%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU975^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:49:19 AM UTC 2026
% Result : Theorem 1.85s 0.57s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 1
% Syntax : Number of formulae : 150 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 1247 ( 795 equ; 0 cnn)
% Maximal formula atoms : 13 ( 8 avg)
% Number of connectives : 3715 ( 688 ~; 553 |; 61 &;2355 @)
% ( 10 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 422 ( 0 ^; 410 !; 12 ?; 422 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cL,type,
cL: a > a ).
thf(tp_cP,type,
cP: a > a > a ).
thf(tp_cR,type,
cR: a > a ).
thf(tp_cZ,type,
cZ: a ).
thf(tp_sK1_SX0,type,
sK1_SX0: a ).
thf(tp_sK2_SY24,type,
sK2_SY24: a ).
thf(tp_sK3_SY20,type,
sK3_SY20: ( a > $o ) > a ).
thf(tp_sK4_SY37,type,
sK4_SY37: ( a > $o ) > a ).
thf(tp_sK5_SY31,type,
sK5_SY31: a > $o ).
thf(tp_sK6_SY38,type,
sK6_SY38: ( a > $o ) > a ).
thf(tp_sK7_SY44,type,
sK7_SY44: ( a > $o ) > a ).
thf(1,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [X: a > $o] :
( ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xt = cZ )
<=> ( Xu = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
=> ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( Xt = Xu ) ) ) )
=> ! [Xx: a,Xy: a] :
( ? [X: a > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [X: a > $o] :
( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPU_LEM2B_pme) ).
thf(2,negated_conjecture,
( ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [X: a > $o] :
( ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xt = cZ )
<=> ( Xu = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
=> ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( Xt = Xu ) ) ) )
=> ! [Xx: a,Xy: a] :
( ? [X: a > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [X: a > $o] :
( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [X: a > $o] :
( ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xt = cZ )
<=> ( Xu = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
=> ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( Xt = Xu ) ) ) )
=> ! [Xx: a,Xy: a] :
( ? [X: a > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [X: a > $o] :
( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( cL @ cZ )
= cZ )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ( cR @ cZ )
= cZ )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [X: a > $o] :
( ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xt = cZ )
<=> ( Xu = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
=> ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( Xt = Xu ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: a,Xy: a] :
( ? [X: a > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [X: a > $o] :
( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ~ ! [Xx: a,Xy: a] :
( ? [X: a > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [X: a > $o] :
( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [X: a > $o] :
( ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xt = cZ )
<=> ( Xu = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) )
=> ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( Xt = Xu ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(16,plain,
( ( ( cR @ cZ )
= cZ )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(17,plain,
( ( ( cL @ cZ )
= cZ )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(18,plain,
( ( ~ ! [Xx: a,Xy: a] :
( ? [X: a > $o] :
( ( X @ ( cP @ Xx @ Xy ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) )
=> ? [X: a > $o] :
( ( X @ ( cP @ ( cL @ Xx ) @ ( cL @ Xy ) ) )
& ! [Xt: a,Xu: a] :
( ( X @ ( cP @ Xt @ Xu ) )
=> ( ( ( Xu = cZ )
=> ( Xt = cZ ) )
& ( X @ ( cP @ ( cL @ Xt ) @ ( cL @ Xu ) ) )
& ( X @ ( cP @ ( cR @ Xt ) @ ( cR @ Xu ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ! [SX0: a] :
~ ( ~ ( ~ ( ( SX0 != cZ ) )
| ( SX0
= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) ) )
| ~ ( ( SX0
!= ( cP @ ( cL @ SX0 ) @ ( cR @ SX0 ) ) )
| ( SX0 != cZ ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [SX0: a > $o] :
( ~ ! [SX1: a,SX2: a] :
( ~ ( SX0 @ ( cP @ SX1 @ SX2 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX1 != cZ )
| ( SX2 = cZ ) )
| ~ ( ( SX2 != cZ )
| ( SX1 = cZ ) ) )
| ~ ( SX0 @ ( cP @ ( cL @ SX1 ) @ ( cL @ SX2 ) ) ) )
| ~ ( SX0 @ ( cP @ ( cR @ SX1 ) @ ( cR @ SX2 ) ) ) ) )
| ! [SX1: a,SX2: a] :
( ~ ( SX0 @ ( cP @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(21,plain,
( ( ~ ! [SX0: a,SX1: a] :
