%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:00:59 AM UTC 2026
% Result : Theorem 4.02s 0.95s
% Output : CNFRefutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 669 ( 333 unt; 0 typ; 0 def)
% Number of atoms : 4874 (2098 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 7568 (2338 ~;1411 |; 78 &;3681 @)
% ( 15 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 8 con; 0-3 aty)
% Number of variables : 1209 ( 0 ^;1167 !; 42 ?;1209 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_and1,type,
and1: $i > $i > $i ).
thf(tp_and2,type,
and2: $i > $i > $i ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_bool,type,
bool: $i > $o ).
thf(tp_d,type,
d: $i > $o ).
thf(tp_err,type,
err: $i ).
thf(tp_exists1,type,
exists1: $i > $i ).
thf(tp_exists2,type,
exists2: $i > $i ).
thf(tp_existsprefers,type,
existsprefers: $i > $i > $o ).
thf(tp_f1,type,
f1: $i > $i > $i > $i ).
thf(tp_f2,type,
f2: $i > $i > $i > $i ).
thf(tp_f3,type,
f3: $i > $i > $i > $i ).
thf(tp_f4,type,
f4: $i > $i > $i > $i ).
thf(tp_f5,type,
f5: $i > $i > $i ).
thf(tp_f6,type,
f6: $i > $i > $i ).
thf(tp_f7,type,
f7: $i > $i ).
thf(tp_false,type,
false: $i ).
thf(tp_false1,type,
false1: $i ).
thf(tp_false2,type,
false2: $i ).
thf(tp_forallprefers,type,
forallprefers: $i > $i > $o ).
thf(tp_impl,type,
impl: $i > $i > $i ).
thf(tp_lazy_and1,type,
lazy_and1: $i > $i > $i ).
thf(tp_lazy_and2,type,
lazy_and2: $i > $i > $i ).
thf(tp_lazy_impl,type,
lazy_impl: $i > $i > $i ).
thf(tp_not1,type,
not1: $i > $i ).
thf(tp_not2,type,
not2: $i > $i ).
thf(tp_or1,type,
or1: $i > $i > $i ).
thf(tp_or2,type,
or2: $i > $i > $i ).
thf(tp_phi,type,
phi: $i > $i ).
thf(tp_prop,type,
prop: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY96,type,
sK2_SY96: $i > $i ).
thf(tp_sK3_SY103,type,
sK3_SY103: $i > $i ).
thf(tp_sK4_SY114,type,
sK4_SY114: $i > $i > $i ).
thf(tp_sK5_SY117,type,
sK5_SY117: $i > $i > $i ).
thf(tp_sK6_SY119,type,
sK6_SY119: $i > $i > $i ).
thf(tp_sK7_SY121,type,
sK7_SY121: $i > $i > $i ).
thf(tp_true,type,
true: $i ).
thf(1,axiom,
! [P: $i] :
( ( not2 @ P )
= ( impl @ P @ false2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_not2) ).
thf(2,axiom,
( ( not1 @ true )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom3) ).
thf(3,axiom,
( ( not1 @ false )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom2) ).
thf(4,axiom,
! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_axiom1) ).
thf(5,axiom,
? [P: $i] :
( ( false2
= ( phi @ ( f7 @ P ) ) )
& ~ ? [P1: $i] : ( forallprefers @ ( f7 @ P1 ) @ ( f7 @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false2) ).
thf(6,axiom,
! [P: $i] :
( ( f7 @ P )
= ( lazy_impl @ ( prop @ P ) @ P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f7) ).
thf(7,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_false1) ).
thf(8,axiom,
! [P: $i] :
? [R: $i] :
( ( ( exists2 @ P )
= ( phi @ ( f6 @ P @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f6 @ P @ R1 ) @ ( f6 @ P @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_exists2) ).
thf(9,axiom,
! [P: $i,R: $i] :
( ( f6 @ P @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( f5 @ P @ R ) @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f6) ).
thf(10,axiom,
! [P: $i,R: $i] :
? [X: $i] :
( ( ( f5 @ P @ R )
= ( phi @ ( f4 @ P @ X @ R ) ) )
& ~ ? [X1: $i] : ( forallprefers @ ( f4 @ P @ X1 @ R ) @ ( f4 @ P @ X @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f5) ).
thf(11,axiom,
! [P: $i,X: $i,R: $i] :
( ( f4 @ P @ X @ R )
= ( impl @ ( apply @ P @ X ) @ R ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f4) ).
thf(12,axiom,
! [P: $i] :
? [X: $i] :
( ( ( exists1 @ P )
= ( phi @ ( apply @ P @ X ) ) )
& ~ ? [X1: $i] : ( existsprefers @ ( apply @ P @ X1 ) @ ( apply @ P @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists1_axiom1) ).
thf(13,axiom,
! [P: $i,Q: $i] :
? [R: $i] :
( ( ( or2 @ P @ Q )
= ( phi @ ( f3 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f3 @ P @ Q @ R1 ) @ ( f3 @ P @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_or2) ).
thf(14,axiom,
! [P: $i,Q: $i,R: $i] :
( ( f3 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( impl @ P @ R ) @ ( impl @ ( impl @ Q @ R ) @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f3) ).
thf(15,axiom,
! [B: $i] :
( ( bool @ B )
=> ( ( or1 @ false @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom4) ).
thf(16,axiom,
! [B: $i] :
( ( bool @ B )
=> ( ( or1 @ true @ B )
= true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom3) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom2) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or1_axiom1) ).
thf(19,axiom,
! [P: $i,Q: $i] :
? [R: $i] :
( ( ( lazy_and2 @ P @ Q )
= ( phi @ ( f2 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f2 @ P @ Q @ R1 ) @ ( f2 @ P @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lazy_and2) ).
thf(20,axiom,
! [P: $i,Q: $i,R: $i] :
( ( f2 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( lazy_impl @ P @ ( impl @ Q @ R ) ) @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f2) ).
thf(21,axiom,
! [B: $i] :
( ( lazy_and1 @ true @ B )
= ( phi @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom3) ).
thf(22,axiom,
! [B: $i] :
( ( lazy_and1 @ false @ B )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom2) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_axiom1) ).
thf(24,axiom,
! [P: $i,Q: $i] :
? [R: $i] :
( ( ( and2 @ P @ Q )
= ( phi @ ( f1 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f1 @ P @ Q @ R1 ) @ ( f1 @ P @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_and2) ).
thf(25,axiom,
! [P: $i,Q: $i,R: $i] :
( ( f1 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( impl @ P @ ( impl @ Q @ R ) ) @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_f1) ).
thf(26,axiom,
! [B: $i] :
( ( bool @ B )
=> ( ( and1 @ true @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom4) ).
thf(27,axiom,
! [B: $i] :
( ( bool @ B )
=> ( ( and1 @ false @ B )
= false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom3) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom2) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_axiom1) ).
thf(30,axiom,
! [B: $i] :
( ( lazy_impl @ true @ B )
= ( phi @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom3) ).
thf(31,axiom,
! [B: $i] :
( ( lazy_impl @ false @ B )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom2) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_impl_axiom1) ).
thf(33,axiom,
! [B: $i] :
( ( bool @ B )
=> ( ( impl @ true @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom4) ).
thf(34,axiom,
! [B: $i] :
( ( bool @ B )
=> ( ( impl @ false @ B )
= true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom3) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom2) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impl_axiom1) ).
thf(37,axiom,
! [X: $i] :
( ( ( prop @ X )
= false )
<=> ~ ( bool @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_false) ).
thf(38,axiom,
! [X: $i] :
( ( ( prop @ X )
= true )
<=> ( bool @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop_true) ).
thf(39,axiom,
! [X: $i] :
( ( ( d @ X )
& ( ( phi @ X )
= X ) )
| ( ~ ( d @ X )
& ( ( phi @ X )
= err ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_phi) ).
thf(40,axiom,
! [X: $i,Y: $i] :
( ( existsprefers @ X @ Y )
<=> ( ( ~ ( d @ X )
& ( d @ Y ) )
| ( ( d @ X )
& ( d @ Y )
& ~ ( bool @ X )
& ( bool @ Y ) )
| ( ( X = true )
& ( Y = false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_existsprefers) ).
thf(41,axiom,
! [X: $i,Y: $i] :
( ( forallprefers @ X @ Y )
<=> ( ( ~ ( d @ X )
& ( d @ Y ) )
| ( ( d @ X )
& ( d @ Y )
& ~ ( bool @ X )
& ( bool @ Y ) )
| ( ( X = false )
& ( Y = true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_forallprefers) ).
thf(42,axiom,
( ( d @ true )
& ( d @ false )
& ( d @ err ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_true_err_in_d) ).
thf(43,axiom,
( ( true != false )
& ( true != err )
& ( false != err ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distinct_false_true_err) ).
thf(44,axiom,
! [X: $i] :
( ( bool @ X )
<=> ( ( X = false )
| ( X = true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_bool) ).
thf(45,conjecture,
false1 = false2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false1_false2) ).
thf(46,negated_conjecture,
( ( false1 = false2 )
= $false ),
inference(negate_conjecture,[status(cth)],[45]) ).
