%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:19:31 PM UTC 2026
% Result : Theorem 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 8 unt; 2 def)
% Number of atoms : 143 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 162 ( 59 ~; 59 |; 27 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 68 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f22,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)],[f2]) ).
fof(f23,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)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ( ( subset(sK0_skl(B,A),A)
| in(sK0_skl(B,A),B) )
& ( ~ subset(sK0_skl(B,A),A)
| ~ in(sK0_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,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f29,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f30,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)],[f29]) ).
fof(f31,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)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f37,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)],[f36]) ).
fof(f38,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)],[f37]) ).
fof(f39,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_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,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f45,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f47,plain,
? [A,B] :
( ? [C] :
( ~ in(C,A)
& in(C,B) )
& element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f48,plain,
( ~ in(sK5_skl,sK3_skl)
& in(sK5_skl,sK4_skl)
& element(sK4_skl,powerset(sK3_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f47]) ).
fof(f49,plain,
element(sK4_skl,powerset(sK3_skl)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
in(sK5_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
~ in(sK5_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f70,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f25]) ).
fof(f73,plain,
( in(sK4_skl,powerset(sK3_skl))
| empty(powerset(sK3_skl)) ),
inference(resolution,[status(thm)],[f32,f49]) ).
fof(f74,definition,
( sQ0_spl
<=> empty(powerset(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ0_spl
| empty(powerset(sK3_skl)) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> in(sK4_skl,powerset(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ1_spl
| in(sK4_skl,powerset(sK3_skl)) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f74,f77]) ).
fof(f81,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f45]) ).
fof(f82,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f99,plain,
( ~ sQ1_spl
| subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f78,f70]) ).
fof(f143,plain,
! [X0] :
( ~ sQ1_spl
| in(X0,sK3_skl)
| ~ in(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f40,f99]) ).
fof(f153,plain,
( ~ sQ1_spl
| in(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f143,f50]) ).
fof(f161,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f51]) ).
fof(f162,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f82,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n002.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:57:17 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.45 % Refutation found
% 0.18/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.51 % Elapsed time: 0.057585 seconds
% 0.18/0.51 % CPU time: 0.076461 seconds
% 0.18/0.51 % Total memory used: 2.571 MB
% 0.18/0.51 % Net memory used: 2.566 MB
%------------------------------------------------------------------------------