( ~ ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX2 @ ( cP @ SX0 @ SX1 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SX2 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SX2 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SX2 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX2 @ ( cP @ ( cL @ SX0 ) @ ( cL @ SX1 ) ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SX2 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SX2 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SX2 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: a] :
( ( ! [SY18: a] :
( ( cR @ ( cP @ SV1 @ SY18 ) )
= SY18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(23,plain,
! [SV2: a] :
( ( ! [SY19: a] :
( ( cL @ ( cP @ SV2 @ SY19 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(24,plain,
! [SV3: a] :
( ( ~ ( ~ ( ~ ( ( SV3 != cZ ) )
| ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) ) )
| ~ ( ( SV3
!= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
| ( SV3 != cZ ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV4: a > $o] :
( ( ~ ! [SY20: a,SY21: a] :
( ~ ( SV4 @ ( cP @ SY20 @ SY21 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY20 != cZ )
| ( SY21 = cZ ) )
| ~ ( ( SY21 != cZ )
| ( SY20 = cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ SY20 ) @ ( cL @ SY21 ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ SY20 ) @ ( cR @ SY21 ) ) ) ) )
| ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX2 @ ( cP @ SX0 @ SX1 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SX2 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SX2 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SX2 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) )
| ~ ! [SX2: a > $o] :
~ ~ ( ~ ( SX2 @ ( cP @ ( cL @ SX0 ) @ ( cL @ SX1 ) ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SX2 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SX2 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SX2 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV5: a,SV1: a] :
( ( ( cR @ ( cP @ SV1 @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: a,SV2: a] :
( ( ( cL @ ( cP @ SV2 @ SV6 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV3: a] :
( ( ~ ( ~ ( ( SV3 != cZ ) )
| ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) ) )
| ~ ( ( SV3
!= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
| ( SV3 != cZ ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV4: a > $o] :
( ( ( ~ ! [SY20: a,SY21: a] :
( ~ ( SV4 @ ( cP @ SY20 @ SY21 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY20 != cZ )
| ( SY21 = cZ ) )
| ~ ( ( SY21 != cZ )
| ( SY20 = cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ SY20 ) @ ( cL @ SY21 ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ SY20 ) @ ( cR @ SY21 ) ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ! [SY24: a] :
( ~ ~ ! [SY25: a > $o] :
~ ~ ( ~ ( SY25 @ ( cP @ sK1_SX0 @ SY24 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY25 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY25 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY25 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) )
| ~ ! [SY28: a > $o] :
~ ~ ( ~ ( SY28 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ SY24 ) ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY28 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY28 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY28 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(32,plain,
! [SV3: a] :
( ( ~ ( ~ ( ( SV3 != cZ ) )
| ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV3: a] :
( ( ~ ( ( SV3
!= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
| ( SV3 != cZ ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: a > $o] :
( ( ( ! [SY20: a,SY21: a] :
( ~ ( SV4 @ ( cP @ SY20 @ SY21 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY20 != cZ )
| ( SY21 = cZ ) )
| ~ ( ( SY21 != cZ )
| ( SY20 = cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ SY20 ) @ ( cL @ SY21 ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ SY20 ) @ ( cR @ SY21 ) ) ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ~ ! [SY31: a > $o] :
~ ~ ( ~ ( SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY31 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY31 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY31 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) )
| ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY34 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY34 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY34 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY34 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(36,plain,
! [SV3: a] :
( ( ~ ( ( SV3 != cZ ) )
| ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV3: a] :
( ( ( SV3
!= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
