TPTP Problem File: GRP806+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : GRP806+1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Group Theory
% Problem : ProofGold problem AIM2_54_pos_th0
% Version : Especial.
% English :
% Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% Source : [Urb20]
% Names : AIM2_54_pos_fof.p [Urb20]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 0 ( 0 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 21 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 171 ( 171 !; 0 ?)
% SPC : FOF_CSA_RFO_PEQ
% Comments : See https://proofgold.org
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fof(id1,axiom,
! [X] : m(X,e) = X ).
fof(id2,axiom,
! [X] : m(e,X) = X ).
fof(b1,axiom,
! [X,Y] : m(X,b(X,Y)) = Y ).
fof(b2,axiom,
! [X,Y] : b(X,m(X,Y)) = Y ).
fof(s1,axiom,
! [X,Y] : m(s(X,Y),Y) = X ).
fof(s2,axiom,
! [X,Y] : s(m(X,Y),Y) = X ).
fof(tdef,axiom,
! [X,U] : t(X,U) = b(X,m(U,X)) ).
fof(i1def,axiom,
! [X,U] : i1(X,U) = m(X,m(U,b(X,e))) ).
fof(j1def,axiom,
! [X,U] : j1(X,U) = m(m(s(e,X),U),X) ).
fof(i2def,axiom,
! [X,U] : i2(X,U) = m(b(X,U),b(b(X,e),e)) ).
fof(j2def,axiom,
! [X,U] : j2(X,U) = m(s(e,s(e,X)),s(U,X)) ).
fof(ldef,axiom,
! [X,Y,U] : l(X,Y,U) = b(m(Y,X),m(Y,m(X,U))) ).
fof(rdef,axiom,
! [X,Y,U] : r(X,Y,U) = s(m(m(U,X),Y),m(X,Y)) ).
fof(ax1,axiom,
! [X14,X15,X16,X17] : r(X14,X15,i2(X16,i2(X14,l(X15,X16,r(X14,X15,i2(X16,i2(X14,l(X15,X16,X17)))))))) = X17 ).
fof(ax2,axiom,
! [X14,X15,X16,X17] : r(X14,X15,i2(X16,j2(X14,r(X15,X16,r(X14,X15,i2(X16,j2(X14,r(X15,X16,r(X14,X15,i2(X16,j2(X14,r(X15,X16,r(X14,X15,i2(X16,j2(X14,r(X15,X16,r(X14,X15,i2(X16,j2(X14,r(X15,X16,X17)))))))))))))))))))) = X17 ).
fof(ax3,axiom,
! [X14,X15,X16,X17] : t(X14,i1(X15,i2(X16,X17))) = i1(X15,i2(X16,t(X14,X17))) ).
fof(ax4,axiom,
! [X14,X15,X16,X17,X18] : l(X14,X15,t(X16,t(X17,X18))) = t(X16,t(X17,l(X14,X15,X18))) ).
fof(ax5,axiom,
! [X14,X15,X16,X17,X18] : i2(X14,j2(X15,i1(X16,t(X17,X18)))) = i1(X16,t(X17,i2(X14,j2(X15,X18)))) ).
fof(ax6,axiom,
! [X14,X15,X16,X17,X18] : i2(X14,i2(X15,t(X16,i2(X17,X18)))) = t(X16,i2(X17,i2(X14,i2(X15,X18)))) ).
fof(ax7,axiom,
! [X14,X15,X16,X17,X18] : t(X14,t(X15,i1(X16,t(X17,X18)))) = i1(X16,t(X17,t(X14,t(X15,X18)))) ).
fof(ax8,axiom,
! [X14,X15,X16,X17,X18] : i2(X14,t(X15,i2(X16,i2(X17,X18)))) = i2(X16,i2(X17,i2(X14,t(X15,X18)))) ).
fof(ax9,axiom,
! [X14,X15,X16,X17,X18] : i2(X14,i1(X15,i1(X16,i1(X17,X18)))) = i1(X16,i1(X17,i2(X14,i1(X15,X18)))) ).
fof(ax10,axiom,
! [X14,X15,X16,X17,X18,X19] : r(X14,X15,i2(X16,i2(X17,j2(X18,X19)))) = i2(X17,j2(X18,r(X14,X15,i2(X16,X19)))) ).
fof(ax11,axiom,
! [X14,X15,X16,X17,X18,X19] : r(X14,X15,i2(X16,i1(X17,i2(X18,X19)))) = i1(X17,i2(X18,r(X14,X15,i2(X16,X19)))) ).
fof(ax12,axiom,
! [X14,X15,X16,X17,X18,X19,X20] : l(X14,X15,i1(X16,l(X17,X18,t(X19,X20)))) = l(X17,X18,t(X19,l(X14,X15,i1(X16,X20)))) ).
fof(ax13,axiom,
! [X14,X15,X16,X17,X18,X19,X20] : r(X14,X15,t(X16,r(X17,X18,i1(X19,X20)))) = r(X17,X18,i1(X19,r(X14,X15,t(X16,X20)))) ).
fof(ax14,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,t(X16,t(X17,r(X18,X19,t(X20,X21))))) = r(X18,X19,t(X20,r(X14,X15,t(X16,t(X17,X21))))) ).
fof(ax15,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,i2(X16,i2(X17,r(X18,X19,i1(X20,X21))))) = r(X18,X19,i1(X20,r(X14,X15,i2(X16,i2(X17,X21))))) ).
fof(ax16,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,j2(X16,i2(X17,l(X18,X19,i1(X20,X21))))) = l(X18,X19,i1(X20,r(X14,X15,j2(X16,i2(X17,X21))))) ).
fof(ax17,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,i1(X16,i2(X17,l(X18,X19,t(X20,X21))))) = l(X18,X19,t(X20,r(X14,X15,i1(X16,i2(X17,X21))))) ).
fof(ax18,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,t(X16,i1(X17,r(X18,X19,i1(X20,X21))))) = r(X18,X19,i1(X20,r(X14,X15,t(X16,i1(X17,X21))))) ).
fof(ax19,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,i1(X16,j2(X17,r(X18,X19,i2(X20,X21))))) = r(X18,X19,i2(X20,r(X14,X15,i1(X16,j2(X17,X21))))) ).
fof(ax20,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : l(X14,X15,j2(X16,i1(X17,r(X18,X19,i1(X20,X21))))) = r(X18,X19,i1(X20,l(X14,X15,j2(X16,i1(X17,X21))))) ).
fof(ax21,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,i2(X16,i2(X17,r(X18,X19,i2(X20,X21))))) = r(X18,X19,i2(X20,r(X14,X15,i2(X16,i2(X17,X21))))) ).
fof(ax22,axiom,
! [X14,X15,X16,X17,X18,X19,X20,X21] : r(X14,X15,i2(X16,t(X17,l(X18,X19,i2(X20,X21))))) = l(X18,X19,i2(X20,r(X14,X15,i2(X16,t(X17,X21))))) ).
fof(conj,conjecture,
! [U,X,Y,Z,W] : a(W,m(s(e,U),r(X,Y,U)),Z) = e ).
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