TSTP Solution File: NUM386+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 : Wed May 31 12:29:00 EDT 2023
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 108 ( 20 unt; 0 def)
% Number of atoms : 299 ( 49 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 298 ( 107 ~; 127 |; 42 &)
% ( 18 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 105 (; 94 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( ( relation(A)
& empty(A)
& function(A) )
=> ( relation(A)
& function(A)
& one_to_one(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A,B] :
( in(A,succ(B))
<=> ( in(A,B)
| A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A,B] :
( in(A,succ(B))
<=> ( in(A,B)
| A = B ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f38,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f39,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [A] :
( ~ empty(A)
| relation(A) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f41,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [A] :
( ~ relation(A)
| ~ empty(A)
| ~ function(A)
| ( relation(A)
& function(A)
& one_to_one(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f45,plain,
! [X0] :
( ~ relation(X0)
| ~ empty(X0)
| ~ function(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f48,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f49,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f55,plain,
! [A,B,C] :
( ( C != set_union2(A,B)
| ! [D] :
( ( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f56,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(miniscoping,[status(esa)],[f55]) ).
fof(f57,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( ~ in(sk0_1(C,B,A),A)
& ~ in(sk0_1(C,B,A),B) ) )
& ( in(sk0_1(C,B,A),C)
| in(sk0_1(C,B,A),A)
| in(sk0_1(C,B,A),B) ) ) ) ),
inference(skolemization,[status(esa)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| in(X3,X0)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f66,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f86,plain,
( empty(sk0_4)
& relation(sk0_4) ),
inference(skolemization,[status(esa)],[f19]) ).
fof(f87,plain,
empty(sk0_4),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f89,plain,
empty(sk0_5),
inference(skolemization,[status(esa)],[f20]) ).
fof(f90,plain,
empty(sk0_5),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f91,plain,
( relation(sk0_6)
& empty(sk0_6)
& function(sk0_6) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f93,plain,
empty(sk0_6),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f94,plain,
function(sk0_6),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f115,plain,
? [A,B] :
( in(A,succ(B))
<~> ( in(A,B)
| A = B ) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f116,plain,
? [A,B] :
( ( in(A,succ(B))
| in(A,B)
| A = B )
& ( ~ in(A,succ(B))
| ( ~ in(A,B)
& A != B ) ) ),
inference(NNF_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
( ( in(sk0_13,succ(sk0_14))
| in(sk0_13,sk0_14)
| sk0_13 = sk0_14 )
& ( ~ in(sk0_13,succ(sk0_14))
| ( ~ in(sk0_13,sk0_14)
& sk0_13 != sk0_14 ) ) ),
inference(skolemization,[status(esa)],[f116]) ).
fof(f118,plain,
( in(sk0_13,succ(sk0_14))
| in(sk0_13,sk0_14)
| sk0_13 = sk0_14 ),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f119,plain,
( ~ in(sk0_13,succ(sk0_14))
| ~ in(sk0_13,sk0_14) ),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f120,plain,
( ~ in(sk0_13,succ(sk0_14))
| sk0_13 != sk0_14 ),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f134,plain,
( spl0_0
<=> in(sk0_13,succ(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( in(sk0_13,succ(sk0_14))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f136,plain,
( ~ in(sk0_13,succ(sk0_14))
| spl0_0 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( spl0_1
<=> in(sk0_13,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f138,plain,
( in(sk0_13,sk0_14)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( spl0_2
<=> sk0_13 = sk0_14 ),
introduced(split_symbol_definition) ).
fof(f141,plain,
( sk0_13 = sk0_14
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f118,f134,f137,f140]) ).
fof(f144,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f119,f134,f137]) ).
fof(f145,plain,
( ~ spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f120,f134,f140]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f147,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f52]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f58]) ).
fof(f149,plain,
! [X0,X1,X2] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f59]) ).
fof(f150,plain,
! [X0,X1,X2] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f60]) ).
fof(f153,plain,
function(sk0_5),
inference(resolution,[status(thm)],[f39,f90]) ).
fof(f154,plain,
function(sk0_4),
inference(resolution,[status(thm)],[f39,f87]) ).
fof(f155,plain,
function(empty_set),
inference(resolution,[status(thm)],[f39,f66]) ).
