 % Elapsed time: 0.100323 seconds
% 0.13/0.47 % CPU time: 0.435525 seconds
% 0.13/0.47 % Total memory used: 77.982 MB
% 0.13/0.47 % Net memory used: 77.508 MB
%------------------------------------------------------------------------------