TPTP Problem File: SWW865+1.p
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%------------------------------------------------------------------------------
% File : SWW865+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : unify__39__t_vars_eqn__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : unify__39__t_vars_eqn__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.2.0, 0.33 v8.1.0, 0.50 v7.5.0, 0.60 v7.4.0, 0.33 v7.3.0
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 36 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 19 ( 1 ~; 1 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 34 ( 34 usr; 12 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% SPC : FOF_CSA_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.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.pred_set.UNION_EMPTY',axiom,
! [V_27A_27] :
( ! [V_27s_27] : s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))) = s__02(cfun__02(V_27A_27,cbool__00),V_27s_27)
& ! [V_27s_27] : s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00))) = s__02(cfun__02(V_27A_27,cbool__00),V_27s_27) ) ).
fof('thm.pred_set.EQUAL_SING',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00))) = s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(V_27A_27,V_27y_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00)))
<=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ).
fof('thm.pred_set.BIGUNION_EMPTY',axiom,
! [V_27A_27] : s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eBIGUNION_27__01(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),c_27const_2epred__set_2eEMPTY_27__00))) = s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00) ).
fof('thm.pred_set.BIGUNION_INSERT',axiom,
! [V_27A_27,V_27s_27,V_27P_27] : s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eBIGUNION_27__01(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27P_27))))) = s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eBIGUNION_27__01(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27P_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_TO_SET',axiom,
! [V_27A_27,V_27B_27,V_27t_27,V_27h_27] :
( s__02(cfun__02(V_27A_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eNIL_27__00))) = s__02(cfun__02(V_27A_27,cbool__00),c_27const_2epred__set_2eEMPTY_27__00)
& s__02(cfun__02(V_27B_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_27),c_27const_2elist_2eCONS_27__02(s__02(V_27B_27,V_27h_27),s__02(c_27type_2elist_2elist_27__01(V_27B_27),V_27t_27))))) = s__02(cfun__02(V_27B_27,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(V_27B_27,V_27h_27),s__02(cfun__02(V_27B_27,cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27B_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.term.vars_def',axiom,
! [V_27A_27] :
( ! [V_27x_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2eterm_2evars_27__01(s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),c_27const_2eterm_2eVar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00)))
& ! [V_27t1_27,V_27t2_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2eterm_2evars_27__01(s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),c_27const_2eterm_2ePair_27__02(s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),V_27t1_27),s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),V_27t2_27))))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2eterm_2evars_27__01(s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),V_27t1_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2eterm_2evars_27__01(s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),V_27t2_27)))))
& ! [V_27v0_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2eterm_2evars_27__01(s__02(c_27type_2eterm_2eterm_27__01(V_27A_27),c_27const_2eterm_2eConst_27__01(s__02(V_27A_27,V_27v0_27))))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00) ) ).
fof('thm.unify.encode_infer_t_def',axiom,
( ! [V_27n_27] : s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__t_27__01(s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2eConst_27__01(s__02(c_27type_2eunify_2eatom_27__00,c_27const_2eunify_2eDB__tag_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))))
& ! [V_27ts_27,V_27tc_27] : s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__t_27__01(s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tapp_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))))) = s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2ePair_27__02(s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2eConst_27__01(s__02(c_27type_2eunify_2eatom_27__00,c_27const_2eunify_2eTapp__tag_27__00))),s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2ePair_27__02(s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2eConst_27__01(s__02(c_27type_2eunify_2eatom_27__00,c_27const_2eunify_2eTC__tag_27__01(s__02(c_27type_2east_2etctor_27__00,V_27tc_27))))),s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__ts_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))))))
& ! [V_27n_27] : s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__t_27__01(s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tuvar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2eVar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
& s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__ts_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eNIL_27__00))) = s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2eConst_27__01(s__02(c_27type_2eunify_2eatom_27__00,c_27const_2eunify_2eNull__tag_27__00)))
& ! [V_27t_27,V_27ts_27] : s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__ts_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),c_27const_2elist_2eCONS_27__02(s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))))) = s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eterm_2ePair_27__02(s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__t_27__01(s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27))),s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__ts_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27))))) ) ).
fof('thm.unify.t_vars_def',axiom,
! [V_27t_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eunify_2et__vars_27__00),s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2eterm_2evars_27__01(s__02(c_27type_2eterm_2eterm_27__01(c_27type_2eunify_2eatom_27__00),c_27const_2eunify_2eencode__infer__t_27__01(s__02(c_27type_2einfer__t_2einfer__t_27__00,V_27t_27))))) ).
fof(conjecture,conjecture,
( ! [V_27x_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eunify_2et__vars_27__00),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tvar__db_27__01(s__02(c_27type_2enum_2enum_27__00,V_27x_27))))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00)
& ! [V_27ts_27,V_27tc_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eunify_2et__vars_27__00),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tapp_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27),s__02(c_27type_2east_2etctor_27__00,V_27tc_27))))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eBIGUNION_27__01(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),cbool__00),c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2elist_2eMAP_27__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eunify_2et__vars_27__00),s__02(c_27type_2elist_2elist_27__01(c_27type_2einfer__t_2einfer__t_27__00),V_27ts_27)))))))
& ! [V_27u_27] : s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2einfer__t_2einfer__t_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),c_27const_2eunify_2et__vars_27__00),s__02(c_27type_2einfer__t_2einfer__t_27__00,c_27const_2einfer__t_2eInfer__Tuvar_27__01(s__02(c_27type_2enum_2enum_27__00,V_27u_27))))) = s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eINSERT_27__02(s__02(c_27type_2enum_2enum_27__00,V_27u_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2eEMPTY_27__00))) ) ).
%------------------------------------------------------------------------------