| ( SV3 != cZ ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: a > $o] :
( ( ( ! [SY37: a] :
( ~ ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ SY37 ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( SY37 = cZ ) )
| ~ ( ( SY37 != cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ SY37 ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ SY37 ) ) ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(39,plain,
( ( ~ ~ ! [SY31: a > $o] :
~ ~ ( ~ ( SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY31 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY31 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY31 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ! [SY34: a > $o] :
~ ~ ( ~ ( SY34 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY34 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY34 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY34 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV3: a] :
( ( ( ~ ( ( SV3 != cZ ) ) )
= $true )
| ( ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV3: a] :
( ( ( SV3
!= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
= $true )
| ( ( SV3 != cZ )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(44,plain,
( ( ~ ! [SY31: a > $o] :
~ ~ ( ~ ( SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY31 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY31 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY31 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ! [SY34: a > $o] :
~ ~ ( ~ ( SY34 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY34 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY34 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY34 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV3: a] :
( ( ( SV3 != cZ )
= $false )
| ( ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV3: a] :
( ( ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
= $false )
| ( ( SV3 != cZ )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [SY31: a > $o] :
~ ~ ( ~ ( SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SX3: a,SX4: a] :
( ~ ( SY31 @ ( cP @ SX3 @ SX4 ) )
| ~ ( ~ ~ ( ~ ( ( SX4 != cZ )
| ( SX3 = cZ ) )
| ~ ( SY31 @ ( cP @ ( cL @ SX3 ) @ ( cL @ SX4 ) ) ) )
| ~ ( SY31 @ ( cP @ ( cR @ SX3 ) @ ( cR @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV7: a > $o] :
( ( ~ ~ ( ~ ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
| ~ ! [SY38: a,SY39: a] :
( ~ ( SV7 @ ( cP @ SY38 @ SY39 ) )
| ~ ( ~ ~ ( ~ ( ( SY39 != cZ )
| ( SY38 = cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ SY38 ) @ ( cL @ SY39 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ SY38 ) @ ( cR @ SY39 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV3: a] :
( ( ( SV3 = cZ )
= $true )
| ( ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV3: a] :
( ( ( SV3 = cZ )
= $false )
| ( ( SV3
= ( cP @ ( cL @ SV3 ) @ ( cR @ SV3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
| ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(56,plain,
( ( ~ ~ ( ~ ( sK5_SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SY40: a,SY41: a] :
( ~ ( sK5_SY31 @ ( cP @ SY40 @ SY41 ) )
| ~ ( ~ ~ ( ~ ( ( SY41 != cZ )
| ( SY40 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SY40 ) @ ( cL @ SY41 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SY40 ) @ ( cR @ SY41 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(57,plain,
! [SV7: a > $o] :
( ( ~ ( ~ ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
| ~ ! [SY38: a,SY39: a] :
( ~ ( SV7 @ ( cP @ SY38 @ SY39 ) )
| ~ ( ~ ~ ( ~ ( ( SY39 != cZ )
| ( SY38 = cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ SY38 ) @ ( cL @ SY39 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ SY38 ) @ ( cR @ SY39 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV8: a,SV4: a > $o] :
( ( ( ! [SY42: a] :
( ~ ( SV4 @ ( cP @ SV8 @ SY42 ) )
| ( SV8 = SY42 ) ) )
= $true )
| ( ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(60,plain,
( ( ~ ( ~ ( sK5_SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SY40: a,SY41: a] :
( ~ ( sK5_SY31 @ ( cP @ SY40 @ SY41 ) )
| ~ ( ~ ~ ( ~ ( ( SY41 != cZ )
| ( SY40 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SY40 ) @ ( cL @ SY41 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SY40 ) @ ( cR @ SY41 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV7: a > $o] :
( ( ~ ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
| ~ ! [SY38: a,SY39: a] :
( ~ ( SV7 @ ( cP @ SY38 @ SY39 ) )
| ~ ( ~ ~ ( ~ ( ( SY39 != cZ )
| ( SY38 = cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ SY38 ) @ ( cL @ SY39 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ SY38 ) @ ( cR @ SY39 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV9: a,SV8: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV8 @ SV9 ) )
