TPTP Problem File: SYO844+1.p
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%------------------------------------------------------------------------------
% File : SYO844+1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Syntactic
% Problem : ProofGold problem AbstrHF_55_pos_fof
% Version : Especial.
% English :
% Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% Source : [Urb20]
% Names : AbstrHF_55_pos_fof.p [Urb20]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0
% Syntax : Number of formulae : 84 ( 62 unt; 0 def)
% Number of atoms : 127 ( 14 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 75 ( 32 ~; 3 |; 1 &)
% ( 2 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 11 usr; 0 prp; 1-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments : See https://proofgold.org
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [X24,X25] :
( ain(X25,apow(X24))
<=> asubq(X25,X24) ) ).
fof(ax2,axiom,
! [X24,X25,X26] :
( ain(X26,asm(X24,X25))
<=> ( ain(X26,X24)
& ~ ain(X26,X25) ) ) ).
fof(ax3,axiom,
! [X24,X25] :
( ain(X25,apow(X24))
=> asubq(X25,X24) ) ).
fof(ax4,axiom,
! [X24,X25,X26] :
( ain(X26,aun(X24,X25))
=> ( ain(X26,X24)
| ain(X26,X25) ) ) ).
fof(ax5,axiom,
! [X24,X25,X26] :
( ain(X26,asm(X24,X25))
=> ain(X26,X24) ) ).
fof(ax6,axiom,
! [X24,X25,X26] :
( asubq(X24,X26)
=> ( asubq(X25,X26)
=> asubq(aun(X24,X25),X26) ) ) ).
fof(ax7,axiom,
! [X24,X25,X26] :
( ain(X26,X25)
=> ~ ain(X26,asm(X24,X25)) ) ).
fof(ax8,axiom,
! [X24,X25] :
( adisjoint(X24,X25)
=> ( aal2(X24)
=> ( aal4(X25)
=> aal6(aun(X24,X25)) ) ) ) ).
fof(ax9,axiom,
! [X24,X25] :
( adisjoint(X24,X25)
=> ( aal4(X24)
=> ( aal2(X25)
=> aal6(aun(X24,X25)) ) ) ) ).
fof(ax10,axiom,
! [X24,X25] :
( aal3(aun(X24,X25))
=> ( aal2(X24)
| aal2(X25) ) ) ).
fof(ax11,axiom,
! [X24,X25,X26] :
( asubq(X26,aun(X24,X25))
=> ! [X27] :
( ain(X27,X25)
=> ( ~ ain(X27,X26)
=> ( aal4(X26)
=> ( aal3(X24)
| aal3(X25) ) ) ) ) ) ).
fof(ax12,axiom,
~ asubq(a2,a1) ).
fof(ax13,axiom,
! [X24] :
( ain(a0,X24)
=> asubq(a1,X24) ) ).
fof(ax14,axiom,
ain(a0,apow(a2)) ).
fof(ax15,axiom,
~ ain(a1,apow(asing(a1))) ).
fof(ax16,axiom,
~ ain(asing(a1),asing(a2)) ).
fof(ax17,axiom,
asubq(asing(a1),aun(asing(a1),asing(asing(a1)))) ).
fof(ax18,axiom,
~ ain(asm(a3,asing(a1)),asing(asing(a1))) ).
fof(ax19,axiom,
asubq(asing(asing(a1)),aun(asing(a1),asing(asing(a1)))) ).
fof(ax20,axiom,
~ ain(asing(a1),asm(apow(a2),apow(asing(a1)))) ).
fof(ax21,axiom,
! [X24] :
( asubq(X24,apow(asing(a1)))
=> ( ain(asing(a1),X24)
=> ( ain(a0,X24)
=> X24 = apow(asing(a1)) ) ) ) ).
fof(ax22,axiom,
apow(asing(a1)) != a3 ).
fof(ax23,axiom,
~ ain(a3,asm(apow(a2),asing(a1))) ).
fof(ax24,axiom,
asm(apow(a2),a2) != apow(a2) ).
fof(ax25,axiom,
ain(asing(a1),aun(asing(asing(a1)),asing(asing(asing(a1))))) ).
