%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP068^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.E4dsQV7EnX true
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:38:43 PM UTC 2025
% Result : Theorem 92.78s 12.41s
% Output : Refutation 92.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 326 ( 116 equ; 68 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2026 ( 42 ~; 8 |; 31 &;1797 @)
% ( 16 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 23 usr; 16 con; 0-6 aty)
% ( 111 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 189 ( 30 ^; 159 !; 0 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(tree_a_type,type,
tree_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(heapIm1140443833left_a_type,type,
heapIm1140443833left_a: tree_a > tree_a ).
thf(l1_type,type,
l1: tree_a ).
thf(v2_type,type,
v2: a ).
thf(la_type,type,
la: tree_a ).
thf(ra_type,type,
ra: tree_a ).
thf(v1_type,type,
v1: a ).
thf('#sk22_type',type,
'#sk22': tree_a > tree_a ).
thf(ord_less_eq_a_type,type,
ord_less_eq_a: a > a > $o ).
thf(e_a_type,type,
e_a: tree_a ).
thf(heapIm1091024090Down_a_type,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(r1_type,type,
r1: tree_a ).
thf(val_a_type,type,
val_a: tree_a > a ).
thf(va_type,type,
va: a ).
thf(is_heap_a_type,type,
is_heap_a: tree_a > $o ).
thf('#sk23_type',type,
'#sk23': tree_a > tree_a ).
thf(t_a_type,type,
t_a: a > tree_a > tree_a > tree_a ).
thf('#sk21_type',type,
'#sk21': tree_a > a ).
thf(heapIm1257206334ight_a_type,type,
heapIm1257206334ight_a: tree_a > tree_a ).
thf(s_comb_type,type,
'#S':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).
thf(c_comb_type,type,
'#C':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).
thf(b_comb_type,type,
'#B':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).
thf(k_comb_type,type,
'#K':
!>[A: $tType,B: $tType] : ( B > A > B ) ).
thf(i_comb_type,type,
'#I':
!>[A: $tType] : ( A > A ) ).
thf(fact_0__C4_Oprems_C_I2_J,axiom,
is_heap_a @ ra ).
thf(zip_derived_cl0,plain,
is_heap_a @ ra,
inference(cnf,[status(esa)],[fact_0__C4_Oprems_C_I2_J]) ).
thf(fact_4_True,axiom,
ord_less_eq_a @ v1 @ v2 ).
thf(zip_derived_cl2,plain,
ord_less_eq_a @ v1 @ v2,
inference(cnf,[status(esa)],[fact_4_True]) ).
thf(conj_0,conjecture,
is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl170,plain,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(fact_5__C4_Oprems_C_I3_J,axiom,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ) ).
thf(zip_derived_cl3,plain,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ),
inference(cnf,[status(esa)],[fact_5__C4_Oprems_C_I3_J]) ).
thf(zip_derived_cl171,plain,
~ ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ va @ la @ ra ) ) ),
inference(demod,[status(thm)],[zip_derived_cl170,zip_derived_cl3]) ).
thf(fact_32_is__heap_Osimps_I3_J,axiom,
! [V: a,Va2: a,Vb2: tree_a,Vc2: tree_a] :
( ( is_heap_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
<=> ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
& ( is_heap_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ).
thf(zip_derived_cl52,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: tree_a] :
( !!
@ ^ [Y3: tree_a] :
( ( is_heap_a @ ( t_a @ Y0 @ e_a @ ( t_a @ Y1 @ Y2 @ Y3 ) ) )
<=> ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Y1 @ Y2 @ Y3 ) ) @ Y0 )
& ( is_heap_a @ ( t_a @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_32_is__heap_Osimps_I3_J]) ).
