TPTP Problem File: SWW914+1.p
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%------------------------------------------------------------------------------
% File : SWW914+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : stack_removeProof__71__tactictoe_prove_70__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : stack_removeProof__71__tactictoe_prove_70__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 52 ( 23 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 39 ( 3 ~; 1 |; 18 &)
% ( 14 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)) ).
fof('HL_BOOL_CASES',axiom,
! [Vt] :
( s__02(cbool__00,Vt) = s__02(cbool__00,cT__00)
| s__02(cbool__00,Vt) = s__02(cbool__00,cF__00) ) ).
fof('HL_EXT',axiom,
! [V_3f2384,V_3f2380,Vf,Vg] :
( ! [Vx] : s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vf),s__02(V_3f2384,Vx))) = s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vg),s__02(V_3f2384,Vx)))
=> s__02(cfun__02(V_3f2384,V_3f2380),Vf) = s__02(cfun__02(V_3f2384,V_3f2380),Vg) ) ).
fof('thm.bool.ETA_AX',axiom,
! [V_27B_27,V_27A_27,V_27t_27,Vx] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27t_27),s__02(V_27A_27,Vx))) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.AND_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,cF__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.list.MAP',axiom,
! [V_27B_27,V_27A_27] :
( ! [V_27f_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eNIL_27__00)
& ! [V_27f_27,V_27h_27,V_27t_27] : s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27h_27))),s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))) ) ).
fof('thm.list.list_induction',axiom,
! [V_27A_27,V_27P_27] :
( ( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))))
& ! [V_27t_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27))))
=> ! [V_27h_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27t_27)))))) ) )
=> ! [V_27l_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cbool__00),V_27P_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27l_27)))) ) ).
fof('thm.list.CONS_11',axiom,
! [V_27A_27,V_27a0_27,V_27a1_27,V_27a0_7c39_7c_27,V_27a1_7c39_7c_27] :
( s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eCONS_27__02(s__02(V_27A_27,V_27a0_7c39_7c_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_7c39_7c_27)))
<=> ( s__02(V_27A_27,V_27a0_27) = s__02(V_27A_27,V_27a0_7c39_7c_27)
& s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_27) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27a1_7c39_7c_27) ) ) ).
fof('thm.wordSem.word_loc_11',axiom,
! [V_27A_27] :
( ! [V_27a_27,V_27a_7c39_7c_27] :
( s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2ewordSem_2eWord_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_27))) = s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2ewordSem_2eWord_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_7c39_7c_27)))
<=> s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_27) = s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27a_7c39_7c_27) )
& ! [V_27a0_27,V_27a1_27,V_27a0_7c39_7c_27,V_27a1_7c39_7c_27] :
( s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27const_2ewordSem_2eLoc_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a0_27),s__02(c_27type_2enum_2enum_27__00,V_27a1_27))) = s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27const_2ewordSem_2eLoc_27__02(s__02(c_27type_2enum_2enum_27__00,V_27a0_7c39_7c_27),s__02(c_27type_2enum_2enum_27__00,V_27a1_7c39_7c_27)))
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27a0_27) = s__02(c_27type_2enum_2enum_27__00,V_27a0_7c39_7c_27)
& s__02(c_27type_2enum_2enum_27__00,V_27a1_27) = s__02(c_27type_2enum_2enum_27__00,V_27a1_7c39_7c_27) ) ) ) ).
fof('thm.stack_removeProof.mem_val_def',axiom,
! [V_27A_27] :
( ! [V_27regs_27,V_27w_27] : s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2estack__removeProof_2emem__val_27__01(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27regs_27))),s__02(c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00)),c_27const_2esum_2eINL_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27))))) = s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2ewordSem_2eWord_27__00),s__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),V_27w_27)))
& ! [V_27regs_27,V_27n_27] : s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2estack__removeProof_2emem__val_27__01(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27regs_27))),s__02(c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00),c_27const_2esum_2eINR_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27),c_27const_2efinite__map_2eFAPPLY_27__02(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27regs_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27ws_27,V_27f_27] : s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2estack__removeProof_2emem__val_27__01(s__02(c_27type_2efinite__map_2efmap_27__02(c_27type_2enum_2enum_27__00,c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),V_27f_27))),s__02(c_27type_2elist_2elist_27__01(c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2esum_2esum_27__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2enum_2enum_27__00)),c_27const_2esum_2eINL_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27)),V_27ws_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27),c_27type_2ewordSem_2eword__loc_27__01(V_27A_27)),c_27const_2ewordSem_2eWord_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2efcp_2ecart_27__02(cbool__00,V_27A_27)),V_27ws_27))) ).
%------------------------------------------------------------------------------