thf(47,plain,
( ( false1 = false2 )
= $false ),
inference(unfold_def,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [P: $i] :
( ( not2 @ P )
= ( impl @ P @ false2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(49,plain,
( ( ( not1 @ true )
= false )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(50,plain,
( ( ( not1 @ false )
= true )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(52,plain,
( ( ? [P: $i] :
( ( false2
= ( phi @ ( f7 @ P ) ) )
& ~ ? [P1: $i] : ( forallprefers @ ( f7 @ P1 ) @ ( f7 @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(53,plain,
( ( ! [P: $i] :
( ( f7 @ P )
= ( lazy_impl @ ( prop @ P ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(54,plain,
( ( false1 = false )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(55,plain,
( ( ! [P: $i] :
? [R: $i] :
( ( ( exists2 @ P )
= ( phi @ ( f6 @ P @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f6 @ P @ R1 ) @ ( f6 @ P @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(56,plain,
( ( ! [P: $i,R: $i] :
( ( f6 @ P @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( f5 @ P @ R ) @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(57,plain,
( ( ! [P: $i,R: $i] :
? [X: $i] :
( ( ( f5 @ P @ R )
= ( phi @ ( f4 @ P @ X @ R ) ) )
& ~ ? [X1: $i] : ( forallprefers @ ( f4 @ P @ X1 @ R ) @ ( f4 @ P @ X @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(58,plain,
( ( ! [P: $i,X: $i,R: $i] :
( ( f4 @ P @ X @ R )
= ( impl @ ( apply @ P @ X ) @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(59,plain,
( ( ! [P: $i] :
? [X: $i] :
( ( ( exists1 @ P )
= ( phi @ ( apply @ P @ X ) ) )
& ~ ? [X1: $i] : ( existsprefers @ ( apply @ P @ X1 ) @ ( apply @ P @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(60,plain,
( ( ! [P: $i,Q: $i] :
? [R: $i] :
( ( ( or2 @ P @ Q )
= ( phi @ ( f3 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f3 @ P @ Q @ R1 ) @ ( f3 @ P @ Q @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(61,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( f3 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( impl @ P @ R ) @ ( impl @ ( impl @ Q @ R ) @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(62,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( or1 @ false @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(63,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( or1 @ true @ B )
= true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(66,plain,
( ( ! [P: $i,Q: $i] :
? [R: $i] :
( ( ( lazy_and2 @ P @ Q )
= ( phi @ ( f2 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f2 @ P @ Q @ R1 ) @ ( f2 @ P @ Q @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(67,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( f2 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( lazy_impl @ P @ ( impl @ Q @ R ) ) @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(68,plain,
( ( ! [B: $i] :
( ( lazy_and1 @ true @ B )
= ( phi @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(69,plain,
( ( ! [B: $i] :
( ( lazy_and1 @ false @ B )
= false ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(71,plain,
( ( ! [P: $i,Q: $i] :
? [R: $i] :
( ( ( and2 @ P @ Q )
= ( phi @ ( f1 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f1 @ P @ Q @ R1 ) @ ( f1 @ P @ Q @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(72,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( f1 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( impl @ P @ ( impl @ Q @ R ) ) @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(73,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( and1 @ true @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(74,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( and1 @ false @ B )
= false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(77,plain,
( ( ! [B: $i] :
( ( lazy_impl @ true @ B )
= ( phi @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(78,plain,
( ( ! [B: $i] :
( ( lazy_impl @ false @ B )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(80,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( impl @ true @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(81,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( impl @ false @ B )
= true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(84,plain,
( ( ! [X: $i] :
( ( ( prop @ X )
= false )
<=> ~ ( bool @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(85,plain,
( ( ! [X: $i] :
( ( ( prop @ X )
= true )
<=> ( bool @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(86,plain,
( ( ! [X: $i] :
( ( ( d @ X )
& ( ( phi @ X )
= X ) )
| ( ~ ( d @ X )
& ( ( phi @ X )
= err ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(87,plain,
( ( ! [X: $i,Y: $i] :
( ( existsprefers @ X @ Y )
<=> ( ( ~ ( d @ X )
& ( d @ Y ) )
| ( ( d @ X )
& ( d @ Y )
& ~ ( bool @ X )
& ( bool @ Y ) )
| ( ( X = true )
& ( Y = false ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(88,plain,
( ( ! [X: $i,Y: $i] :
( ( forallprefers @ X @ Y )
<=> ( ( ~ ( d @ X )
& ( d @ Y ) )
| ( ( d @ X )
& ( d @ Y )
& ~ ( bool @ X )
& ( bool @ Y ) )
| ( ( X = false )
& ( Y = true ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(89,plain,
( ( ( d @ true )
& ( d @ false )
& ( d @ err ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(90,plain,
( ( ( true != false )
& ( true != err )
& ( false != err ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(91,plain,
( ( ! [X: $i] :
( ( bool @ X )
<=> ( ( X = false )
| ( X = true ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(92,plain,
( ( false1 != false2 )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(93,plain,
( ( ! [X: $i] :
( ( bool @ X )
<=> ( ( X = false )
| ( X = true ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(94,plain,
( ( ( true != false )
& ( true != err )
& ( false != err ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(95,plain,
( ( ( d @ true )
& ( d @ false )
& ( d @ err ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(96,plain,
( ( ! [X: $i,Y: $i] :
( ( forallprefers @ X @ Y )
<=> ( ( ~ ( d @ X )
& ( d @ Y ) )
| ( ( d @ X )
& ( d @ Y )
& ~ ( bool @ X )
& ( bool @ Y ) )
| ( ( X = false )
& ( Y = true ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i] :
( ( existsprefers @ X @ Y )
<=> ( ( ~ ( d @ X )
& ( d @ Y ) )
| ( ( d @ X )
& ( d @ Y )
& ~ ( bool @ X )
& ( bool @ Y ) )
| ( ( X = true )
& ( Y = false ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(98,plain,
( ( ! [X: $i] :
( ( ( d @ X )
& ( ( phi @ X )
= X ) )
| ( ~ ( d @ X )
& ( ( phi @ X )
= err ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(99,plain,
( ( ! [X: $i] :
( ( ( prop @ X )
= true )
<=> ( bool @ X ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(100,plain,
( ( ! [X: $i] :
( ( ( prop @ X )
= false )
<=> ~ ( bool @ X ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( impl @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( impl @ A @ B )
= ( phi @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(103,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( impl @ false @ B )
= true ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(104,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( impl @ true @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_impl @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(106,plain,
( ( ! [B: $i] :
( ( lazy_impl @ false @ B )
= true ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(107,plain,
( ( ! [B: $i] :
( ( lazy_impl @ true @ B )
= ( phi @ B ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( and1 @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( and1 @ A @ B )
= ( phi @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(110,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( and1 @ false @ B )
= false ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(111,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( and1 @ true @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(112,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( f1 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( impl @ P @ ( impl @ Q @ R ) ) @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(113,plain,
( ( ! [P: $i,Q: $i] :
? [R: $i] :
( ( ( and2 @ P @ Q )
= ( phi @ ( f1 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f1 @ P @ Q @ R1 ) @ ( f1 @ P @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( lazy_and1 @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(115,plain,
( ( ! [B: $i] :
( ( lazy_and1 @ false @ B )
= false ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(116,plain,
( ( ! [B: $i] :
( ( lazy_and1 @ true @ B )
= ( phi @ B ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(117,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( f2 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( lazy_impl @ P @ ( impl @ Q @ R ) ) @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(118,plain,
( ( ! [P: $i,Q: $i] :
? [R: $i] :
( ( ( lazy_and2 @ P @ Q )
= ( phi @ ( f2 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f2 @ P @ Q @ R1 ) @ ( f2 @ P @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ~ ( bool @ A )
=> ( ( or1 @ A @ B )
= ( phi @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
( ( ( bool @ A )
& ~ ( bool @ B ) )
=> ( ( or1 @ A @ B )
= ( phi @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(121,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( or1 @ true @ B )
= true ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(122,plain,
( ( ! [B: $i] :
( ( bool @ B )
=> ( ( or1 @ false @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(123,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( f3 @ P @ Q @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( impl @ P @ R ) @ ( impl @ ( impl @ Q @ R ) @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(124,plain,
( ( ! [P: $i,Q: $i] :
? [R: $i] :
( ( ( or2 @ P @ Q )
= ( phi @ ( f3 @ P @ Q @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f3 @ P @ Q @ R1 ) @ ( f3 @ P @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(125,plain,
( ( ! [P: $i] :
? [X: $i] :
( ( ( exists1 @ P )
= ( phi @ ( apply @ P @ X ) ) )