fof(ax26,axiom,
ain(asing(asing(a1)),asm(apow(aun(asing(a1),asing(asing(a1)))),asing(aun(asing(a1),asing(asing(a1)))))) ).
fof(ax27,axiom,
~ ain(asing(a1),aun(asm(apow(a2),apow(asing(a1))),apow(asing(asing(a1))))) ).
fof(ax28,axiom,
ain(a0,asm(a4,asing(a1))) ).
fof(ax29,axiom,
~ ain(apow(a2),aun(apow(a2),asing(asing(a2)))) ).
fof(ax30,axiom,
ain(asing(a2),aun(asing(a2),apow(asing(a2)))) ).
fof(ax31,axiom,
ain(a0,aun(a1,asing(a3))) ).
fof(ax32,axiom,
~ ain(asm(apow(a2),a2),a4) ).
fof(ax33,axiom,
~ ain(a0,aun(asing(asing(a1)),asing(a3))) ).
fof(ax34,axiom,
ain(a2,asm(a4,apow(asing(a2)))) ).
fof(ax35,axiom,
ain(a3,aun(apow(asing(a2)),asing(a3))) ).
fof(ax36,axiom,
ain(a1,asm(aun(asing(asing(a2)),a4),asm(apow(a2),asing(a1)))) ).
fof(ax37,axiom,
ain(asing(a2),asm(aun(asing(asing(a2)),a4),asm(apow(a2),asing(a1)))) ).
fof(ax38,axiom,
ain(a3,aun(asing(asing(a2)),a4)) ).
fof(ax39,axiom,
ain(a2,aun(asing(asing(a2)),a4)) ).
fof(ax40,axiom,
ain(a1,aun(asm(apow(a2),apow(asing(a1))),aun(asing(asing(a2)),asing(apow(a2))))) ).
fof(ax41,axiom,
ain(a1,aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2))))) ).
fof(ax42,axiom,
~ asubq(aun(asm(apow(a2),apow(asing(a1))),apow(asing(asing(a1)))),a3) ).
fof(ax43,axiom,
asubq(a3,aun(a3,asing(apow(asing(a1))))) ).
fof(ax44,axiom,
asubq(a3,aun(a3,asing(apow(a2)))) ).
fof(ax45,axiom,
asubq(asm(apow(a2),apow(asing(a1))),aun(asm(apow(a2),apow(asing(a2))),apow(asing(asing(a1))))) ).
fof(ax46,axiom,
~ asubq(aun(asing(asing(a2)),aun(a4,asing(apow(a2)))),aun(a4,asing(apow(a2)))) ).
fof(ax47,axiom,
asubq(asm(apow(a2),apow(asing(a1))),asm(a3,asing(a0))) ).
fof(ax48,axiom,
! [X24] :
( ain(X24,asm(apow(a2),asing(a2)))
=> ( X24 != asing(a1)
=> ain(X24,a2) ) ) ).
fof(ax49,axiom,
asubq(asm(asm(apow(a2),a2),asing(asing(a1))),asing(a2)) ).
fof(ax50,axiom,
asubq(asm(asm(apow(a2),a2),asing(a2)),asing(asing(a1))) ).
fof(ax51,axiom,
asubq(asm(asm(apow(a2),apow(asing(a2))),asing(a2)),aun(asing(a1),asing(asing(a1)))) ).
fof(ax52,axiom,
asm(apow(a2),asing(asing(a1))) = a3 ).
fof(ax53,axiom,
asm(asm(apow(aun(asing(a1),asing(asing(a1)))),asing(aun(asing(a1),asing(asing(a1))))),asing(a0)) = aun(asing(asing(a1)),asing(asing(asing(a1)))) ).
fof(ax54,axiom,
asm(aun(asm(apow(a2),apow(asing(a2))),apow(asing(asing(a1)))),asing(a2)) = aun(aun(asing(a1),asing(asing(a1))),apow(asing(asing(a1)))) ).
fof(ax55,axiom,
asm(aun(asm(apow(a2),apow(asing(a2))),apow(asing(asing(a1)))),asing(asing(asing(a1)))) = apow(a2) ).
fof(ax56,axiom,
! [X24] :
( ain(X24,asm(a4,a2))
=> ( X24 != a3
=> ain(X24,asing(a2)) ) ) ).
