TPTP Problem File: SWW937+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWW937+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : cfMonad__4__tactictoe_prove_3__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : cfMonad__4__tactictoe_prove_3__dep [Kum18]
% Status : Theorem
% Rating : 0.78 v8.2.0, 0.81 v7.5.0, 0.91 v7.4.0, 0.90 v7.3.0
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 146 ( 17 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 153 ( 36 ~; 22 |; 30 &)
% ( 30 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 67 !; 5 ?)
% 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.IMP_ANTISYM_AX',axiom,
! [V_27t1_27,V_27t2_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> p__01(s__02(cbool__00,V_27t2_27)) )
=> ( ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t1_27)) )
=> s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27) ) ) ).
fof('thm.bool.IMP_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,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
=> 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,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)) ) ) ).
fof('thm.bool.NOT_CLAUSES',axiom,
( ! [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,cF__00)) )
& ( ~ p__01(s__02(cbool__00,cF__00))
<=> p__01(s__02(cbool__00,cT__00)) ) ) ).
fof('thm.bool.EQ_REFL',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
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.bool.AND_IMP_INTRO',axiom,
! [V_27t1_27,V_27t2_27,V_27t3_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t3_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27)) )
=> p__01(s__02(cbool__00,V_27t3_27)) ) ) ).
fof('thm.bool.IMP_CONG',axiom,
! [V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27x_27) = s__02(cbool__00,V_27x_7c39_7c_27)
& ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> s__02(cbool__00,V_27y_27) = s__02(cbool__00,V_27y_7c39_7c_27) ) )
=> ( ( p__01(s__02(cbool__00,V_27x_27))
=> p__01(s__02(cbool__00,V_27y_27)) )
<=> ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> p__01(s__02(cbool__00,V_27y_7c39_7c_27)) ) ) ) ).
fof('thm.sat.NOT_NOT',axiom,
! [V_27t_27] :
( ~ ~ p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.sat.AND_INV_IMP',axiom,
! [V_27A_270] :
( p__01(s__02(cbool__00,V_27A_270))
=> ( ~ p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) ) ) ).
fof('thm.sat.OR_DUAL2',axiom,
! [V_27B_27,V_27A_270] :
( ( ~ ( p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_27)) )
=> p__01(s__02(cbool__00,cF__00)) )
<=> ( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> ( ~ p__01(s__02(cbool__00,V_27B_27))
=> p__01(s__02(cbool__00,cF__00)) ) ) ) ).
fof('thm.sat.OR_DUAL3',axiom,
! [V_27B_27,V_27A_270] :
( ( ~ ( ~ p__01(s__02(cbool__00,V_27A_270))
| p__01(s__02(cbool__00,V_27B_27)) )
=> p__01(s__02(cbool__00,cF__00)) )
<=> ( p__01(s__02(cbool__00,V_27A_270))
=> ( ~ p__01(s__02(cbool__00,V_27B_27))
=> p__01(s__02(cbool__00,cF__00)) ) ) ) ).
fof('thm.sat.AND_INV2',axiom,
! [V_27A_270] :
( ( ~ p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> ( ( p__01(s__02(cbool__00,V_27A_270))
=> p__01(s__02(cbool__00,cF__00)) )
=> p__01(s__02(cbool__00,cF__00)) ) ) ).
fof('thm.sat.dc_eq',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> s__02(cbool__00,V_27q_27) = s__02(cbool__00,V_27r_27) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) )
& ( p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_conj',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
& p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) )
& ( p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_disj',axiom,
! [V_27r_27,V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ( p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27q_27)) )
& ( p__01(s__02(cbool__00,V_27p_27))
| ~ p__01(s__02(cbool__00,V_27r_27)) )
& ( p__01(s__02(cbool__00,V_27q_27))
| p__01(s__02(cbool__00,V_27r_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.dc_neg',axiom,
! [V_27q_27,V_27p_27] :
( ( p__01(s__02(cbool__00,V_27p_27))
<=> ~ p__01(s__02(cbool__00,V_27q_27)) )
<=> ( ( p__01(s__02(cbool__00,V_27p_27))
| p__01(s__02(cbool__00,V_27q_27)) )
& ( ~ p__01(s__02(cbool__00,V_27q_27))
| ~ p__01(s__02(cbool__00,V_27p_27)) ) ) ) ).