& ~ ? [X1: $i] : ( existsprefers @ ( apply @ P @ X1 ) @ ( apply @ P @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(126,plain,
( ( ! [P: $i,X: $i,R: $i] :
( ( f4 @ P @ X @ R )
= ( impl @ ( apply @ P @ X ) @ R ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(127,plain,
( ( ! [P: $i,R: $i] :
? [X: $i] :
( ( ( f5 @ P @ R )
= ( phi @ ( f4 @ P @ X @ R ) ) )
& ~ ? [X1: $i] : ( forallprefers @ ( f4 @ P @ X1 @ R ) @ ( f4 @ P @ X @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(128,plain,
( ( ! [P: $i,R: $i] :
( ( f6 @ P @ R )
= ( lazy_impl @ ( prop @ R ) @ ( impl @ ( f5 @ P @ R ) @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(129,plain,
( ( ! [P: $i] :
? [R: $i] :
( ( ( exists2 @ P )
= ( phi @ ( f6 @ P @ R ) ) )
& ~ ? [R1: $i] : ( forallprefers @ ( f6 @ P @ R1 ) @ ( f6 @ P @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(130,plain,
( ( false1 = false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(131,plain,
( ( ! [P: $i] :
( ( f7 @ P )
= ( lazy_impl @ ( prop @ P ) @ P ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(132,plain,
( ( ? [P: $i] :
( ( false2
= ( phi @ ( f7 @ P ) ) )
& ~ ? [P1: $i] : ( forallprefers @ ( f7 @ P1 ) @ ( f7 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(133,plain,
( ( ! [A: $i] :
( ~ ( bool @ A )
=> ( ( not1 @ A )
= ( phi @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(134,plain,
( ( ( not1 @ false )
= true )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(135,plain,
( ( ( not1 @ true )
= false )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(136,plain,
( ( ! [P: $i] :
( ( not2 @ P )
= ( impl @ P @ false2 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(137,plain,
( ( false1 != false2 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(138,plain,
( ( ~ ( ~ ~ ( ~ ( d @ true )
| ~ ( d @ false ) )
| ~ ( d @ err ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( bool @ SX0 )
| ( ( lazy_and1 @ SX0 @ SX1 )
= ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(140,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( prop @ SX0 )
!= true )
| ( bool @ SX0 ) )
| ~ ( ~ ( bool @ SX0 )
| ( ( prop @ SX0 )
= true ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( existsprefers @ SX0 @ SX1 )
| ~ ( ~ ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ~ ( bool @ SX0 ) )
| ~ ( bool @ SX1 ) )
| ~ ( ( SX0 != true )
| ( SX1 != false ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ~ ( bool @ SX0 ) )
| ~ ( bool @ SX1 ) )
| ~ ( ( SX0 != true )
| ( SX1 != false ) ) )
| ( existsprefers @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ( ( and2 @ SX0 @ SX1 )
!= ( phi @ ( f1 @ SX0 @ SX1 @ SX2 ) ) )
| ~ ~ ~ ! [SX3: $i] :
~ ( forallprefers @ ( f1 @ SX0 @ SX1 @ SX3 ) @ ( f1 @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(143,plain,
( ( ! [SX0: $i] :
( ~ ( bool @ SX0 )
| ( ( and1 @ false @ SX0 )
= false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(144,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ( false2
!= ( phi @ ( f7 @ SX0 ) ) )
| ~ ~ ~ ! [SX1: $i] :
~ ( forallprefers @ ( f7 @ SX1 ) @ ( f7 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(145,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( d @ SX0 )
| ( ( phi @ SX0 )
!= SX0 ) )
| ~ ( ~ ~ ( d @ SX0 )
| ( ( phi @ SX0 )
!= err ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( bool @ SX0 )
| ~ ~ ( bool @ SX1 ) )
| ( ( and1 @ SX0 @ SX1 )
= ( phi @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(147,plain,
( ( ~ ( ~ ~ ( ~ ( ( true != false ) )
| ~ ( ( true != err ) ) )
| ~ ( ( false != err ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ( ( lazy_and2 @ SX0 @ SX1 )
!= ( phi @ ( f2 @ SX0 @ SX1 @ SX2 ) ) )
| ~ ~ ~ ! [SX3: $i] :
~ ( forallprefers @ ( f2 @ SX0 @ SX1 @ SX3 ) @ ( f2 @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( forallprefers @ SX0 @ SX1 )
| ~ ( ~ ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ~ ( bool @ SX0 ) )
| ~ ( bool @ SX1 ) )
| ~ ( ( SX0 != false )
| ( SX1 != true ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SX0 )
| ~ ( d @ SX1 ) )
| ~ ~ ( bool @ SX0 ) )
| ~ ( bool @ SX1 ) )
| ~ ( ( SX0 != false )
| ( SX1 != true ) ) )
| ( forallprefers @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( bool @ SX0 )
| ( ( impl @ SX0 @ SX1 )
= ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ~ ( bool @ SX0 )
| ( ( not1 @ SX0 )
= ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(152,plain,
( ( ! [SX0: $i] :
( ~ ( bool @ SX0 )
| ( ( and1 @ true @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( bool @ SX0 )
| ( ( and1 @ SX0 @ SX1 )
= ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(154,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ( ( exists2 @ SX0 )
!= ( phi @ ( f6 @ SX0 @ SX1 ) ) )
| ~ ~ ~ ! [SX2: $i] :
~ ( forallprefers @ ( f6 @ SX0 @ SX2 ) @ ( f6 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( bool @ SX0 )
| ( ( or1 @ SX0 @ SX1 )
= ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(156,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( bool @ SX0 )
| ( SX0 = false )
| ( SX0 = true ) )
| ~ ( ~ ( ( SX0 = false )
| ( SX0 = true ) )
| ( bool @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( bool @ SX0 )
| ~ ~ ( bool @ SX1 ) )
| ( ( or1 @ SX0 @ SX1 )
= ( phi @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ( ( f5 @ SX0 @ SX1 )
!= ( phi @ ( f4 @ SX0 @ SX2 @ SX1 ) ) )
| ~ ~ ~ ! [SX3: $i] :
~ ( forallprefers @ ( f4 @ SX0 @ SX3 @ SX1 ) @ ( f4 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(159,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ( ( exists1 @ SX0 )
!= ( phi @ ( apply @ SX0 @ SX1 ) ) )
| ~ ~ ~ ! [SX2: $i] :
~ ( existsprefers @ ( apply @ SX0 @ SX2 ) @ ( apply @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( bool @ SX0 )
| ( ( lazy_impl @ SX0 @ SX1 )
= ( phi @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(161,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( prop @ SX0 )
!= false )
| ~ ( bool @ SX0 ) )
| ~ ( ~ ~ ( bool @ SX0 )
| ( ( prop @ SX0 )
= false ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(162,plain,
( ( ! [SX0: $i] :
( ~ ( bool @ SX0 )
| ( ( or1 @ false @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ( ( or2 @ SX0 @ SX1 )
!= ( phi @ ( f3 @ SX0 @ SX1 @ SX2 ) ) )
| ~ ~ ~ ! [SX3: $i] :
~ ( forallprefers @ ( f3 @ SX0 @ SX1 @ SX3 ) @ ( f3 @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(164,plain,
( ( ! [SX0: $i] :
( ~ ( bool @ SX0 )
| ( ( or1 @ true @ SX0 )
= true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( bool @ SX0 )
| ~ ~ ( bool @ SX1 ) )
| ( ( impl @ SX0 @ SX1 )
= ( phi @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(166,plain,
( ( ! [SX0: $i] :
( ~ ( bool @ SX0 )
| ( ( impl @ false @ SX0 )
= true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(167,plain,
( ( ! [SX0: $i] :
( ~ ( bool @ SX0 )
| ( ( impl @ true @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(168,plain,
! [SV1: $i] :
( ( ( lazy_impl @ false @ SV1 )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(169,plain,
! [SV2: $i] :
( ( ( lazy_impl @ true @ SV2 )
= ( phi @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(170,plain,
! [SV3: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ( f1 @ SV3 @ SY75 @ SY76 )
= ( lazy_impl @ ( prop @ SY76 ) @ ( impl @ ( impl @ SV3 @ ( impl @ SY75 @ SY76 ) ) @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(171,plain,
! [SV4: $i] :
( ( ( lazy_and1 @ false @ SV4 )
= false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(172,plain,
! [SV5: $i] :
( ( ( lazy_and1 @ true @ SV5 )
= ( phi @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(173,plain,
! [SV6: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ( f2 @ SV6 @ SY77 @ SY78 )
= ( lazy_impl @ ( prop @ SY78 ) @ ( impl @ ( lazy_impl @ SV6 @ ( impl @ SY77 @ SY78 ) ) @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(174,plain,
! [SV7: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ( f3 @ SV7 @ SY79 @ SY80 )
= ( lazy_impl @ ( prop @ SY80 ) @ ( impl @ ( impl @ SV7 @ SY80 ) @ ( impl @ ( impl @ SY79 @ SY80 ) @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(175,plain,
! [SV8: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ( f4 @ SV8 @ SY81 @ SY82 )
= ( impl @ ( apply @ SV8 @ SY81 ) @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(176,plain,
! [SV9: $i] :
( ( ! [SY83: $i] :
( ( f6 @ SV9 @ SY83 )
= ( lazy_impl @ ( prop @ SY83 ) @ ( impl @ ( f5 @ SV9 @ SY83 ) @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(177,plain,
! [SV10: $i] :
( ( ( f7 @ SV10 )
= ( lazy_impl @ ( prop @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(178,plain,
! [SV11: $i] :
( ( ( not2 @ SV11 )
= ( impl @ SV11 @ false2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(179,plain,
( ( false1 = false2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(180,plain,
( ( ~ ~ ( ~ ( d @ true )
| ~ ( d @ false ) )
| ~ ( d @ err ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(181,plain,
! [SV12: $i] :
( ( ! [SY84: $i] :
( ~ ~ ( bool @ SV12 )
| ( ( lazy_and1 @ SV12 @ SY84 )
= ( phi @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(182,plain,
! [SV13: $i] :
( ( ~ ( ~ ( ( ( prop @ SV13 )
!= true )
| ( bool @ SV13 ) )
| ~ ( ~ ( bool @ SV13 )
| ( ( prop @ SV13 )
= true ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(183,plain,
! [SV14: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ~ ( existsprefers @ SV14 @ SY85 )
| ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SY85 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SY85 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SY85 ) )
| ~ ( ( SV14 != true )
| ( SY85 != false ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SY85 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SY85 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SY85 ) )
| ~ ( ( SV14 != true )
| ( SY85 != false ) ) )
| ( existsprefers @ SV14 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(184,plain,
! [SV15: $i] :
( ( ! [SY86: $i] :
~ ! [SY87: $i] :
~ ~ ( ( ( and2 @ SV15 @ SY86 )
!= ( phi @ ( f1 @ SV15 @ SY86 @ SY87 ) ) )
| ~ ~ ~ ! [SY88: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SY86 @ SY88 ) @ ( f1 @ SV15 @ SY86 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(185,plain,