| ( SV8 = SV9 ) )
= $true )
| ( ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) ) )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( ~ ( sK5_SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
| ~ ! [SY40: a,SY41: a] :
( ~ ( sK5_SY31 @ ( cP @ SY40 @ SY41 ) )
| ~ ( ~ ~ ( ~ ( ( SY41 != cZ )
| ( SY40 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SY40 ) @ ( cL @ SY41 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SY40 ) @ ( cR @ SY41 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV7: a > $o] :
( ( ( ~ ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) ) )
= $true )
| ( ( ~ ! [SY38: a,SY39: a] :
( ~ ( SV7 @ ( cP @ SY38 @ SY39 ) )
| ~ ( ~ ~ ( ~ ( ( SY39 != cZ )
| ( SY38 = cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ SY38 ) @ ( cL @ SY39 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ SY38 ) @ ( cR @ SY39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV9: a,SV8: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV8 @ SV9 ) ) )
= $true )
| ( ( SV8 = SV9 )
= $true )
| ( ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
| ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( ~ ( sK5_SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ~ ! [SY40: a,SY41: a] :
( ~ ( sK5_SY31 @ ( cP @ SY40 @ SY41 ) )
| ~ ( ~ ~ ( ~ ( ( SY41 != cZ )
| ( SY40 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SY40 ) @ ( cL @ SY41 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SY40 ) @ ( cR @ SY41 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV7: a > $o] :
( ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false )
| ( ( ~ ! [SY38: a,SY39: a] :
( ~ ( SV7 @ ( cP @ SY38 @ SY39 ) )
| ~ ( ~ ~ ( ~ ( ( SY39 != cZ )
| ( SY38 = cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ SY38 ) @ ( cL @ SY39 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ SY38 ) @ ( cR @ SY39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV9: a,SV8: a,SV4: a > $o] :
( ( ( SV4 @ ( cP @ SV8 @ SV9 ) )
= $false )
| ( ( SV8 = SV9 )
= $true )
| ( ( SV4 @ ( cP @ ( sK3_SY20 @ SV4 ) @ ( sK4_SY37 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV4: a > $o] :
( ( ( ~ ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(73,plain,
( ( sK5_SY31 @ ( cP @ sK1_SX0 @ sK2_SY24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
( ( ! [SY40: a,SY41: a] :
( ~ ( sK5_SY31 @ ( cP @ SY40 @ SY41 ) )
| ~ ( ~ ~ ( ~ ( ( SY41 != cZ )
| ( SY40 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SY40 ) @ ( cL @ SY41 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SY40 ) @ ( cR @ SY41 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV7: a > $o] :
( ( ( ! [SY38: a,SY39: a] :
( ~ ( SV7 @ ( cP @ SY38 @ SY39 ) )
| ~ ( ~ ~ ( ~ ( ( SY39 != cZ )
| ( SY38 = cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ SY38 ) @ ( cL @ SY39 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ SY38 ) @ ( cR @ SY39 ) ) ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) ) )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV10: a] :
( ( ! [SY43: a] :
( ~ ( sK5_SY31 @ ( cP @ SV10 @ SY43 ) )
| ~ ( ~ ~ ( ~ ( ( SY43 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SY43 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SY43 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV7: a > $o] :
( ( ( ! [SY44: a] :
( ~ ( SV7 @ ( cP @ ( sK6_SY38 @ SV7 ) @ SY44 ) )
| ~ ( ~ ~ ( ~ ( ( SY44 != cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ SY44 ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ SY44 ) ) ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(79,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
| ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV11: a,SV10: a] :
( ( ~ ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
| ~ ( ~ ~ ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV7: a > $o] :
( ( ( ~ ( SV7 @ ( cP @ ( sK6_SY38 @ SV7 ) @ ( sK7_SY44 @ SV7 ) ) )
| ~ ( ~ ~ ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(82,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV11: a,SV10: a] :
( ( ( ~ ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV7: a > $o] :
( ( ( ~ ( SV7 @ ( cP @ ( sK6_SY38 @ SV7 ) @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(85,plain,
! [SV7: a > $o] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV4: a > $o] :
( ( ( ( ( sK3_SY20 @ SV4 )
!= cZ )
| ( ( sK4_SY37 @ SV4 )
= cZ ) )
= $false )
| ( ( ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV11: a,SV10: a] :
( ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV7: a > $o] :
