%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV124^5 : 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 : n002.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 10:49:35 AM UTC 2026
% Result : Theorem 0.92s 0.43s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 1
% Syntax : Number of formulae : 115 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 1167 ( 437 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 3502 ( 673 ~; 535 |; 58 &;2171 @)
% ( 0 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 631 ( 631 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-6 aty)
% Number of variables : 751 ( 78 ^; 644 !; 29 ?; 751 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_SV7,type,
sK10_SV7: ( a > a > $o ) > a > a > ( a > a > $o ) > a ).
thf(tp_sK11_SY132,type,
sK11_SY132: ( a > a > $o ) > a > a > ( a > a > $o ) > a > a > $o ).
thf(tp_sK12_SY135,type,
sK12_SY135: ( a > a > $o ) > a > a > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK13_SY139,type,
sK13_SY139: ( a > a > $o ) > a > a > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(tp_sK1_PROP,type,
sK1_PROP: ( a > a > $o ) > $o ).
thf(tp_sK2_SY18,type,
sK2_SY18: ( a > a > $o ) > $o ).
thf(tp_sK3_SY35,type,
sK3_SY35: a ).
thf(tp_sK4_SY51,type,
sK4_SY51: a ).
thf(tp_sK5_SX0,type,
sK5_SX0: a > a > $o ).
thf(tp_sK6_SY80,type,
sK6_SY80: ( a > a > $o ) > a ).
thf(tp_sK7_SY92,type,
sK7_SY92: ( a > a > $o ) > a ).
thf(tp_sK8_SY102,type,
sK8_SY102: ( a > a > $o ) > a > a > $o ).
thf(tp_sK9_SV6,type,
sK9_SV6: a > a > ( a > a > $o ) > ( a > a > $o ) > a ).
thf(1,conjecture,
! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ( S @ R )
& ( R @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ? [Q: a > a > $o] :
( ( S @ Q )
& ( R
= ( ^ [Xx1: a,Xy1: a] :
! [Xp0: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( Q @ Xx2 @ Xy2 )
=> ( Xp0 @ Xx2 @ Xy2 ) )
& ( PROP @ Xp0 ) )
=> ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
& ( R @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM254_A_pme) ).
thf(2,negated_conjecture,
( ( ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ( S @ R )
& ( R @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ? [Q: a > a > $o] :
( ( S @ Q )
& ( R
= ( ^ [Xx1: a,Xy1: a] :
! [Xp0: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( Q @ Xx2 @ Xy2 )
=> ( Xp0 @ Xx2 @ Xy2 ) )
& ( PROP @ Xp0 ) )
=> ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
& ( R @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [PROP: ( a > a > $o ) > $o,S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
( ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ( S @ R )
& ( R @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) )
=> ! [Xp: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ? [Q: a > a > $o] :
( ( S @ Q )
& ( R
= ( ^ [Xx1: a,Xy1: a] :
! [Xp0: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( Q @ Xx2 @ Xy2 )
=> ( Xp0 @ Xx2 @ Xy2 ) )
& ( PROP @ Xp0 ) )
=> ( Xp0 @ Xx1 @ Xy1 ) ) ) ) )
& ( R @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY18: ( a > a > $o ) > $o,SY19: a,SY20: a] :
( ! [SY21: a > a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > $o] :
( ( SY18 @ R )
& ( R @ Xx0 @ Xy0 ) )
=> ( SY21 @ Xx0 @ Xy0 ) )
& ( sK1_PROP @ SY21 ) )
=> ( SY21 @ SY19 @ SY20 ) )
=> ! [SY25: a > a > $o] :
( ( ! [SY26: a,SY27: a] :
( ? [SY28: a > a > $o] :
( ? [SY29: a > a > $o] :
( ( SY18 @ SY29 )
& ( SY28
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY29 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY28 @ SY26 @ SY27 ) )
=> ( SY25 @ SY26 @ SY27 ) )
& ( sK1_PROP @ SY25 ) )
=> ( SY25 @ SY19 @ SY20 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY35: a,SY36: a] :
( ! [SY37: a > a > $o] :
( ( ! [SY38: a,SY39: a] :
( ? [SY40: a > a > $o] :
( ( sK2_SY18 @ SY40 )
& ( SY40 @ SY38 @ SY39 ) )
=> ( SY37 @ SY38 @ SY39 ) )
& ( sK1_PROP @ SY37 ) )
=> ( SY37 @ SY35 @ SY36 ) )
=> ! [SY41: a > a > $o] :
( ( ! [SY42: a,SY43: a] :
( ? [SY44: a > a > $o] :
( ? [SY45: a > a > $o] :
( ( sK2_SY18 @ SY45 )
& ( SY44