! [SV16: $i] :
( ( ~ ( bool @ SV16 )
| ( ( and1 @ false @ SV16 )
= false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(186,plain,
( ( ! [SX0: $i] :
~ ~ ( ( false2
!= ( phi @ ( f7 @ SX0 ) ) )
| ~ ~ ~ ! [SX1: $i] :
~ ( forallprefers @ ( f7 @ SX1 ) @ ( f7 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(187,plain,
! [SV17: $i] :
( ( ~ ( ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= SV17 ) )
| ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(188,plain,
! [SV18: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ( bool @ SV18 )
| ~ ~ ( bool @ SY89 ) )
| ( ( and1 @ SV18 @ SY89 )
= ( phi @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(189,plain,
( ( ~ ~ ( ~ ( ( true != false ) )
| ~ ( ( true != err ) ) )
| ~ ( ( false != err ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(190,plain,
! [SV19: $i] :
( ( ! [SY90: $i] :
~ ! [SY91: $i] :
~ ~ ( ( ( lazy_and2 @ SV19 @ SY90 )
!= ( phi @ ( f2 @ SV19 @ SY90 @ SY91 ) ) )
| ~ ~ ~ ! [SY92: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SY90 @ SY92 ) @ ( f2 @ SV19 @ SY90 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(191,plain,
! [SV20: $i] :
( ( ! [SY93: $i] :
~ ( ~ ( ~ ( forallprefers @ SV20 @ SY93 )
| ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SY93 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SY93 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SY93 ) )
| ~ ( ( SV20 != false )
| ( SY93 != true ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SY93 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SY93 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SY93 ) )
| ~ ( ( SV20 != false )
| ( SY93 != true ) ) )
| ( forallprefers @ SV20 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(192,plain,
! [SV21: $i] :
( ( ! [SY94: $i] :
( ~ ~ ( bool @ SV21 )
| ( ( impl @ SV21 @ SY94 )
= ( phi @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(193,plain,
! [SV22: $i] :
( ( ~ ~ ( bool @ SV22 )
| ( ( not1 @ SV22 )
= ( phi @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(194,plain,
! [SV23: $i] :
( ( ~ ( bool @ SV23 )
| ( ( and1 @ true @ SV23 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(195,plain,
! [SV24: $i] :
( ( ! [SY95: $i] :
( ~ ~ ( bool @ SV24 )
| ( ( and1 @ SV24 @ SY95 )
= ( phi @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(196,plain,
! [SV25: $i] :
( ( ~ ! [SY96: $i] :
~ ~ ( ( ( exists2 @ SV25 )
!= ( phi @ ( f6 @ SV25 @ SY96 ) ) )
| ~ ~ ~ ! [SY97: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY97 ) @ ( f6 @ SV25 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(197,plain,
! [SV26: $i] :
( ( ! [SY98: $i] :
( ~ ~ ( bool @ SV26 )
| ( ( or1 @ SV26 @ SY98 )
= ( phi @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(198,plain,
! [SV27: $i] :
( ( ~ ( ~ ( ~ ( bool @ SV27 )
| ( SV27 = false )
| ( SV27 = true ) )
| ~ ( ~ ( ( SV27 = false )
| ( SV27 = true ) )
| ( bool @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(199,plain,
! [SV28: $i] :
( ( ! [SY99: $i] :
( ~ ~ ( ~ ( bool @ SV28 )
| ~ ~ ( bool @ SY99 ) )
| ( ( or1 @ SV28 @ SY99 )
= ( phi @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(200,plain,
! [SV29: $i] :
( ( ! [SY100: $i] :
~ ! [SY101: $i] :
~ ~ ( ( ( f5 @ SV29 @ SY100 )
!= ( phi @ ( f4 @ SV29 @ SY101 @ SY100 ) ) )
| ~ ~ ~ ! [SY102: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY102 @ SY100 ) @ ( f4 @ SV29 @ SY101 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(201,plain,
! [SV30: $i] :
( ( ~ ! [SY103: $i] :
~ ~ ( ( ( exists1 @ SV30 )
!= ( phi @ ( apply @ SV30 @ SY103 ) ) )
| ~ ~ ~ ! [SY104: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY104 ) @ ( apply @ SV30 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(202,plain,
! [SV31: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( bool @ SV31 )
| ( ( lazy_impl @ SV31 @ SY105 )
= ( phi @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(203,plain,
! [SV32: $i] :
( ( ~ ( ~ ( ( ( prop @ SV32 )
!= false )
| ~ ( bool @ SV32 ) )
| ~ ( ~ ~ ( bool @ SV32 )
| ( ( prop @ SV32 )
= false ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(204,plain,
! [SV33: $i] :
( ( ~ ( bool @ SV33 )
| ( ( or1 @ false @ SV33 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(205,plain,
! [SV34: $i] :
( ( ! [SY106: $i] :
~ ! [SY107: $i] :
~ ~ ( ( ( or2 @ SV34 @ SY106 )
!= ( phi @ ( f3 @ SV34 @ SY106 @ SY107 ) ) )
| ~ ~ ~ ! [SY108: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SY106 @ SY108 ) @ ( f3 @ SV34 @ SY106 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(206,plain,
! [SV35: $i] :
( ( ~ ( bool @ SV35 )
| ( ( or1 @ true @ SV35 )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(207,plain,
! [SV36: $i] :
( ( ! [SY109: $i] :
( ~ ~ ( ~ ( bool @ SV36 )
| ~ ~ ( bool @ SY109 ) )
| ( ( impl @ SV36 @ SY109 )
= ( phi @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(208,plain,
! [SV37: $i] :
( ( ~ ( bool @ SV37 )
| ( ( impl @ false @ SV37 )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(209,plain,
! [SV38: $i] :
( ( ~ ( bool @ SV38 )
| ( ( impl @ true @ SV38 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(210,plain,
! [SV39: $i,SV3: $i] :
( ( ! [SY110: $i] :
( ( f1 @ SV3 @ SV39 @ SY110 )
= ( lazy_impl @ ( prop @ SY110 ) @ ( impl @ ( impl @ SV3 @ ( impl @ SV39 @ SY110 ) ) @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(211,plain,
! [SV40: $i,SV6: $i] :
( ( ! [SY111: $i] :
( ( f2 @ SV6 @ SV40 @ SY111 )
= ( lazy_impl @ ( prop @ SY111 ) @ ( impl @ ( lazy_impl @ SV6 @ ( impl @ SV40 @ SY111 ) ) @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(212,plain,
! [SV41: $i,SV7: $i] :
( ( ! [SY112: $i] :
( ( f3 @ SV7 @ SV41 @ SY112 )
= ( lazy_impl @ ( prop @ SY112 ) @ ( impl @ ( impl @ SV7 @ SY112 ) @ ( impl @ ( impl @ SV41 @ SY112 ) @ SY112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(213,plain,
! [SV42: $i,SV8: $i] :
( ( ! [SY113: $i] :
( ( f4 @ SV8 @ SV42 @ SY113 )
= ( impl @ ( apply @ SV8 @ SV42 ) @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(214,plain,
! [SV43: $i,SV9: $i] :
( ( ( f6 @ SV9 @ SV43 )
= ( lazy_impl @ ( prop @ SV43 ) @ ( impl @ ( f5 @ SV9 @ SV43 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(215,plain,
( ( ~ ~ ( ~ ( d @ true )
| ~ ( d @ false ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(216,plain,
( ( ~ ( d @ err ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(217,plain,
! [SV44: $i,SV12: $i] :
( ( ~ ~ ( bool @ SV12 )
| ( ( lazy_and1 @ SV12 @ SV44 )
= ( phi @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(218,plain,
! [SV13: $i] :
( ( ~ ( ( ( prop @ SV13 )
!= true )
| ( bool @ SV13 ) )
| ~ ( ~ ( bool @ SV13 )
| ( ( prop @ SV13 )
= true ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(219,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( existsprefers @ SV14 @ SV45 )
| ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
| ( existsprefers @ SV14 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(220,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ! [SY114: $i] :
~ ~ ( ( ( and2 @ SV15 @ SV46 )
!= ( phi @ ( f1 @ SV15 @ SV46 @ SY114 ) ) )
| ~ ~ ~ ! [SY115: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY115 ) @ ( f1 @ SV15 @ SV46 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(221,plain,
! [SV16: $i] :
( ( ( ~ ( bool @ SV16 ) )
= $true )
| ( ( ( and1 @ false @ SV16 )
= false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(222,plain,
( ( ~ ~ ( ( false2
!= ( phi @ ( f7 @ sK1_SX0 ) ) )
| ~ ~ ~ ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[186]) ).
thf(223,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= SV17 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV47: $i,SV18: $i] :
( ( ~ ~ ( ~ ( bool @ SV18 )
| ~ ~ ( bool @ SV47 ) )
| ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
( ( ~ ~ ( ~ ( ( true != false ) )
| ~ ( ( true != err ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(226,plain,
( ( ~ ( ( false != err ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(227,plain,
! [SV48: $i,SV19: $i] :
( ( ~ ! [SY117: $i] :
~ ~ ( ( ( lazy_and2 @ SV19 @ SV48 )
!= ( phi @ ( f2 @ SV19 @ SV48 @ SY117 ) ) )
| ~ ~ ~ ! [SY118: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY118 ) @ ( f2 @ SV19 @ SV48 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(228,plain,
! [SV49: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( forallprefers @ SV20 @ SV49 )
| ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
| ( forallprefers @ SV20 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV50: $i,SV21: $i] :
( ( ~ ~ ( bool @ SV21 )
| ( ( impl @ SV21 @ SV50 )
= ( phi @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV22: $i] :
( ( ( ~ ~ ( bool @ SV22 ) )
= $true )
| ( ( ( not1 @ SV22 )
= ( phi @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(231,plain,
! [SV23: $i] :
( ( ( ~ ( bool @ SV23 ) )
= $true )
| ( ( ( and1 @ true @ SV23 )
= SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(232,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ~ ( bool @ SV24 )
| ( ( and1 @ SV24 @ SV51 )
= ( phi @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(233,plain,
! [SV25: $i] :
( ( ! [SY96: $i] :
~ ~ ( ( ( exists2 @ SV25 )
!= ( phi @ ( f6 @ SV25 @ SY96 ) ) )
| ~ ~ ~ ! [SY97: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY97 ) @ ( f6 @ SV25 @ SY96 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(234,plain,
! [SV52: $i,SV26: $i] :
( ( ~ ~ ( bool @ SV26 )
| ( ( or1 @ SV26 @ SV52 )
= ( phi @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(235,plain,
! [SV27: $i] :
( ( ~ ( ~ ( bool @ SV27 )
| ( SV27 = false )
| ( SV27 = true ) )
| ~ ( ~ ( ( SV27 = false )
| ( SV27 = true ) )
| ( bool @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(236,plain,
! [SV53: $i,SV28: $i] :
( ( ~ ~ ( ~ ( bool @ SV28 )
| ~ ~ ( bool @ SV53 ) )
| ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(237,plain,
! [SV54: $i,SV29: $i] :
( ( ~ ! [SY119: $i] :
~ ~ ( ( ( f5 @ SV29 @ SV54 )
!= ( phi @ ( f4 @ SV29 @ SY119 @ SV54 ) ) )
| ~ ~ ~ ! [SY120: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY120 @ SV54 ) @ ( f4 @ SV29 @ SY119 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(238,plain,
! [SV30: $i] :
( ( ! [SY103: $i] :
~ ~ ( ( ( exists1 @ SV30 )