thf(zip_derived_cl53,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ is_heap_a ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#C' @ t_a @ e_a ) ) ) ) @ t_a ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ ord_less_eq_a ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ val_a ) ) @ t_a ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ is_heap_a ) ) @ t_a ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl491,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ is_heap_a ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( t_a @ X2 @ e_a ) ) ) @ t_a ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ ord_less_eq_a ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ val_a ) ) @ t_a ) ) ) ) @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ is_heap_a ) ) @ t_a ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl492,plain,
! [X2: a,X4: a] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ is_heap_a ) @ ( '#B' @ ( '#B' @ ( t_a @ X2 @ e_a ) ) @ ( t_a @ X4 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ ord_less_eq_a ) @ ( '#B' @ ( '#B' @ val_a ) @ ( t_a @ X4 ) ) ) ) @ X2 ) ) ) @ ( '#B' @ ( '#B' @ is_heap_a ) @ ( t_a @ X4 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl491]) ).
thf(zip_derived_cl493,plain,
! [X2: a,X4: a,X6: tree_a] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ is_heap_a @ ( '#B' @ ( t_a @ X2 @ e_a ) @ ( t_a @ X4 @ X6 ) ) ) ) @ ( '#S' @ ( '#B' @ (&) @ ( '#C' @ ( '#B' @ ord_less_eq_a @ ( '#B' @ val_a @ ( t_a @ X4 @ X6 ) ) ) @ X2 ) ) @ ( '#B' @ is_heap_a @ ( t_a @ X4 @ X6 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl492]) ).
thf(zip_derived_cl494,plain,
! [X2: a,X4: a,X6: tree_a,X8: tree_a] :
( ( is_heap_a @ ( t_a @ X2 @ e_a @ ( t_a @ X4 @ X6 @ X8 ) ) )
<=> ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X4 @ X6 @ X8 ) ) @ X2 )
& ( is_heap_a @ ( t_a @ X4 @ X6 @ X8 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl493]) ).
thf(zip_derived_cl495,plain,
! [X2: a,X4: a,X6: tree_a,X8: tree_a] :
( ( is_heap_a @ ( t_a @ X2 @ e_a @ ( t_a @ X4 @ X6 @ X8 ) ) )
= ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X4 @ X6 @ X8 ) ) @ X2 )
& ( is_heap_a @ ( t_a @ X4 @ X6 @ X8 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl494]) ).
thf(fact_22_val_Osimps,axiom,
! [V: a,Uu: tree_a,Uv: tree_a] :
( ( val_a @ ( t_a @ V @ Uu @ Uv ) )
= V ) ).
thf(zip_derived_cl32,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: tree_a] :
( !!
@ ^ [Y2: tree_a] :
( ( val_a @ ( t_a @ Y0 @ Y1 @ Y2 ) )
= Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_22_val_Osimps]) ).
thf(zip_derived_cl33,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ val_a ) ) @ t_a ) ) ) ) @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl276,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ val_a ) @ ( t_a @ X2 ) ) ) ) @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl277,plain,
! [X2: a,X4: tree_a] : ( !! @ ( '#C' @ ( '#B' @ (=) @ ( '#B' @ val_a @ ( t_a @ X2 @ X4 ) ) ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl276]) ).
thf(zip_derived_cl278,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( val_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl277]) ).
thf(zip_derived_cl279,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( val_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl496,plain,
! [X2: a,X4: a,X6: tree_a,X8: tree_a] :
( ( is_heap_a @ ( t_a @ X2 @ e_a @ ( t_a @ X4 @ X6 @ X8 ) ) )
= ( ( ord_less_eq_a @ X4 @ X2 )
& ( is_heap_a @ ( t_a @ X4 @ X6 @ X8 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl495,zip_derived_cl279]) ).
thf(fact_30_siftDown_Osimps_I4_J,axiom,
! [Va2: a,Vb2: tree_a,Vc2: tree_a,V: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
=> ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
= ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) )
& ( ~ ( ord_less_eq_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ V )
=> ( ( heapIm1091024090Down_a @ ( t_a @ V @ e_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) )
= ( t_a @ ( val_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ V @ ( heapIm1140443833left_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl48,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: tree_a] :
( !!