fof('thm.sat.pth_ni1',axiom,
! [V_27q_27,V_27p_27] :
( ~ ( p__01(s__02(cbool__00,V_27p_27))
=> p__01(s__02(cbool__00,V_27q_27)) )
=> p__01(s__02(cbool__00,V_27p_27)) ) ).
fof('thm.sat.pth_ni2',axiom,
! [V_27q_27,V_27p_27] :
( ~ ( p__01(s__02(cbool__00,V_27p_27))
=> p__01(s__02(cbool__00,V_27q_27)) )
=> ~ p__01(s__02(cbool__00,V_27q_27)) ) ).
fof('thm.pred_set.DISJOINT_UNION',axiom,
! [V_27A_27,V_27s_27,V_27t_27,V_27u_27] :
( p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(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),V_27t_27))),s__02(cfun__02(V_27A_27,cbool__00),V_27u_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27A_27,cbool__00),V_27u_27))))
& p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27t_27),s__02(cfun__02(V_27A_27,cbool__00),V_27u_27)))) ) ) ).
fof('thm.set_sep.SPLIT_def',axiom,
! [V_27A_27,V_27s_27,V_27u_27,V_27v_27] :
( p__01(s__02(cbool__00,c_27const_2eset__sep_2eSPLIT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),cfun__02(V_27A_27,cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_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_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_27))) = s__02(cfun__02(V_27A_27,cbool__00),V_27s_27)
& p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_27)))) ) ) ).
fof('thm.set_sep.STAR_def',axiom,
! [V_27A_27,V_27p_27,V_27q_27,Vx] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27p_27),s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27q_27))),s__02(cfun__02(V_27A_27,cbool__00),Vx))))
<=> ? [V_27u_27,V_27v_27] :
( p__01(s__02(cbool__00,c_27const_2eset__sep_2eSPLIT_27__02(s__02(cfun__02(V_27A_27,cbool__00),Vx),s__02(c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),cfun__02(V_27A_27,cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_27))))))
& p__01(s__02(cbool__00,chapp__02(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),V_27u_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27q_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_27)))) ) ) ).
fof('thm.cfHeapsBase.SPLIT3_def',axiom,
! [V_27A_27,V_27s_27,V_27u_27,V_27v_27,V_27w_27] :
( p__01(s__02(cbool__00,c_27const_2ecfHeapsBase_2eSPLIT3_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),cfun__02(V_27A_27,cbool__00))),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),cfun__02(V_27A_27,cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27v_27),s__02(cfun__02(V_27A_27,cbool__00),V_27w_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_2eUNION_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_27))),s__02(cfun__02(V_27A_27,cbool__00),V_27w_27))) = s__02(cfun__02(V_27A_27,cbool__00),V_27s_27)
& p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27v_27))))
& p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27v_27),s__02(cfun__02(V_27A_27,cbool__00),V_27w_27))))
& p__01(s__02(cbool__00,c_27const_2epred__set_2eDISJOINT_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27u_27),s__02(cfun__02(V_27A_27,cbool__00),V_27w_27)))) ) ) ).
fof(conjecture,conjecture,
! [V_27A_27,V_27H1_27,V_27H2_27,V_27H3_27,V_27h_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),c_27const_2eset__sep_2eSTAR_27__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27H1_27),s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27H2_27))),s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27H3_27))),s__02(cfun__02(V_27A_27,cbool__00),V_27h_27))))
=> ? [V_27h1_27,V_27h2_27,V_27h3_27] :
( p__01(s__02(cbool__00,c_27const_2ecfHeapsBase_2eSPLIT3_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27h_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),cfun__02(V_27A_27,cbool__00))),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27h1_27),s__02(c_27type_2epair_2eprod_27__02(cfun__02(V_27A_27,cbool__00),cfun__02(V_27A_27,cbool__00)),c_27const_2epair_2e_2c_27__02(s__02(cfun__02(V_27A_27,cbool__00),V_27h2_27),s__02(cfun__02(V_27A_27,cbool__00),V_27h3_27))))))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27H1_27),s__02(cfun__02(V_27A_27,cbool__00),V_27h1_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27H2_27),s__02(cfun__02(V_27A_27,cbool__00),V_27h2_27))))
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(cfun__02(V_27A_27,cbool__00),cbool__00),V_27H3_27),s__02(cfun__02(V_27A_27,cbool__00),V_27h3_27)))) ) ) ).
%------------------------------------------------------------------------------