!= ( phi @ ( apply @ SV30 @ SY103 ) ) )
| ~ ~ ~ ! [SY104: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY104 ) @ ( apply @ SV30 @ SY103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(239,plain,
! [SV55: $i,SV31: $i] :
( ( ~ ~ ( bool @ SV31 )
| ( ( lazy_impl @ SV31 @ SV55 )
= ( phi @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(240,plain,
! [SV32: $i] :
( ( ~ ( ( ( prop @ SV32 )
!= false )
| ~ ( bool @ SV32 ) )
| ~ ( ~ ~ ( bool @ SV32 )
| ( ( prop @ SV32 )
= false ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV33: $i] :
( ( ( ~ ( bool @ SV33 ) )
= $true )
| ( ( ( or1 @ false @ SV33 )
= SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV56: $i,SV34: $i] :
( ( ~ ! [SY121: $i] :
~ ~ ( ( ( or2 @ SV34 @ SV56 )
!= ( phi @ ( f3 @ SV34 @ SV56 @ SY121 ) ) )
| ~ ~ ~ ! [SY122: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY122 ) @ ( f3 @ SV34 @ SV56 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV35: $i] :
( ( ( ~ ( bool @ SV35 ) )
= $true )
| ( ( ( or1 @ true @ SV35 )
= true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV57: $i,SV36: $i] :
( ( ~ ~ ( ~ ( bool @ SV36 )
| ~ ~ ( bool @ SV57 ) )
| ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV37: $i] :
( ( ( ~ ( bool @ SV37 ) )
= $true )
| ( ( ( impl @ false @ SV37 )
= true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV38: $i] :
( ( ( ~ ( bool @ SV38 ) )
= $true )
| ( ( ( impl @ true @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV58: $i,SV39: $i,SV3: $i] :
( ( ( f1 @ SV3 @ SV39 @ SV58 )
= ( lazy_impl @ ( prop @ SV58 ) @ ( impl @ ( impl @ SV3 @ ( impl @ SV39 @ SV58 ) ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(248,plain,
! [SV59: $i,SV40: $i,SV6: $i] :
( ( ( f2 @ SV6 @ SV40 @ SV59 )
= ( lazy_impl @ ( prop @ SV59 ) @ ( impl @ ( lazy_impl @ SV6 @ ( impl @ SV40 @ SV59 ) ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(249,plain,
! [SV60: $i,SV41: $i,SV7: $i] :
( ( ( f3 @ SV7 @ SV41 @ SV60 )
= ( lazy_impl @ ( prop @ SV60 ) @ ( impl @ ( impl @ SV7 @ SV60 ) @ ( impl @ ( impl @ SV41 @ SV60 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(250,plain,
! [SV61: $i,SV42: $i,SV8: $i] :
( ( ( f4 @ SV8 @ SV42 @ SV61 )
= ( impl @ ( apply @ SV8 @ SV42 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(251,plain,
( ( ~ ( ~ ( d @ true )
| ~ ( d @ false ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(252,plain,
( ( d @ err )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(253,plain,
! [SV44: $i,SV12: $i] :
( ( ( ~ ~ ( bool @ SV12 ) )
= $true )
| ( ( ( lazy_and1 @ SV12 @ SV44 )
= ( phi @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(254,plain,
! [SV13: $i] :
( ( ~ ( ( ( prop @ SV13 )
!= true )
| ( bool @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(255,plain,
! [SV13: $i] :
( ( ~ ( ~ ( bool @ SV13 )
| ( ( prop @ SV13 )
= true ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(256,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( existsprefers @ SV14 @ SV45 )
| ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
| ( existsprefers @ SV14 @ SV45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(257,plain,
! [SV46: $i,SV15: $i] :
( ( ! [SY114: $i] :
~ ~ ( ( ( and2 @ SV15 @ SV46 )
!= ( phi @ ( f1 @ SV15 @ SV46 @ SY114 ) ) )
| ~ ~ ~ ! [SY115: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY115 ) @ ( f1 @ SV15 @ SV46 @ SY114 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(258,plain,
! [SV16: $i] :
( ( ( bool @ SV16 )
= $false )
| ( ( ( and1 @ false @ SV16 )
= false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(259,plain,
( ( ~ ( ( false2
!= ( phi @ ( f7 @ sK1_SX0 ) ) )
| ~ ~ ~ ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(260,plain,
! [SV17: $i] :
( ( ( ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= SV17 ) )
= $false )
| ( ( ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(261,plain,
! [SV47: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( bool @ SV18 )
| ~ ~ ( bool @ SV47 ) ) )
= $true )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(262,plain,
( ( ~ ( ~ ( ( true != false ) )
| ~ ( ( true != err ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(263,plain,
( ( false != err )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(264,plain,
! [SV48: $i,SV19: $i] :
( ( ! [SY117: $i] :
~ ~ ( ( ( lazy_and2 @ SV19 @ SV48 )
!= ( phi @ ( f2 @ SV19 @ SV48 @ SY117 ) ) )
| ~ ~ ~ ! [SY118: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY118 ) @ ( f2 @ SV19 @ SV48 @ SY117 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(265,plain,
! [SV49: $i,SV20: $i] :
( ( ~ ( ~ ( forallprefers @ SV20 @ SV49 )
| ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
| ~ ( ~ ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
| ( forallprefers @ SV20 @ SV49 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(266,plain,
! [SV50: $i,SV21: $i] :
( ( ( ~ ~ ( bool @ SV21 ) )
= $true )
| ( ( ( impl @ SV21 @ SV50 )
= ( phi @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(267,plain,
! [SV22: $i] :
( ( ( ~ ( bool @ SV22 ) )
= $false )
| ( ( ( not1 @ SV22 )
= ( phi @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(268,plain,
! [SV23: $i] :
( ( ( bool @ SV23 )
= $false )
| ( ( ( and1 @ true @ SV23 )
= SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(269,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ~ ( bool @ SV24 ) )
= $true )
| ( ( ( and1 @ SV24 @ SV51 )
= ( phi @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(270,plain,
! [SV25: $i] :
( ( ~ ~ ( ( ( exists2 @ SV25 )
!= ( phi @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
| ~ ~ ~ ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(271,plain,
! [SV52: $i,SV26: $i] :
( ( ( ~ ~ ( bool @ SV26 ) )
= $true )
| ( ( ( or1 @ SV26 @ SV52 )
= ( phi @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(272,plain,
! [SV27: $i] :
( ( ~ ( ~ ( bool @ SV27 )
| ( SV27 = false )
| ( SV27 = true ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(273,plain,
! [SV27: $i] :
( ( ~ ( ~ ( ( SV27 = false )
| ( SV27 = true ) )
| ( bool @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(274,plain,
! [SV53: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( bool @ SV28 )
| ~ ~ ( bool @ SV53 ) ) )
= $true )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(275,plain,
! [SV54: $i,SV29: $i] :
( ( ! [SY119: $i] :
~ ~ ( ( ( f5 @ SV29 @ SV54 )
!= ( phi @ ( f4 @ SV29 @ SY119 @ SV54 ) ) )
| ~ ~ ~ ! [SY120: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY120 @ SV54 ) @ ( f4 @ SV29 @ SY119 @ SV54 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(276,plain,
! [SV30: $i] :
( ( ~ ~ ( ( ( exists1 @ SV30 )
!= ( phi @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
| ~ ~ ~ ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(277,plain,
! [SV55: $i,SV31: $i] :
( ( ( ~ ~ ( bool @ SV31 ) )
= $true )
| ( ( ( lazy_impl @ SV31 @ SV55 )
= ( phi @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(278,plain,
! [SV32: $i] :
( ( ~ ( ( ( prop @ SV32 )
!= false )
| ~ ( bool @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(279,plain,
! [SV32: $i] :
( ( ~ ( ~ ~ ( bool @ SV32 )
| ( ( prop @ SV32 )
= false ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(280,plain,
! [SV33: $i] :
( ( ( bool @ SV33 )
= $false )
| ( ( ( or1 @ false @ SV33 )
= SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(281,plain,
! [SV56: $i,SV34: $i] :
( ( ! [SY121: $i] :
~ ~ ( ( ( or2 @ SV34 @ SV56 )
!= ( phi @ ( f3 @ SV34 @ SV56 @ SY121 ) ) )
| ~ ~ ~ ! [SY122: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY122 ) @ ( f3 @ SV34 @ SV56 @ SY121 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(282,plain,
! [SV35: $i] :
( ( ( bool @ SV35 )
= $false )
| ( ( ( or1 @ true @ SV35 )
= true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(283,plain,
! [SV57: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( bool @ SV36 )
| ~ ~ ( bool @ SV57 ) ) )
= $true )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(284,plain,
! [SV37: $i] :
( ( ( bool @ SV37 )
= $false )
| ( ( ( impl @ false @ SV37 )
= true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(285,plain,
! [SV38: $i] :
( ( ( bool @ SV38 )
= $false )
| ( ( ( impl @ true @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(286,plain,
( ( ~ ( d @ true )
| ~ ( d @ false ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(287,plain,
! [SV44: $i,SV12: $i] :
( ( ( ~ ( bool @ SV12 ) )
= $false )
| ( ( ( lazy_and1 @ SV12 @ SV44 )
= ( phi @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(288,plain,
! [SV13: $i] :
( ( ( ( prop @ SV13 )
!= true )
| ( bool @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(289,plain,
! [SV13: $i] :
( ( ~ ( bool @ SV13 )
| ( ( prop @ SV13 )
= true ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(290,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( existsprefers @ SV14 @ SV45 )
| ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(291,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
| ( existsprefers @ SV14 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(292,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ~ ( ( ( and2 @ SV15 @ SV46 )
!= ( phi @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
| ~ ~ ~ ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(293,plain,
( ( ( false2
!= ( phi @ ( f7 @ sK1_SX0 ) ) )
| ~ ~ ~ ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(294,plain,
! [SV17: $i] :
( ( ( ~ ( d @ SV17 ) )
= $false )
| ( ( ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(295,plain,
! [SV17: $i] :
( ( ( ( phi @ SV17 )
!= SV17 )
= $false )
| ( ( ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(296,plain,
! [SV47: $i,SV18: $i] :
( ( ( ~ ( ~ ( bool @ SV18 )
| ~ ~ ( bool @ SV47 ) ) )
= $false )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(297,plain,
( ( ~ ( ( true != false ) )
| ~ ( ( true != err ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(298,plain,
( ( false = err )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(299,plain,
! [SV48: $i,SV19: $i] :
( ( ~ ~ ( ( ( lazy_and2 @ SV19 @ SV48 )
!= ( phi @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
| ~ ~ ~ ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[264]) ).