@ ^ [Y2: tree_a] :
( !!
@ ^ [Y3: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) @ Y3 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ Y3 @ e_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) )
= ( t_a @ Y3 @ e_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) ) )
& ( ( (~) @ ( ord_less_eq_a @ ( val_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) @ Y3 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ Y3 @ e_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) )
= ( t_a @ ( val_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ Y3 @ ( heapIm1140443833left_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_30_siftDown_Osimps_I4_J]) ).
thf(zip_derived_cl49,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ord_less_eq_a ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ val_a ) ) @ t_a ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) ) ) @ t_a ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) ) ) @ t_a ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (~) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ord_less_eq_a ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ val_a ) ) @ t_a ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) ) ) @ t_a ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ t_a ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ val_a ) ) @ t_a ) ) ) ) @ e_a ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ t_a ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1140443833left_a ) ) @ t_a ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1257206334ight_a ) ) @ t_a ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl757,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ord_less_eq_a ) @ ( '#B' @ ( '#B' @ val_a ) @ ( t_a @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) ) @ ( t_a @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) ) @ ( t_a @ X2 ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (~) ) ) @ ( '#B' @ ( '#B' @ ord_less_eq_a ) @ ( '#B' @ ( '#B' @ val_a ) @ ( t_a @ X2 ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) ) @ ( t_a @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ t_a ) @ ( '#B' @ ( '#B' @ val_a ) @ ( t_a @ X2 ) ) ) ) @ e_a ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#C' @ t_a ) ) @ ( '#B' @ ( '#B' @ heapIm1140443833left_a ) @ ( t_a @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ heapIm1257206334ight_a ) @ ( t_a @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl758,plain,
! [X2: a,X4: tree_a] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ord_less_eq_a @ ( '#B' @ val_a @ ( t_a @ X2 @ X4 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) @ ( t_a @ X2 @ X4 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) @ ( t_a @ X2 @ X4 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ (~) ) @ ( '#B' @ ord_less_eq_a @ ( '#B' @ val_a @ ( t_a @ X2 @ X4 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) @ ( '#B' @ ( '#C' @ ( '#C' @ t_a @ e_a ) ) @ ( t_a @ X2 @ X4 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#C' @ ( '#B' @ t_a @ ( '#B' @ val_a @ ( t_a @ X2 @ X4 ) ) ) @ e_a ) ) @ ( '#B' @ ( '#B' @ heapIm1091024090Down_a ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#C' @ t_a ) @ ( '#B' @ heapIm1140443833left_a @ ( t_a @ X2 @ X4 ) ) ) ) @ ( '#B' @ heapIm1257206334ight_a @ ( t_a @ X2 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl757]) ).
thf(zip_derived_cl759,plain,
! [X2: a,X4: tree_a,X6: tree_a] : ( !! @ ( '#S' @ ( '#B' @ (&) @ ( '#S' @ ( '#B' @ (=>) @ ( ord_less_eq_a @ ( val_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ heapIm1091024090Down_a @ ( '#C' @ ( '#C' @ t_a @ e_a ) @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) @ ( '#C' @ ( '#C' @ t_a @ e_a ) @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ (~) @ ( ord_less_eq_a @ ( val_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) ) @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ heapIm1091024090Down_a @ ( '#C' @ ( '#C' @ t_a @ e_a ) @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) @ ( '#B' @ ( t_a @ ( val_a @ ( t_a @ X2 @ X4 @ X6 ) ) @ e_a ) @ ( '#B' @ heapIm1091024090Down_a @ ( '#C' @ ( '#C' @ t_a @ ( heapIm1140443833left_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl758]) ).
thf(zip_derived_cl760,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a] :
( ( ( ord_less_eq_a @ ( val_a @ ( t_a @ X2 @ X4 @ X6 ) ) @ X8 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) )
& ( ( (~) @ ( ord_less_eq_a @ ( val_a @ ( t_a @ X2 @ X4 @ X6 ) ) @ X8 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ ( val_a @ ( t_a @ X2 @ X4 @ X6 ) ) @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X8 @ ( heapIm1140443833left_a @ ( t_a @ X2 @ X4 @ X6 ) ) @ ( heapIm1257206334ight_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl759]) ).
thf(zip_derived_cl279_001,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( val_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl279_002,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( val_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl279_003,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( val_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl278]) ).
thf(fact_20_left_Osimps,axiom,
! [V: a,L: tree_a,R: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ V @ L @ R ) )
= L ) ).
thf(zip_derived_cl28,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: tree_a] :
( !!