fof(ax57,axiom,
! [X24] :
( ain(X24,asm(a4,asing(a1)))
=> ( X24 != a0
=> ain(X24,asm(a4,a2)) ) ) ).
fof(ax58,axiom,
asm(asm(a4,apow(asing(a2))),asing(a3)) = asm(apow(a2),apow(asing(a1))) ).
fof(ax59,axiom,
asm(a4,asing(a0)) = asm(a4,apow(asing(a2))) ).
fof(ax60,axiom,
asubq(asm(a3,asing(a1)),aun(a4,asing(apow(a2)))) ).
fof(ax61,axiom,
asubq(asm(apow(a2),apow(asing(a1))),a4) ).
fof(ax62,axiom,
! [X24] :
( ain(X24,aun(asing(asing(a1)),aun(asing(asing(a2)),a4)))
=> ( ain(X24,aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))))
=> ~ ain(X24,asing(apow(a2))) ) ) ).
fof(ax63,axiom,
asubq(asm(a3,asing(a1)),aint(aun(asing(asing(a1)),a4),aun(asing(a2),apow(asing(a2))))) ).
fof(ax64,axiom,
aint(aun(asing(asing(a2)),a4),asm(apow(a2),asing(a1))) = asm(a3,asing(a1)) ).
fof(ax65,axiom,
~ aal3(aun(a1,asing(a3))) ).
fof(ax66,axiom,
! [X24] :
( ain(X24,asm(apow(a2),asing(a2)))
=> ~ aal3(asm(asm(apow(a2),asing(a2)),asing(X24))) ) ).
fof(ax67,axiom,
~ aal4(asm(apow(a2),apow(asing(a2)))) ).
fof(ax68,axiom,
~ aal5(apow(a2)) ).
fof(ax69,axiom,
~ aal5(aun(asm(apow(a2),apow(asing(a1))),apow(asing(asing(a1))))) ).
fof(ax70,axiom,
! [X24] :
( aal5(asm(aun(asm(apow(a2),apow(asing(a2))),apow(asing(asing(a1)))),asing(X24)))
=> X24 != a1 ) ).
fof(ax71,axiom,
~ aal6(aun(asing(apow(asing(a1))),a4)) ).
fof(ax72,axiom,
aal4(aun(a3,asing(asm(apow(a2),a2)))) ).
fof(ax73,axiom,
aex3(aun(a2,asing(apow(a2)))) ).
fof(ax74,axiom,
aex3(aun(asing(asing(asing(a1))),aun(a1,asing(apow(a2))))) ).
fof(ax75,axiom,
aex4(aint(aun(apow(a2),asing(asing(a2))),aun(asing(asing(a2)),aun(a4,asing(apow(a2)))))) ).
fof(ax76,axiom,
aex5(aun(asing(apow(asing(a1))),a4)) ).
fof(ax77,axiom,
aex5(aun(a4,asing(asm(apow(a2),a2)))) ).
fof(ax78,axiom,
aex4(asm(aun(a4,asing(apow(a2))),asing(a3))) ).
fof(ax79,axiom,
aex3(asm(aun(asing(asing(a1)),a4),aun(asing(a2),apow(asing(a2))))) ).
fof(ax80,axiom,
! [X24] :
( ain(X24,a4)
=> ( ~ ain(X24,asing(a1))
=> ( ain(X24,aun(aun(asing(a1),asing(asing(a1))),aun(apow(asing(a2)),asing(a3))))
=> ain(X24,aun(apow(asing(a2)),asing(a3))) ) ) ) ).
fof(ax81,axiom,
! [X24] :
( ain(X24,apow(asing(a2)))
=> ( ~ ain(X24,asing(asing(a2)))
=> ain(X24,aun(a3,asing(apow(a2)))) ) ) ).
fof(ax82,axiom,
asubq(asm(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),asing(asing(a2))),aun(a3,asing(apow(a2)))) ).
fof(ax83,axiom,
! [X24] :
( ain(X24,apow(asing(a2)))
=> ~ aal5(asm(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),asing(X24))) ) ).
fof(conj,conjecture,
~ asubq(asm(apow(a2),asing(a2)),aun(asing(a1),asing(asing(a1)))) ).
%------------------------------------------------------------------------------