thf(300,plain,
! [SV49: $i,SV20: $i] :
( ( ~ ( ~ ( forallprefers @ SV20 @ SV49 )
| ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(301,plain,
! [SV49: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
| ( forallprefers @ SV20 @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(302,plain,
! [SV50: $i,SV21: $i] :
( ( ( ~ ( bool @ SV21 ) )
= $false )
| ( ( ( impl @ SV21 @ SV50 )
= ( phi @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(303,plain,
! [SV22: $i] :
( ( ( bool @ SV22 )
= $true )
| ( ( ( not1 @ SV22 )
= ( phi @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(304,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( bool @ SV24 ) )
= $false )
| ( ( ( and1 @ SV24 @ SV51 )
= ( phi @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(305,plain,
! [SV25: $i] :
( ( ~ ( ( ( exists2 @ SV25 )
!= ( phi @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
| ~ ~ ~ ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(306,plain,
! [SV52: $i,SV26: $i] :
( ( ( ~ ( bool @ SV26 ) )
= $false )
| ( ( ( or1 @ SV26 @ SV52 )
= ( phi @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(307,plain,
! [SV27: $i] :
( ( ~ ( bool @ SV27 )
| ( SV27 = false )
| ( SV27 = true ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(308,plain,
! [SV27: $i] :
( ( ~ ( ( SV27 = false )
| ( SV27 = true ) )
| ( bool @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(309,plain,
! [SV53: $i,SV28: $i] :
( ( ( ~ ( ~ ( bool @ SV28 )
| ~ ~ ( bool @ SV53 ) ) )
= $false )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(310,plain,
! [SV54: $i,SV29: $i] :
( ( ~ ~ ( ( ( f5 @ SV29 @ SV54 )
!= ( phi @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
| ~ ~ ~ ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[275]) ).
thf(311,plain,
! [SV30: $i] :
( ( ~ ( ( ( exists1 @ SV30 )
!= ( phi @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
| ~ ~ ~ ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(312,plain,
! [SV55: $i,SV31: $i] :
( ( ( ~ ( bool @ SV31 ) )
= $false )
| ( ( ( lazy_impl @ SV31 @ SV55 )
= ( phi @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(313,plain,
! [SV32: $i] :
( ( ( ( prop @ SV32 )
!= false )
| ~ ( bool @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(314,plain,
! [SV32: $i] :
( ( ~ ~ ( bool @ SV32 )
| ( ( prop @ SV32 )
= false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(315,plain,
! [SV56: $i,SV34: $i] :
( ( ~ ~ ( ( ( or2 @ SV34 @ SV56 )
!= ( phi @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
| ~ ~ ~ ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[281]) ).
thf(316,plain,
! [SV57: $i,SV36: $i] :
( ( ( ~ ( ~ ( bool @ SV36 )
| ~ ~ ( bool @ SV57 ) ) )
= $false )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(317,plain,
( ( ~ ( d @ true ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(318,plain,
( ( ~ ( d @ false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(319,plain,
! [SV44: $i,SV12: $i] :
( ( ( bool @ SV12 )
= $true )
| ( ( ( lazy_and1 @ SV12 @ SV44 )
= ( phi @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(320,plain,
! [SV13: $i] :
( ( ( ( prop @ SV13 )
!= true )
= $true )
| ( ( bool @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV13: $i] :
( ( ( ~ ( bool @ SV13 ) )
= $true )
| ( ( ( prop @ SV13 )
= true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( existsprefers @ SV14 @ SV45 )
| ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(323,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
| ( existsprefers @ SV14 @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(324,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ( ( ( and2 @ SV15 @ SV46 )
!= ( phi @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
| ~ ~ ~ ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(325,plain,
( ( false2
!= ( phi @ ( f7 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(326,plain,
( ( ~ ~ ~ ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(327,plain,
! [SV17: $i] :
( ( ( d @ SV17 )
= $true )
| ( ( ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(328,plain,
! [SV17: $i] :
( ( ( ( phi @ SV17 )
= SV17 )
= $true )
| ( ( ~ ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(329,plain,
! [SV47: $i,SV18: $i] :
( ( ( ~ ( bool @ SV18 )
| ~ ~ ( bool @ SV47 ) )
= $true )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(330,plain,
( ( ~ ( ( true != false ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(331,plain,
( ( ~ ( ( true != err ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(332,plain,
! [SV48: $i,SV19: $i] :
( ( ~ ( ( ( lazy_and2 @ SV19 @ SV48 )
!= ( phi @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
| ~ ~ ~ ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(333,plain,
! [SV49: $i,SV20: $i] :
( ( ~ ( forallprefers @ SV20 @ SV49 )
| ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(334,plain,
! [SV49: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
| ( forallprefers @ SV20 @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(335,plain,
! [SV50: $i,SV21: $i] :
( ( ( bool @ SV21 )
= $true )
| ( ( ( impl @ SV21 @ SV50 )
= ( phi @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(336,plain,
! [SV51: $i,SV24: $i] :
( ( ( bool @ SV24 )
= $true )
| ( ( ( and1 @ SV24 @ SV51 )
= ( phi @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(337,plain,
! [SV25: $i] :
( ( ( ( exists2 @ SV25 )
!= ( phi @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
| ~ ~ ~ ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(338,plain,
! [SV52: $i,SV26: $i] :
( ( ( bool @ SV26 )
= $true )
| ( ( ( or1 @ SV26 @ SV52 )
= ( phi @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(339,plain,
! [SV27: $i] :
( ( ( ~ ( bool @ SV27 ) )
= $true )
| ( ( ( SV27 = false )
| ( SV27 = true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(340,plain,
! [SV27: $i] :
( ( ( ~ ( ( SV27 = false )
| ( SV27 = true ) ) )
= $true )
| ( ( bool @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(341,plain,
! [SV53: $i,SV28: $i] :
( ( ( ~ ( bool @ SV28 )
| ~ ~ ( bool @ SV53 ) )
= $true )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(342,plain,
! [SV54: $i,SV29: $i] :
( ( ~ ( ( ( f5 @ SV29 @ SV54 )
!= ( phi @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
| ~ ~ ~ ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(343,plain,
! [SV30: $i] :
( ( ( ( exists1 @ SV30 )
!= ( phi @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
| ~ ~ ~ ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(344,plain,
! [SV55: $i,SV31: $i] :
( ( ( bool @ SV31 )
= $true )
| ( ( ( lazy_impl @ SV31 @ SV55 )
= ( phi @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(345,plain,
! [SV32: $i] :
( ( ( ( prop @ SV32 )
!= false )
= $true )
| ( ( ~ ( bool @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(346,plain,
! [SV32: $i] :
( ( ( ~ ~ ( bool @ SV32 ) )
= $true )
| ( ( ( prop @ SV32 )
= false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(347,plain,
! [SV56: $i,SV34: $i] :
( ( ~ ( ( ( or2 @ SV34 @ SV56 )
!= ( phi @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
| ~ ~ ~ ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(348,plain,
! [SV57: $i,SV36: $i] :
( ( ( ~ ( bool @ SV36 )
| ~ ~ ( bool @ SV57 ) )
= $true )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(349,plain,
( ( d @ true )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(350,plain,
( ( d @ false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(351,plain,
! [SV13: $i] :
( ( ( ( prop @ SV13 )
= true )
= $false )
| ( ( bool @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(352,plain,
! [SV13: $i] :
( ( ( bool @ SV13 )
= $false )
| ( ( ( prop @ SV13 )
= true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(353,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( existsprefers @ SV14 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(354,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(355,plain,
! [SV46: $i,SV15: $i] :
( ( ( ( and2 @ SV15 @ SV46 )
!= ( phi @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
| ~ ~ ~ ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(356,plain,
( ( false2
= ( phi @ ( f7 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(357,plain,
( ( ~ ~ ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(358,plain,
! [SV17: $i] :
( ( ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) )
= $false )
| ( ( d @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(359,plain,
! [SV17: $i] :
( ( ( ~ ~ ( d @ SV17 )
| ( ( phi @ SV17 )
!= err ) )
= $false )
| ( ( ( phi @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(360,plain,
! [SV47: $i,SV18: $i] :
( ( ( ~ ( bool @ SV18 ) )
= $true )
| ( ( ~ ~ ( bool @ SV47 ) )
= $true )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(361,plain,
( ( true != false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(362,plain,
( ( true != err )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(363,plain,
! [SV48: $i,SV19: $i] :
( ( ( ( lazy_and2 @ SV19 @ SV48 )
!= ( phi @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
| ~ ~ ~ ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(364,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( forallprefers @ SV20 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(365,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(366,plain,
! [SV25: $i] :
( ( ( exists2 @ SV25 )
!= ( phi @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(367,plain,
! [SV25: $i] :
( ( ~ ~ ~ ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(368,plain,
! [SV27: $i] :
( ( ( bool @ SV27 )
= $false )
| ( ( ( SV27 = false )
| ( SV27 = true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(369,plain,
! [SV27: $i] :
( ( ( ( SV27 = false )
| ( SV27 = true ) )
= $false )
| ( ( bool @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(370,plain,
! [SV53: $i,SV28: $i] :
( ( ( ~ ( bool @ SV28 ) )
= $true )
| ( ( ~ ~ ( bool @ SV53 ) )
= $true )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(371,plain,
! [SV54: $i,SV29: $i] :
( ( ( ( f5 @ SV29 @ SV54 )
!= ( phi @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
| ~ ~ ~ ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(372,plain,
! [SV30: $i] :
( ( ( exists1 @ SV30 )
!= ( phi @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(373,plain,
! [SV30: $i] :
( ( ~ ~ ~ ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(374,plain,
! [SV32: $i] :
( ( ( ( prop @ SV32 )
= false )
= $false )
| ( ( ~ ( bool @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(375,plain,
! [SV32: $i] :
( ( ( ~ ( bool @ SV32 ) )
= $false )
| ( ( ( prop @ SV32 )
= false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(376,plain,
! [SV56: $i,SV34: $i] :
( ( ( ( or2 @ SV34 @ SV56 )
!= ( phi @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
| ~ ~ ~ ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(377,plain,
! [SV57: $i,SV36: $i] :
( ( ( ~ ( bool @ SV36 ) )
= $true )
| ( ( ~ ~ ( bool @ SV57 ) )
= $true )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(378,plain,
! [SV45: $i,SV14: $i] :
( ( ( existsprefers @ SV14 @ SV45 )
= $false )
| ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(379,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
| ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(380,plain,
! [SV46: $i,SV15: $i] :
( ( ( and2 @ SV15 @ SV46 )
!= ( phi @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(381,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ~ ~ ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(382,plain,
( ( ~ ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(383,plain,
! [SV17: $i] :
( ( ( ~ ~ ( d @ SV17 ) )
= $false )
| ( ( d @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(384,plain,
! [SV17: $i] :
( ( ( ( phi @ SV17 )
!= err )
= $false )
| ( ( d @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(385,plain,
! [SV17: $i] :
( ( ( ~ ~ ( d @ SV17 ) )
= $false )
| ( ( ( phi @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(386,plain,
! [SV17: $i] :
( ( ( ( phi @ SV17 )
!= err )
= $false )
| ( ( ( phi @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(387,plain,
! [SV47: $i,SV18: $i] :
( ( ( bool @ SV18 )
= $false )
| ( ( ~ ~ ( bool @ SV47 ) )
= $true )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(388,plain,
( ( true = false )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(389,plain,
( ( true = err )
= $false ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(390,plain,
! [SV48: $i,SV19: $i] :
( ( ( lazy_and2 @ SV19 @ SV48 )
!= ( phi @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(391,plain,
! [SV48: $i,SV19: $i] :
( ( ~ ~ ~ ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(392,plain,
! [SV49: $i,SV20: $i] :
( ( ( forallprefers @ SV20 @ SV49 )
= $false )
| ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(393,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
| ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(394,plain,
! [SV25: $i] :
( ( ( exists2 @ SV25 )
= ( phi @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(395,plain,
! [SV25: $i] :
( ( ~ ~ ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(396,plain,
! [SV27: $i] :
( ( ( SV27 = false )
= $true )
| ( ( SV27 = true )
= $true )
| ( ( bool @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(397,plain,
! [SV27: $i] :
( ( ( SV27 = false )
= $false )
| ( ( bool @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(398,plain,
! [SV27: $i] :
( ( ( SV27 = true )
= $false )
| ( ( bool @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(399,plain,
! [SV53: $i,SV28: $i] :
( ( ( bool @ SV28 )
= $false )
| ( ( ~ ~ ( bool @ SV53 ) )
= $true )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(400,plain,
! [SV54: $i,SV29: $i] :
( ( ( f5 @ SV29 @ SV54 )
!= ( phi @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(401,plain,
! [SV54: $i,SV29: $i] :
( ( ~ ~ ~ ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(402,plain,
! [SV30: $i] :
( ( ( exists1 @ SV30 )
= ( phi @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(403,plain,
! [SV30: $i] :
( ( ~ ~ ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(404,plain,
! [SV32: $i] :
( ( ( bool @ SV32 )
= $false )
| ( ( ( prop @ SV32 )
= false )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(405,plain,
! [SV32: $i] :
( ( ( bool @ SV32 )