@ ^ [Y2: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ Y0 @ Y1 @ Y2 ) )
= Y1 ) ) ) ),
inference(cnf,[status(esa)],[fact_20_left_Osimps]) ).
thf(zip_derived_cl29,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1140443833left_a ) ) @ t_a ) ) ) ) @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl280,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ heapIm1140443833left_a ) @ ( t_a @ X2 ) ) ) ) @ '#I' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl281,plain,
! [X2: a,X4: tree_a] : ( !! @ ( '#C' @ ( '#B' @ (=) @ ( '#B' @ heapIm1140443833left_a @ ( t_a @ X2 @ X4 ) ) ) @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl280]) ).
thf(zip_derived_cl282,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X4 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl281]) ).
thf(zip_derived_cl283,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( heapIm1140443833left_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X4 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl282]) ).
thf(fact_34_right_Osimps,axiom,
! [V: a,L: tree_a,R: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ V @ L @ R ) )
= R ) ).
thf(zip_derived_cl56,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: tree_a] :
( !!
@ ^ [Y2: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ Y0 @ Y1 @ Y2 ) )
= Y2 ) ) ) ),
inference(cnf,[status(esa)],[fact_34_right_Osimps]) ).
thf(zip_derived_cl57,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ heapIm1257206334ight_a ) ) @ t_a ) ) ) ) @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl288,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ heapIm1257206334ight_a ) @ ( t_a @ X2 ) ) ) ) @ '#I' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl289,plain,
! [X2: a,X4: tree_a] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ heapIm1257206334ight_a @ ( t_a @ X2 @ X4 ) ) ) @ '#I' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl288]) ).
thf(zip_derived_cl290,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X6 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl289]) ).
thf(zip_derived_cl291,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X6 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl290]) ).
thf(zip_derived_cl761,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a] :
( ( ( ord_less_eq_a @ X2 @ X8 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) )
& ( ( (~) @ ( ord_less_eq_a @ X2 @ X8 ) )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ X2 @ e_a @ ( heapIm1091024090Down_a @ ( t_a @ X8 @ X4 @ X6 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl760,zip_derived_cl279,zip_derived_cl279,zip_derived_cl279,zip_derived_cl283,zip_derived_cl291]) ).
thf(zip_derived_cl762,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a] :
( ( ord_less_eq_a @ X2 @ X8 )
=> ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl761]) ).
thf(zip_derived_cl764,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a] :
( ~ ( ord_less_eq_a @ X2 @ X8 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl762]) ).
thf(zip_derived_cl766,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a] :
( ~ ( ord_less_eq_a @ X2 @ X8 )
| ( ( heapIm1091024090Down_a @ ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) )
= ( t_a @ X8 @ e_a @ ( t_a @ X2 @ X4 @ X6 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl764]) ).
thf(zip_derived_cl291_004,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( heapIm1257206334ight_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X6 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl290]) ).
thf(zip_derived_cl3_005,plain,
( ( t_a @ v2 @ e_a @ ( t_a @ v1 @ l1 @ r1 ) )
= ( t_a @ va @ la @ ra ) ),
inference(cnf,[status(esa)],[fact_5__C4_Oprems_C_I3_J]) ).
thf(fact_15_Tree_Odistinct_I1_J,axiom,
! [X21: a,X22: tree_a,X23: tree_a] :
( e_a
!= ( t_a @ X21 @ X22 @ X23 ) ) ).
thf(zip_derived_cl18,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: tree_a] :
( !!