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY45 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY44 @ SY42 @ SY43 ) )
=> ( SY41 @ SY42 @ SY43 ) )
& ( sK1_PROP @ SY41 ) )
=> ( SY41 @ SY35 @ SY36 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY51: a] :
( ! [SY52: a > a > $o] :
( ( ! [SY38: a,SY39: a] :
( ? [SY40: a > a > $o] :
( ( sK2_SY18 @ SY40 )
& ( SY40 @ SY38 @ SY39 ) )
=> ( SY52 @ SY38 @ SY39 ) )
& ( sK1_PROP @ SY52 ) )
=> ( SY52 @ sK3_SY35 @ SY51 ) )
=> ! [SY56: a > a > $o] :
( ( ! [SY42: a,SY43: a] :
( ? [SY44: a > a > $o] :
( ? [SY45: a > a > $o] :
( ( sK2_SY18 @ SY45 )
& ( SY44
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY45 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY44 @ SY42 @ SY43 ) )
=> ( SY56 @ SY42 @ SY43 ) )
& ( sK1_PROP @ SY56 ) )
=> ( SY56 @ sK3_SY35 @ SY51 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY66: a > a > $o] :
( ( ! [SY38: a,SY39: a] :
( ? [SY40: a > a > $o] :
( ( sK2_SY18 @ SY40 )
& ( SY40 @ SY38 @ SY39 ) )
=> ( SY66 @ SY38 @ SY39 ) )
& ( sK1_PROP @ SY66 ) )
=> ( SY66 @ sK3_SY35 @ sK4_SY51 ) )
=> ! [SY70: a > a > $o] :
( ( ! [SY42: a,SY43: a] :
( ? [SY44: a > a > $o] :
( ? [SY45: a > a > $o] :
( ( sK2_SY18 @ SY45 )
& ( SY44
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY45 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY44 @ SY42 @ SY43 ) )
=> ( SY70 @ SY42 @ SY43 ) )
& ( sK1_PROP @ SY70 ) )
=> ( SY70 @ sK3_SY35 @ sK4_SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY66: a > a > $o] :
( ( ! [SY38: a,SY39: a] :
( ? [SY40: a > a > $o] :
( ( sK2_SY18 @ SY40 )
& ( SY40 @ SY38 @ SY39 ) )
=> ( SY66 @ SY38 @ SY39 ) )
& ( sK1_PROP @ SY66 ) )
=> ( SY66 @ sK3_SY35 @ sK4_SY51 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY70: a > a > $o] :
( ( ! [SY42: a,SY43: a] :
( ? [SY44: a > a > $o] :
( ? [SY45: a > a > $o] :
( ( sK2_SY18 @ SY45 )
& ( SY44
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY45 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY44 @ SY42 @ SY43 ) )
=> ( SY70 @ SY42 @ SY43 ) )
& ( sK1_PROP @ SY70 ) )
=> ( SY70 @ sK3_SY35 @ sK4_SY51 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SY70: a > a > $o] :
( ( ! [SY42: a,SY43: a] :
( ? [SY44: a > a > $o] :
( ? [SY45: a > a > $o] :
( ( sK2_SY18 @ SY45 )
& ( SY44
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY45 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY44 @ SY42 @ SY43 ) )
=> ( SY70 @ SY42 @ SY43 ) )
& ( sK1_PROP @ SY70 ) )
=> ( SY70 @ sK3_SY35 @ sK4_SY51 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY66: a > a > $o] :
( ( ! [SY38: a,SY39: a] :
( ? [SY40: a > a > $o] :
( ( sK2_SY18 @ SY40 )
& ( SY40 @ SY38 @ SY39 ) )
=> ( SY66 @ SY38 @ SY39 ) )
& ( sK1_PROP @ SY66 ) )
=> ( SY66 @ sK3_SY35 @ sK4_SY51 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ! [SY70: a > a > $o] :
( ( ! [SY42: a,SY43: a] :
( ? [SY44: a > a > $o] :
( ? [SY45: a > a > $o] :
( ( sK2_SY18 @ SY45 )
& ( SY44
= ( ^ [SY30: a,SY31: a] :
! [SY32: a > a > $o] :
( ( ! [Xx2: a,Xy2: a] :
( ( SY45 @ Xx2 @ Xy2 )
=> ( SY32 @ Xx2 @ Xy2 ) )
& ( sK1_PROP @ SY32 ) )
=> ( SY32 @ SY30 @ SY31 ) ) ) ) )
& ( SY44 @ SY42 @ SY43 ) )
=> ( SY70 @ SY42 @ SY43 ) )
& ( sK1_PROP @ SY70 ) )
=> ( SY70 @ sK3_SY35 @ sK4_SY51 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SX1 @ SX2 ) )
| ( SX0 @ SX1 @ SX2 ) )
| ~ ( sK1_PROP @ SX0 ) )
| ( SX0 @ sK3_SY35 @ sK4_SY51 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SX1 @ SX2 ) )
| ( SX0 @ SX1 @ SX2 ) )
| ~ ( sK1_PROP @ SX0 ) )
| ( SX0 @ sK3_SY35 @ sK4_SY51 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SX0: a > a > $o] :
( ~ ~ ( ~ ! [SX1: a,SX2: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SX1 @ SX2 ) )
| ( SX0 @ SX1 @ SX2 ) )
| ~ ( sK1_PROP @ SX0 ) )
| ( SX0 @ sK3_SY35 @ sK4_SY51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: a > a > $o] :
( ( ~ ~ ( ~ ! [SY80: a,SY81: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SY80 @ SY81 ) )
| ( SV1 @ SY80 @ SY81 ) )
| ~ ( sK1_PROP @ SV1 ) )
| ( SV1 @ sK3_SY35 @ sK4_SY51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SY83: a,SY84: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SY83 @ SY84 ) )