( ( ( SV7 @ ( cP @ ( sK6_SY38 @ SV7 ) @ ( sK7_SY44 @ SV7 ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV7: a > $o] :
( ( ( ~ ~ ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
| ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV4: a > $o] :
( ( ( ( sK3_SY20 @ SV4 )
!= cZ )
= $false )
| ( ( ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(91,plain,
! [SV4: a > $o] :
( ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(92,plain,
! [SV10: a,SV11: a] :
( ( ( ~ ~ ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) )
| ~ ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SV11 ) ) ) )
= $false )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV7: a > $o] :
( ( ( ~ ~ ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV4: a > $o] :
( ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(95,plain,
! [SV4: a > $o] :
( ( ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(96,plain,
! [SV10: a,SV11: a] :
( ( ( ~ ~ ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) ) )
= $false )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV11: a,SV10: a] :
( ( ( ~ ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SV11 ) ) ) )
= $false )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV7: a > $o] :
( ( ( ~ ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) ) )
= $false )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV4: a > $o] :
( ( ( ( ( sK4_SY37 @ SV4 )
!= cZ )
| ( ( sK3_SY20 @ SV4 )
= cZ ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV4: a > $o] :
( ( ( ( sK4_SY37 @ SV4 )
!= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV4: a > $o] :
( ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV10: a,SV11: a] :
( ( ( ~ ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) ) )
= $true )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV11: a,SV10: a] :
( ( ( sK5_SY31 @ ( cP @ ( cR @ SV10 ) @ ( cR @ SV11 ) ) )
= $true )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV7: a > $o] :
( ( ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
| ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(105,plain,
! [SV4: a > $o] :
( ( ( ( sK4_SY37 @ SV4 )
!= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV4: a > $o] :
( ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV4: a > $o] :
( ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV10: a,SV11: a] :
( ( ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) )
| ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) )
= $false )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV7: a > $o] :
( ( ( ~ ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV4: a > $o] :
( ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(115,plain,
! [SV10: a,SV11: a] :
( ( ( ~ ( ( SV11 != cZ )
| ( SV10 = cZ ) ) )
= $false )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(116,plain,
! [SV11: a,SV10: a] :
( ( ( ~ ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) ) )
= $false )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(117,plain,
! [SV7: a > $o] :
( ( ( ( ( sK7_SY44 @ SV7 )
!= cZ )
| ( ( sK6_SY38 @ SV7 )
= cZ ) )
= $false )
| ( ( ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( ~ ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) ) )
= $true )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV12: a,SV4: a > $o] :
( ( ( ! [SY45: a] :
( ~ ( SV4 @ ( cP @ SV12 @ SY45 ) )
| ( SV12 = SY45 ) ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV10: a,SV11: a] :
( ( ( ( SV11 != cZ )
| ( SV10 = cZ ) )
= $true )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(123,plain,
! [SV11: a,SV10: a] :
( ( ( sK5_SY31 @ ( cP @ ( cL @ SV10 ) @ ( cL @ SV11 ) ) )
= $true )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(124,plain,
! [SV7: a > $o] :
( ( ( ( sK7_SY44 @ SV7 )
!= cZ )
= $false )
| ( ( ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV7: a > $o] :
( ( ( ( sK6_SY38 @ SV7 )
= cZ )
= $false )
| ( ( ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(126,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ! [SY22: a,SY23: a] :
( ~ ( SV4 @ ( cP @ SY22 @ SY23 ) )
| ( SY22 = SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV13: a,SV4: a > $o] :
( ( ( ! [SY46: a] :
( ~ ( SV4 @ ( cP @ SV13 @ SY46 ) )
| ( SV13 = SY46 ) ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV14: a,SV4: a > $o] :
( ( ( ! [SY47: a] :
( ~ ( SV4 @ ( cP @ SV14 @ SY47 ) )
| ( SV14 = SY47 ) ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV15: a,SV12: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV12 @ SV15 ) )
| ( SV12 = SV15 ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV10: a,SV11: a] :
( ( ( SV11 != cZ )
= $true )
| ( ( SV10 = cZ )
= $true )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV7: a > $o] :