@ ^ [Y2: tree_a] :
( e_a
!= ( t_a @ Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[fact_15_Tree_Odistinct_I1_J]) ).
thf(zip_derived_cl19,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( tree_a != e_a ) ) ) @ t_a ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl183,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( tree_a != e_a ) ) @ ( t_a @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl184,plain,
! [X2: a,X4: tree_a] : ( !! @ ( '#B' @ ( tree_a != e_a ) @ ( t_a @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl183]) ).
thf(zip_derived_cl185,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( e_a
!= ( t_a @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl184]) ).
thf(zip_derived_cl186,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( e_a
!= ( t_a @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl185]) ).
thf(fact_17_Tree_Oexhaust,axiom,
! [Y: tree_a] :
( ( Y != e_a )
=> ~ ! [X212: a,X222: tree_a,X232: tree_a] :
( Y
!= ( t_a @ X212 @ X222 @ X232 ) ) ) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: tree_a] :
( ( Y0 != e_a )
=> ( (~)
@ ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: tree_a] :
( !!
@ ^ [Y3: tree_a] :
( Y0
!= ( t_a @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_17_Tree_Oexhaust]) ).
thf(zip_derived_cl23,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ != @ e_a ) ) @ ( '#B' @ (~) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ != ) ) ) @ t_a ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl330,plain,
! [X2: tree_a] :
( ( X2 != e_a )
=> ( (~) @ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( tree_a != X2 ) ) ) @ t_a ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl331,plain,
! [X2: tree_a] :
( ~ ( ( X2 != e_a ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( tree_a != X2 ) ) ) @ t_a ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl330]) ).
thf(zip_derived_cl332,plain,
! [X2: tree_a] :
( ( X2 = e_a )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( tree_a != X2 ) ) ) @ t_a ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl331]) ).
thf(zip_derived_cl333,plain,
! [X2: tree_a] :
( ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( tree_a != X2 ) ) @ ( t_a @ ( '#sk21' @ X2 ) ) ) ) )
| ( X2 = e_a ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl332]) ).
thf(zip_derived_cl334,plain,
! [X2: tree_a] :
( ~ ( !! @ ( '#B' @ ( tree_a != X2 ) @ ( t_a @ ( '#sk21' @ X2 ) @ ( '#sk22' @ X2 ) ) ) )
| ( X2 = e_a ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl333]) ).
thf(zip_derived_cl335,plain,
! [X2: tree_a] :
( ~ ( ( X2
!= ( t_a @ ( '#sk21' @ X2 ) @ ( '#sk22' @ X2 ) @ ( '#sk23' @ X2 ) ) ) )
| ( X2 = e_a ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl334]) ).
thf(zip_derived_cl336,plain,
! [X2: tree_a] :
( ( X2
= ( t_a @ ( '#sk21' @ X2 ) @ ( '#sk22' @ X2 ) @ ( '#sk23' @ X2 ) ) )
| ( X2 = e_a ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl335]) ).
thf(fact_13_Tree_Oinject,axiom,
! [X21: a,X22: tree_a,X23: tree_a,Y21: a,Y22: tree_a,Y23: tree_a] :
( ( ( t_a @ X21 @ X22 @ X23 )
= ( t_a @ Y21 @ Y22 @ Y23 ) )
<=> ( ( X21 = Y21 )
& ( X22 = Y22 )
& ( X23 = Y23 ) ) ) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: tree_a] :
( !!
@ ^ [Y2: tree_a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: tree_a] :
( !!
