TPTP Problem File: SWW930+1.p
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%------------------------------------------------------------------------------
% File : SWW930+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : stack_allocProof__109__prog_comp_lambda__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : stack_allocProof__109__prog_comp_lambda__dep [Kum18]
% Status : Theorem
% Rating : 1.00 v7.3.0
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 38 ( 15 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 25 ( 1 ~; 1 |; 10 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 44 ( 44 !; 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.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.FUN_EQ_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27g_27] :
( s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27) = s__02(cfun__02(V_27A_27,V_27B_27),V_27g_27)
<=> ! [V_27x_27] : 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_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27g_27),s__02(V_27A_27,V_27x_27))) ) ).
fof('thm.pair.CLOSED_PAIR_EQ',axiom,
! [V_27A_27,V_27B_27,V_27x_27,V_27y_27,V_27a_27,V_27b_27] :
( s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x_27),s__02(V_27B_27,V_27y_27))) = s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27a_27),s__02(V_27B_27,V_27b_27)))
<=> ( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27)
& s__02(V_27B_27,V_27y_27) = s__02(V_27B_27,V_27b_27) ) ) ).
fof('thm.pair.UNCURRY_DEF',axiom,
! [V_27C_27,V_27A_27,V_27B_27,V_27f_27,V_27x_27,V_27y_27] : s__02(V_27C_27,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27C_27),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27))),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27x_27),s__02(V_27B_27,V_27y_27))))) = s__02(V_27C_27,chapp__02(s__02(cfun__02(V_27B_27,V_27C_27),chapp__02(s__02(cfun__02(V_27A_27,cfun__02(V_27B_27,V_27C_27)),V_27f_27),s__02(V_27A_27,V_27x_27))),s__02(V_27B_27,V_27y_27))) ).
fof('thm.pair.FORALL_PROD',axiom,
! [V_27A_27,V_27B_27,V_27P_27] :
( ! [V_27p_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),V_27P_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),V_27p_27))))
<=> ! [V_27p__1_27,V_27p__2_27] : p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),cbool__00),V_27P_27),s__02(c_27type_2epair_2eprod_27__02(V_27A_27,V_27B_27),c_27const_2epair_2e_2c_27__02(s__02(V_27A_27,V_27p__1_27),s__02(V_27B_27,V_27p__2_27)))))) ) ).
fof('thm.stack_alloc.prog_comp_def',axiom,
! [V_27A_27,V_27n_27,V_27p_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27))),c_27const_2estack__alloc_2eprog__comp_27__00),s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),V_27p_27))))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2enum_2enum_27__00),c_27const_2estack__alloc_2ecomp_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2estack__alloc_2enext__lab_27__02(s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),V_27p_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),V_27p_27))))))) ).
fof(conjecture,conjecture,
! [V_27A_27,V__1] :
( ! [V_27n_27,V_27p_27] : s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),chapp__02(s__02(cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),V_27p_27))) = s__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27const_2epair_2eFST_27__01(s__02(c_27type_2epair_2eprod_27__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2enum_2enum_27__00),c_27const_2estack__alloc_2ecomp_27__03(s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2estack__alloc_2enext__lab_27__02(s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),V_27p_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eNUMERAL_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eBIT1_27__01(s__02(c_27type_2enum_2enum_27__00,c_27const_2earithmetic_2eZERO_27__00))))))),s__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),V_27p_27)))))))
=> ! [V__0] :
( ! [V_27n_27] : s__02(cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)))),V__1),s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
=> s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27))),c_27const_2estack__alloc_2eprog__comp_27__00) = s__02(cfun__02(c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27))),c_27const_2epair_2eUNCURRY_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2estackLang_2eprog_27__01(V_27A_27),c_27type_2epair_2eprod_27__02(c_27type_2enum_2enum_27__00,c_27type_2estackLang_2eprog_27__01(V_27A_27)))),V__0))) ) ) ).
%------------------------------------------------------------------------------