fof(f166,plain,
! [X0] :
( ~ empty(X0)
| ~ function(X0)
| one_to_one(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f41]) ).
fof(f167,plain,
( spl0_3
<=> empty(empty_set) ),
introduced(split_symbol_definition) ).
fof(f169,plain,
( ~ empty(empty_set)
| spl0_3 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( spl0_4
<=> one_to_one(empty_set) ),
introduced(split_symbol_definition) ).
fof(f173,plain,
( ~ empty(empty_set)
| one_to_one(empty_set) ),
inference(resolution,[status(thm)],[f166,f155]) ).
fof(f174,plain,
( ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f173,f167,f170]) ).
fof(f175,plain,
( spl0_5
<=> empty(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f177,plain,
( ~ empty(sk0_4)
| spl0_5 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( spl0_6
<=> one_to_one(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f181,plain,
( ~ empty(sk0_4)
| one_to_one(sk0_4) ),
inference(resolution,[status(thm)],[f166,f154]) ).
fof(f182,plain,
( ~ spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f181,f175,f178]) ).
fof(f183,plain,
( spl0_7
<=> empty(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f185,plain,
( ~ empty(sk0_5)
| spl0_7 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( spl0_8
<=> one_to_one(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f189,plain,
( ~ empty(sk0_5)
| one_to_one(sk0_5) ),
inference(resolution,[status(thm)],[f166,f153]) ).
fof(f190,plain,
( ~ spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f189,f183,f186]) ).
fof(f215,plain,
( spl0_15
<=> empty(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f217,plain,
( ~ empty(sk0_6)
| spl0_15 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( spl0_16
<=> one_to_one(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f221,plain,
( ~ empty(sk0_6)
| one_to_one(sk0_6) ),
inference(resolution,[status(thm)],[f166,f94]) ).
fof(f222,plain,
( ~ spl0_15
| spl0_16 ),
inference(split_clause,[status(thm)],[f221,f215,f218]) ).
fof(f231,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f93]) ).
fof(f232,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f90]) ).
fof(f234,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f235,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f87]) ).
fof(f236,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f66]) ).
fof(f238,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f258,plain,
! [X0] :
( in(sk0_13,set_union2(sk0_14,X0))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f149,f138]) ).
fof(f264,plain,
( in(sk0_13,succ(sk0_14))
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f47,f258]) ).
fof(f265,plain,
( $false
| spl0_0
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f136]) ).
fof(f266,plain,
( spl0_0
| ~ spl0_1 ),
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f467,plain,
! [X0,X1] : in(X0,set_union2(X1,singleton(X0))),
inference(resolution,[status(thm)],[f150,f147]) ).
fof(f473,plain,
! [X0] : in(X0,succ(X0)),
inference(paramodulation,[status(thm)],[f47,f467]) ).
fof(f512,plain,
! [X0,X1] :
( ~ in(X0,succ(X1))
| in(X0,X1)
| in(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f47,f148]) ).
fof(f527,plain,
( spl0_26
<=> in(sk0_13,singleton(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f528,plain,
( in(sk0_13,singleton(sk0_14))
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( in(sk0_13,sk0_14)
| in(sk0_13,singleton(sk0_14))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f512,f135]) ).
fof(f531,plain,
( spl0_1
| spl0_26
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f530,f137,f527,f134]) ).
fof(f560,plain,
( ~ in(sk0_13,succ(sk0_13))
| ~ spl0_2
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f141,f136]) ).
fof(f561,plain,
( $false
| ~ spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f473]) ).
fof(f562,plain,
( ~ spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f563,plain,
( sk0_13 = sk0_14
| ~ spl0_26 ),
inference(resolution,[status(thm)],[f528,f146]) ).
fof(f564,plain,
( spl0_2
| ~ spl0_26 ),
inference(split_clause,[status(thm)],[f563,f140,f527]) ).
fof(f570,plain,
$false,
inference(sat_refutation,[status(thm)],[f143,f144,f145,f174,f182,f190,f222,f232,f234,f236,f238,f266,f531,f562,f564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:55:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.042574 seconds
% 0.12/0.39 % CPU time: 0.187695 seconds
% 0.12/0.39 % Memory used: 25.120 MB
%------------------------------------------------------------------------------