( ( ( ( sK7_SY44 @ SV7 )
= cZ )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(132,plain,
! [SV7: a > $o] :
( ( ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( ( sK6_SY38 @ SV7 )
= cZ )
= $false )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV16: a,SV4: a > $o] :
( ( ( ! [SY48: a] :
( ~ ( SV4 @ ( cP @ SV16 @ SY48 ) )
| ( SV16 = SY48 ) ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV17: a,SV13: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV13 @ SV17 ) )
| ( SV13 = SV17 ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV18: a,SV14: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV14 @ SV18 ) )
| ( SV14 = SV18 ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV15: a,SV12: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV12 @ SV15 ) ) )
= $true )
| ( ( SV12 = SV15 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV10: a,SV11: a] :
( ( ( SV11 = cZ )
= $false )
| ( ( SV10 = cZ )
= $true )
| ( ( sK5_SY31 @ ( cP @ SV10 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV7: a > $o] :
( ( ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( ( sK7_SY44 @ SV7 )
= cZ )
= $true )
| ( ( ~ ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) ) )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV7: a > $o] :
( ( ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( ( sK6_SY38 @ SV7 )
= cZ )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV19: a,SV16: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV16 @ SV19 ) )
| ( SV16 = SV19 ) )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(141,plain,
! [SV17: a,SV13: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV13 @ SV17 ) ) )
= $true )
| ( ( SV13 = SV17 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(142,plain,
! [SV18: a,SV14: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV14 @ SV18 ) ) )
= $true )
| ( ( SV14 = SV18 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV15: a,SV12: a,SV4: a > $o] :
( ( ( SV4 @ ( cP @ SV12 @ SV15 ) )
= $false )
| ( ( SV12 = SV15 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV7: a > $o] :
( ( ( SV7 @ ( cP @ ( cR @ ( sK6_SY38 @ SV7 ) ) @ ( cR @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( ( sK7_SY44 @ SV7 )
= cZ )
= $true )
| ( ( SV7 @ ( cP @ ( cL @ ( sK6_SY38 @ SV7 ) ) @ ( cL @ ( sK7_SY44 @ SV7 ) ) ) )
= $false )
| ( ( SV7 @ ( cP @ ( cL @ sK1_SX0 ) @ ( cL @ sK2_SY24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(145,plain,
! [SV19: a,SV16: a,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( cP @ SV16 @ SV19 ) ) )
= $true )
| ( ( SV16 = SV19 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(146,plain,
! [SV17: a,SV13: a,SV4: a > $o] :
( ( ( SV4 @ ( cP @ SV13 @ SV17 ) )
= $false )
| ( ( SV13 = SV17 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $false )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(147,plain,
! [SV18: a,SV14: a,SV4: a > $o] :
( ( ( SV4 @ ( cP @ SV14 @ SV18 ) )
= $false )
| ( ( SV14 = SV18 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $false )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV19: a,SV16: a,SV4: a > $o] :
( ( ( SV4 @ ( cP @ SV16 @ SV19 ) )
= $false )
| ( ( SV16 = SV19 )
= $true )
| ( ( SV4 @ ( cP @ ( cL @ ( sK3_SY20 @ SV4 ) ) @ ( cL @ ( sK4_SY37 @ SV4 ) ) ) )
= $false )
| ( ( ( sK3_SY20 @ SV4 )
= cZ )
= $true )
| ( ( ( sK4_SY37 @ SV4 )
= cZ )
= $true )
| ( ( SV4 @ ( cP @ ( cR @ ( sK3_SY20 @ SV4 ) ) @ ( cR @ ( sK4_SY37 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(149,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,148,147,146,144,143,139,137,123,103,88,73,71,53,52,28,27,17]) ).
thf(150,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU975^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Oct 6 15:37:00 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.85/0.57
% 1.85/0.57 No.of.Axioms: 0
% 1.85/0.57
% 1.85/0.57 Length.of.Defs: 0
% 1.85/0.57
% 1.85/0.57 Contains.Choice.Funs: false
% 1.85/0.57 .....
% 1.85/0.57
% 1.85/0.57 ********************************
% 1.85/0.57 * All subproblems solved! *
% 1.85/0.57 ********************************
% 1.85/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:149,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.85/0.57
% 1.85/0.57 %**** Beginning of derivation protocol ****
% 1.85/0.57 % SZS output start CNFRefutation
% See solution above
% 1.85/0.58
% 1.85/0.58 %**** End of derivation protocol ****
% 1.85/0.58 %**** no. of clauses in derivation: 150 ****
% 1.85/0.58 %**** clause counter: 149 ****
% 1.85/0.58
% 1.85/0.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:149,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------