TSTP Solution File: SEU173+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:41:21 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 5 unt; 0 def)
% Number of atoms : 142 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 165 ( 62 ~; 61 |; 26 &)
% ( 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 : 88 ( 82 !; 6 ?)
% 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)
<=> in(B,A) ) )
& ( empty(A)
=> ( element(B,A)
<=> empty(B) ) ) ),
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(f11,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f19,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [A,B] :
( ( B != powerset(A)
| ! [C] :
( ( ~ in(C,B)
| subset(C,A) )
& ( in(C,B)
| ~ subset(C,A) ) ) )
& ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f24,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f25,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ( ( ~ in(sk0_0(B,A),B)
| ~ subset(sk0_0(B,A),A) )
& ( in(sk0_0(B,A),B)
| subset(sk0_0(B,A),A) ) ) ) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f27,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| in(X2,X0)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f30,plain,
! [A,B] :
( ( empty(A)
| ( element(B,A)
<=> in(B,A) ) )
& ( ~ empty(A)
| ( element(B,A)
<=> empty(B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f31,plain,
! [A,B] :
( ( empty(A)
| ( ( ~ element(B,A)
| in(B,A) )
& ( element(B,A)
| ~ in(B,A) ) ) )
& ( ~ empty(A)
| ( ( ~ element(B,A)
| empty(B) )
& ( element(B,A)
| ~ empty(B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( ! [A] :
( empty(A)
| ( ! [B] :
( ~ element(B,A)
| in(B,A) )
& ! [B] :
( element(B,A)
| ~ in(B,A) ) ) )
& ! [A] :
( ~ empty(A)
| ( ! [B] :
( ~ element(B,A)
| empty(B) )
& ! [B] :
( element(B,A)
| ~ empty(B) ) ) ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( empty(X0)
| element(X1,X0)
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f37,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f38,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_1(B,A),A)
& ~ in(sk0_1(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f48,plain,
? [A,B] :
( ! [C] :
( ~ in(C,A)
| in(C,B) )
& ~ element(A,powerset(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f49,plain,
( ! [C] :
( ~ in(C,sk0_3)
| in(C,sk0_4) )
& ~ element(sk0_3,powerset(sk0_4)) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ in(X0,sk0_3)
| in(X0,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
~ element(sk0_3,powerset(sk0_4)),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f67,plain,
! [A,B] :
( ~ in(A,B)
| ~ empty(B) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f68,plain,
! [B] :
( ! [A] : ~ in(A,B)
| ~ empty(B) ),
inference(miniscoping,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f74,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f27]) ).
fof(f95,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f69]) ).
fof(f96,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f95,f74]) ).
fof(f97,plain,
~ subset(sk0_3,sk0_4),
inference(resolution,[status(thm)],[f96,f51]) ).
fof(f126,plain,
! [X0] :
( subset(sk0_3,X0)
| in(sk0_1(X0,sk0_3),sk0_4) ),
inference(resolution,[status(thm)],[f42,f50]) ).
fof(f140,plain,
( spl0_6
<=> subset(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f141,plain,
( subset(sk0_3,sk0_4)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,sk0_4) ),
inference(resolution,[status(thm)],[f126,f43]) ).
fof(f144,plain,
spl0_6,
inference(split_clause,[status(thm)],[f143,f140]) ).
fof(f147,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f97]) ).
fof(f148,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
$false,
inference(sat_refutation,[status(thm)],[f144,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU173+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 19:50:25 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.11/0.35 % Refutation found
% 0.11/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37 % Elapsed time: 0.027924 seconds
% 0.16/0.37 % CPU time: 0.057639 seconds
% 0.16/0.37 % Total memory used: 16.418 MB
% 0.16/0.37 % Net memory used: 16.308 MB
%------------------------------------------------------------------------------