= $true )
| ( ( ( prop @ SV32 )
= false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(406,plain,
! [SV56: $i,SV34: $i] :
( ( ( or2 @ SV34 @ SV56 )
!= ( phi @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(407,plain,
! [SV56: $i,SV34: $i] :
( ( ~ ~ ~ ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(408,plain,
! [SV57: $i,SV36: $i] :
( ( ( bool @ SV36 )
= $false )
| ( ( ~ ~ ( bool @ SV57 ) )
= $true )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(409,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(410,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(411,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(412,plain,
! [SV46: $i,SV15: $i] :
( ( ( and2 @ SV15 @ SV46 )
= ( phi @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(413,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ~ ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(414,plain,
( ( ! [SY116: $i] :
~ ( forallprefers @ ( f7 @ SY116 ) @ ( f7 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(415,plain,
! [SV17: $i] :
( ( ( ~ ( d @ SV17 ) )
= $true )
| ( ( d @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(416,plain,
! [SV17: $i] :
( ( ( ( phi @ SV17 )
= err )
= $true )
| ( ( d @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(417,plain,
! [SV17: $i] :
( ( ( ~ ( d @ SV17 ) )
= $true )
| ( ( ( phi @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(418,plain,
! [SV17: $i] :
( ( ( ( phi @ SV17 )
= err )
= $true )
| ( ( ( phi @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(419,plain,
! [SV18: $i,SV47: $i] :
( ( ( ~ ( bool @ SV47 ) )
= $false )
| ( ( bool @ SV18 )
= $false )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(420,plain,
! [SV48: $i,SV19: $i] :
( ( ( lazy_and2 @ SV19 @ SV48 )
= ( phi @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(421,plain,
! [SV48: $i,SV19: $i] :
( ( ~ ~ ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(422,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(423,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(424,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(425,plain,
! [SV25: $i] :
( ( ~ ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(426,plain,
! [SV28: $i,SV53: $i] :
( ( ( ~ ( bool @ SV53 ) )
= $false )
| ( ( bool @ SV28 )
= $false )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(427,plain,
! [SV54: $i,SV29: $i] :
( ( ( f5 @ SV29 @ SV54 )
= ( phi @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(428,plain,
! [SV54: $i,SV29: $i] :
( ( ~ ~ ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(429,plain,
! [SV30: $i] :
( ( ~ ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(430,plain,
! [SV56: $i,SV34: $i] :
( ( ( or2 @ SV34 @ SV56 )
= ( phi @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(431,plain,
! [SV56: $i,SV34: $i] :
( ( ~ ~ ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(432,plain,
! [SV36: $i,SV57: $i] :
( ( ( ~ ( bool @ SV57 ) )
= $false )
| ( ( bool @ SV36 )
= $false )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(433,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(434,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(435,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(436,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(437,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(438,plain,
! [SV62: $i] :
( ( ~ ( forallprefers @ ( f7 @ SV62 ) @ ( f7 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(439,plain,
! [SV17: $i] :
( ( ( d @ SV17 )
= $false )
| ( ( d @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(440,plain,
! [SV17: $i] :
( ( ( d @ SV17 )
= $false )
| ( ( ( phi @ SV17 )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(441,plain,
! [SV18: $i,SV47: $i] :
( ( ( bool @ SV47 )
= $true )
| ( ( bool @ SV18 )
= $false )
| ( ( ( and1 @ SV18 @ SV47 )
= ( phi @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(442,plain,
! [SV48: $i,SV19: $i] :
( ( ~ ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(443,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(444,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(445,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(446,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(447,plain,
! [SV25: $i] :
( ( ! [SY123: $i] :
~ ( forallprefers @ ( f6 @ SV25 @ SY123 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(448,plain,
! [SV28: $i,SV53: $i] :
( ( ( bool @ SV53 )
= $true )
| ( ( bool @ SV28 )
= $false )
| ( ( ( or1 @ SV28 @ SV53 )
= ( phi @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(449,plain,
! [SV54: $i,SV29: $i] :
( ( ~ ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(450,plain,
! [SV30: $i] :
( ( ! [SY124: $i] :
~ ( existsprefers @ ( apply @ SV30 @ SY124 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(451,plain,
! [SV56: $i,SV34: $i] :
( ( ~ ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(452,plain,
! [SV36: $i,SV57: $i] :
( ( ( bool @ SV57 )
= $true )
| ( ( bool @ SV36 )
= $false )
| ( ( ( impl @ SV36 @ SV57 )
= ( phi @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(453,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(454,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(455,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(456,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $true )
| ( ( SV45 != false )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(457,plain,
! [SV46: $i,SV15: $i] :
( ( ! [SY125: $i] :
~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SY125 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(458,plain,
! [SV62: $i] :
( ( forallprefers @ ( f7 @ SV62 ) @ ( f7 @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(459,plain,
! [SV48: $i,SV19: $i] :
( ( ! [SY126: $i] :
~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SY126 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(460,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(461,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(462,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(463,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $true )
| ( ( SV49 != true )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(464,plain,
! [SV63: $i,SV25: $i] :
( ( ~ ( forallprefers @ ( f6 @ SV25 @ SV63 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(465,plain,
! [SV54: $i,SV29: $i] :
( ( ! [SY127: $i] :
~ ( forallprefers @ ( f4 @ SV29 @ SY127 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(466,plain,
! [SV64: $i,SV30: $i] :
( ( ~ ( existsprefers @ ( apply @ SV30 @ SV64 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(467,plain,
! [SV56: $i,SV34: $i] :
( ( ! [SY128: $i] :
~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SY128 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(468,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( d @ SV14 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(469,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( d @ SV45 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(470,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( d @ SV14 ) )
= $true )
| ( ( ~ ( d @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(471,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(472,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $false )
| ( ( SV45 != false )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(473,plain,
! [SV65: $i,SV46: $i,SV15: $i] :
( ( ~ ( forallprefers @ ( f1 @ SV15 @ SV46 @ SV65 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(474,plain,
! [SV66: $i,SV48: $i,SV19: $i] :
( ( ~ ( forallprefers @ ( f2 @ SV19 @ SV48 @ SV66 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(475,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( d @ SV20 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(476,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( d @ SV49 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(477,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( d @ SV20 ) )
= $true )
| ( ( ~ ( d @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(478,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(479,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $false )
| ( ( SV49 != true )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(480,plain,
! [SV63: $i,SV25: $i] :
( ( forallprefers @ ( f6 @ SV25 @ SV63 ) @ ( f6 @ SV25 @ ( sK2_SY96 @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(481,plain,
! [SV54: $i,SV67: $i,SV29: $i] :
( ( ~ ( forallprefers @ ( f4 @ SV29 @ SV67 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(482,plain,
! [SV64: $i,SV30: $i] :
( ( existsprefers @ ( apply @ SV30 @ SV64 ) @ ( apply @ SV30 @ ( sK3_SY103 @ SV30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(483,plain,
! [SV68: $i,SV56: $i,SV34: $i] :
( ( ~ ( forallprefers @ ( f3 @ SV34 @ SV56 @ SV68 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(484,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(485,plain,
! [SV14: $i,SV45: $i] :
( ( ( d @ SV45 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(486,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 ) )
= $false )
| ( ( ~ ( d @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(487,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) ) )
= $false )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(488,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $false )
| ( ( SV14 = true )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(489,plain,
! [SV65: $i,SV46: $i,SV15: $i] :
( ( forallprefers @ ( f1 @ SV15 @ SV46 @ SV65 ) @ ( f1 @ SV15 @ SV46 @ ( sK4_SY114 @ SV46 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(490,plain,
! [SV66: $i,SV48: $i,SV19: $i] :
( ( forallprefers @ ( f2 @ SV19 @ SV48 @ SV66 ) @ ( f2 @ SV19 @ SV48 @ ( sK5_SY117 @ SV48 @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(491,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(492,plain,
! [SV20: $i,SV49: $i] :
( ( ( d @ SV49 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(493,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 ) )
= $false )
| ( ( ~ ( d @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(494,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) ) )
= $false )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(495,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $false )
| ( ( SV20 = false )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(496,plain,
! [SV54: $i,SV67: $i,SV29: $i] :
( ( forallprefers @ ( f4 @ SV29 @ SV67 @ SV54 ) @ ( f4 @ SV29 @ ( sK6_SY119 @ SV54 @ SV29 ) @ SV54 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(497,plain,
! [SV68: $i,SV56: $i,SV34: $i] :
( ( forallprefers @ ( f3 @ SV34 @ SV56 @ SV68 ) @ ( f3 @ SV34 @ SV56 @ ( sK7_SY121 @ SV56 @ SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(498,plain,
! [SV45: $i,SV14: $i] :
( ( ( d @ SV14 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) ) )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(499,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(500,plain,
! [SV45: $i,SV14: $i] :
( ( ( d @ SV14 )
= $true )
| ( ( ~ ( d @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(501,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(502,plain,
! [SV49: $i,SV20: $i] :
( ( ( d @ SV20 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) ) )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(503,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(504,plain,
! [SV49: $i,SV20: $i] :
( ( ( d @ SV20 )
= $true )
| ( ( ~ ( d @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(505,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(506,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
| ~ ( bool @ SV45 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(507,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(508,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( bool @ SV45 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(509,plain,
! [SV14: $i,SV45: $i] :
( ( ( d @ SV45 )
= $false )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(510,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $true )
| ( ( ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(511,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
| ~ ( bool @ SV49 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(512,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(513,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( bool @ SV49 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(514,plain,
! [SV20: $i,SV49: $i] :
( ( ( d @ SV49 )
= $false )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(515,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $true )
| ( ( ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(516,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(517,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( bool @ SV45 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(518,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) ) )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(519,plain,
! [SV14: $i,SV45: $i] :
( ( ( bool @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(520,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $false )
| ( ( ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(521,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(522,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( bool @ SV49 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(523,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) ) )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(524,plain,
! [SV20: $i,SV49: $i] :
( ( ( bool @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(525,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $false )
| ( ( ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(526,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) ) )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(527,plain,
! [SV14: $i,SV45: $i] :
( ( ( bool @ SV45 )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(528,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(529,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(530,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
= $true )
| ( ( ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(531,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) ) )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(532,plain,
! [SV20: $i,SV49: $i] :
( ( ( bool @ SV49 )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(533,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(534,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(535,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
= $true )
| ( ( ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(536,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
| ~ ~ ( bool @ SV14 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(537,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(538,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(539,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( bool @ SV14 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(540,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(541,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(542,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 ) )
= $true )
| ( ( ~ ( d @ SV45 ) )
= $true )
| ( ( ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(543,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
| ~ ~ ( bool @ SV20 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(544,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(545,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(546,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( bool @ SV20 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(547,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(548,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(549,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 ) )
= $true )
| ( ( ~ ( d @ SV49 ) )
= $true )
| ( ( ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(550,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(551,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ~ ( bool @ SV14 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(552,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(553,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(554,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(555,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( bool @ SV14 ) )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(556,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(557,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(558,plain,
! [SV45: $i,SV14: $i] :
( ( ( d @ SV14 )
= $false )
| ( ( ~ ( d @ SV45 ) )
= $true )
| ( ( ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(559,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(560,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ~ ( bool @ SV20 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(561,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(562,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(563,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(564,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( bool @ SV20 ) )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(565,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(566,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(567,plain,
! [SV49: $i,SV20: $i] :
( ( ( d @ SV20 )
= $false )
| ( ( ~ ( d @ SV49 ) )
= $true )
| ( ( ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(568,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) ) )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(569,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( bool @ SV14 ) )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(570,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(571,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(572,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(573,plain,
! [SV45: $i,SV14: $i] :
( ( ( bool @ SV14 )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(574,plain,
! [SV14: $i,SV45: $i] :
( ( ( d @ SV45 )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ~ ( bool @ SV14 ) )
= $true )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(575,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) ) )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(576,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( bool @ SV20 ) )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(577,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(578,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(579,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(580,plain,
! [SV49: $i,SV20: $i] :
( ( ( bool @ SV20 )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(581,plain,
! [SV20: $i,SV49: $i] :
( ( ( d @ SV49 )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ~ ( bool @ SV20 ) )
= $true )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(582,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 )
| ~ ( d @ SV45 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(583,plain,
! [SV45: $i,SV14: $i] :
( ( ( bool @ SV14 )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(584,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(585,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( d @ SV45 ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(586,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(587,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( bool @ SV14 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $false )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(588,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 )
| ~ ( d @ SV49 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(589,plain,
! [SV49: $i,SV20: $i] :
( ( ( bool @ SV20 )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(590,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(591,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( d @ SV49 ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(592,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(593,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( bool @ SV20 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $false )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(594,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( d @ SV14 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(595,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( d @ SV45 ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(596,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(597,plain,
! [SV45: $i,SV14: $i] :
( ( ( d @ SV14 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(598,plain,
! [SV14: $i,SV45: $i] :
( ( ( d @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(599,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(600,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(601,plain,
! [SV45: $i,SV14: $i] :
( ( ( bool @ SV14 )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $false )
| ( ( ~ ( bool @ SV45 ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(602,plain,
! [SV49: $i,SV20: $i] :
( ( ( ~ ( d @ SV20 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(603,plain,
! [SV20: $i,SV49: $i] :
( ( ( ~ ( d @ SV49 ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(604,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(605,plain,
! [SV49: $i,SV20: $i] :
( ( ( d @ SV20 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(606,plain,
! [SV20: $i,SV49: $i] :
( ( ( d @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(607,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(608,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(609,plain,
! [SV49: $i,SV20: $i] :
( ( ( bool @ SV20 )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $false )
| ( ( ~ ( bool @ SV49 ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(610,plain,
! [SV45: $i,SV14: $i] :
( ( ( d @ SV14 )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(611,plain,
! [SV14: $i,SV45: $i] :
( ( ( d @ SV45 )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( ~ ( ( SV14 != true )
| ( SV45 != false ) ) )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(612,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(613,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(614,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(615,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(616,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(617,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(618,plain,
! [SV14: $i,SV45: $i] :
( ( ( bool @ SV45 )
= $false )
| ( ( d @ SV45 )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(619,plain,
! [SV49: $i,SV20: $i] :
( ( ( d @ SV20 )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(620,plain,
! [SV20: $i,SV49: $i] :
( ( ( d @ SV49 )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( ~ ( ( SV20 != false )
| ( SV49 != true ) ) )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(621,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(622,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(623,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(624,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(625,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(626,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(627,plain,
! [SV20: $i,SV49: $i] :
( ( ( bool @ SV49 )
= $false )
| ( ( d @ SV49 )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(628,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(629,plain,
! [SV45: $i,SV14: $i] :
( ( ( ( SV14 != true )
| ( SV45 != false ) )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(630,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(631,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( bool @ SV14 )
= $false )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(632,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(633,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(634,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(635,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(636,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(637,plain,
! [SV49: $i,SV20: $i] :
( ( ( ( SV20 != false )
| ( SV49 != true ) )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(638,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(639,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( bool @ SV20 )
= $false )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(640,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(641,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(642,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(643,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(644,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(645,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(646,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 != true )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(647,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 != false )
= $false )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(648,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(649,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(650,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(651,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(652,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(653,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(654,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 != false )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(655,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 != true )
= $false )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(656,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(657,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(658,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(659,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(660,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(661,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV14 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(662,plain,
! [SV45: $i,SV14: $i] :
( ( ( SV14 = true )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(663,plain,
! [SV14: $i,SV45: $i] :
( ( ( SV45 = false )
= $true )
| ( ( d @ SV14 )
= $false )
| ( ( d @ SV45 )
= $true )
| ( ( existsprefers @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(664,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(665,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV20 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(666,plain,
! [SV49: $i,SV20: $i] :
( ( ( SV20 = false )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(667,plain,
! [SV20: $i,SV49: $i] :
( ( ( SV49 = true )
= $true )
| ( ( d @ SV20 )
= $false )
| ( ( d @ SV49 )
= $true )
| ( ( forallprefers @ SV20 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(668,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[130,667,666,665,664,663,662,661,660,659,658,657,656,651,650,649,648,639,638,631,630,627,626,625,618,617,616,578,577,571,570,566,565,557,556,514,509,497,496,495,490,489,488,482,480,458,452,448,441,440,439,430,427,420,418,416,412,405,404,402,398,397,396,394,389,388,356,352,351,350,349,344,338,336,335,319,303,298,285,284,282,280,268,258,252,250,249,248,247,214,179,178,177,172,171,169,168,135,134]) ).
thf(669,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 16:50:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.02/0.95
% 4.02/0.95 No.of.Axioms: 44
% 4.02/0.95
% 4.02/0.95 Length.of.Defs: 0
% 4.02/0.95
% 4.02/0.95 Contains.Choice.Funs: false
% 4.02/0.95 ................
% 4.02/0.95
% 4.02/0.95 ********************************
% 4.02/0.95 * All subproblems solved! *
% 4.02/0.95 ********************************
% 4.02/0.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:44,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:668,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.02/0.95
% 4.02/0.95 %**** Beginning of derivation protocol ****
% 4.02/0.95 % SZS output start CNFRefutation
% See solution above
% 4.02/0.95
% 4.02/0.95 %**** End of derivation protocol ****
% 4.02/0.95 %**** no. of clauses in derivation: 669 ****
% 4.02/0.95 %**** clause counter: 668 ****
% 4.02/0.95
% 4.02/0.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:44,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:668,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------