@ ^ [Y5: tree_a] :
( ( ( t_a @ Y0 @ Y1 @ Y2 )
= ( t_a @ Y3 @ Y4 @ Y5 ) )
<=> ( ( Y0 = Y3 )
& ( Y1 = Y4 )
& ( Y2 = Y5 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_13_Tree_Oinject]) ).
thf(zip_derived_cl16,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ t_a ) ) ) ) ) ) @ t_a ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) ) @ (=) ) ) ) ) ) ) @ (=) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl364,plain,
! [X2: a] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ ( t_a @ X2 ) ) ) ) ) ) @ t_a ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (&) @ ( a = X2 ) ) ) ) @ (=) ) ) ) ) ) @ (=) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl365,plain,
! [X2: a,X4: tree_a] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( t_a @ X2 @ X4 ) ) ) ) ) @ t_a ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (&) @ ( a = X2 ) ) ) @ ( tree_a = X4 ) ) ) ) ) @ (=) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl364]) ).
thf(zip_derived_cl366,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( !!
@ ( '#B' @ !!
@ ( '#B' @ ( '#B' @ !! )
@ ( '#S'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) )
@ ( '#B'
@ ( '#B'
@ ( '#B'
@ ( tree_a
= ( t_a @ X2 @ X4 @ X6 ) ) ) )
@ t_a ) ) ) )
@ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (&) @ ( a = X2 ) ) ) @ ( tree_a = X4 ) ) ) ) @ ( tree_a = X6 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl365]) ).
thf(zip_derived_cl367,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a] :
( !!
@ ( '#B' @ !!
@ ( '#S'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ (<=>) )
@ ( '#B'
@ ( '#B'
@ ( tree_a
= ( t_a @ X2 @ X4 @ X6 ) ) )
@ ( t_a @ X8 ) ) ) )
@ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( (&) @ ( X2 = X8 ) ) @ ( tree_a = X4 ) ) ) @ ( tree_a = X6 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl366]) ).
thf(zip_derived_cl368,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a,X10: tree_a] :
( !!
@ ( '#S'
@ ( '#B' @ (<=>)
@ ( '#B'
@ ( tree_a
= ( t_a @ X2 @ X4 @ X6 ) )
@ ( t_a @ X8 @ X10 ) ) )
@ ( '#B'
@ ( ( X2 = X8 )
& ( X4 = X10 ) )
@ ( tree_a = X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl367]) ).
thf(zip_derived_cl369,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a,X10: tree_a,X12: tree_a] :
( ( ( t_a @ X2 @ X4 @ X6 )
= ( t_a @ X8 @ X10 @ X12 ) )
<=> ( ( X2 = X8 )
& ( X4 = X10 )
& ( X6 = X12 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl368]) ).
thf(zip_derived_cl370,plain,
! [X2: a,X4: tree_a,X6: tree_a,X8: a,X10: tree_a,X12: tree_a] :
( ( ( t_a @ X2 @ X4 @ X6 )
= ( t_a @ X8 @ X10 @ X12 ) )
= ( ( X2 = X8 )
& ( X4 = X10 )
& ( X6 = X12 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl369]) ).
thf(zip_derived_cl279_006,plain,
! [X2: a,X4: tree_a,X6: tree_a] :
( ( val_a @ ( t_a @ X2 @ X4 @ X6 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl7955,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl0,zip_derived_cl2,zip_derived_cl171,zip_derived_cl496,zip_derived_cl766,zip_derived_cl291,zip_derived_cl3,zip_derived_cl186,zip_derived_cl336,zip_derived_cl370,zip_derived_cl279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP068^1 : TPTP v9.2.0. Released v7.5.0.
% 0.06/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.E4dsQV7EnX true
% 0.13/0.36 % Computer : n023.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 15:35:53 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.56/0.66 % Total configuration time : 828
% 0.56/0.66 % Estimated wc time : 1656
% 0.56/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.88 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 92.78/12.41 % Solved by lams/40_b.comb.sh.
% 92.78/12.41 % done 353 iterations in 11.546s
% 92.78/12.41 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 92.78/12.41 % SZS output start Refutation
% See solution above
% 92.78/12.41
% 92.78/12.41
% 92.78/12.41 % Terminating...
% 93.43/12.55 % Runner terminated.
% 93.43/12.56 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------