| ~ ( sK1_PROP @ sK5_SX0 ) )
| ( sK5_SX0 @ sK3_SY35 @ sK4_SY51 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY80: a,SY81: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SY80 @ SY81 ) )
| ( SV1 @ SY80 @ SY81 ) )
| ~ ( sK1_PROP @ SV1 ) ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( ~ ! [SY83: a,SY84: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SY83 @ SY84 ) )
| ~ ( sK1_PROP @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( sK5_SX0 @ sK3_SY35 @ sK4_SY51 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ~ ! [SY80: a,SY81: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SY80 @ SY81 ) )
| ( SV1 @ SY80 @ SY81 ) )
| ~ ( sK1_PROP @ SV1 ) ) )
= $false )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( ~ ! [SY83: a,SY84: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SY83 @ SY84 ) )
| ~ ( sK1_PROP @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY80: a,SY81: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SY80 @ SY81 ) )
| ( SV1 @ SY80 @ SY81 ) )
| ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ! [SY83: a,SY84: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SY83 @ SY84 ) )
| ~ ( sK1_PROP @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY80: a,SY81: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SY80 @ SY81 ) )
| ( SV1 @ SY80 @ SY81 ) ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ! [SY83: a,SY84: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SY83 @ SY84 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( sK1_PROP @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY80: a,SY81: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX3 )
| ~ ( SX3 @ SY80 @ SY81 ) )
| ( SV1 @ SY80 @ SY81 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [SY83: a,SY84: a] :
( ~ ~ ! [SX3: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SX3
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SX3 @ SY83 @ SY84 ) )
| ( sK5_SX0 @ SY83 @ SY84 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( sK1_PROP @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY92: a] :
( ~ ~ ! [SY93: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY93 )
| ~ ( SY93 @ ( sK6_SY80 @ SV1 ) @ SY92 ) )
| ( SV1 @ ( sK6_SY80 @ SV1 ) @ SY92 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(32,plain,
! [SV2: a] :
( ( ! [SY94: a] :
( ~ ~ ! [SY95: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SY95
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SY95 @ SV2 @ SY94 ) )
| ( sK5_SX0 @ SV2 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ! [SY102: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY102 )
| ~ ( SY102 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) )
| ( SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(34,plain,
! [SV3: a,SV2: a] :
( ( ~ ~ ! [SY103: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SY103
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SY103 @ SV2 @ SV3 ) )
| ( sK5_SX0 @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ! [SY102: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY102 )
| ~ ( SY102 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV1: a > a > $o] :
( ( ( SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ~ ! [SY103: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SY103
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SY103 @ SV2 @ SV3 ) ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: a > a > $o] :
( ( ( ~ ! [SY102: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY102 )
| ~ ( SY102 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: a > a > $o] :
( ( ( sK1_PROP @ SV1 )
= $false )
| ( ( SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV3: a,SV2: a] :
( ( ( ~ ! [SY103: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SY103
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SY103 @ SV2 @ SV3 ) ) )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: a > a > $o] :
( ( ( ! [SY102: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY102 )
| ~ ( SY102 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: a,SV2: a] :
( ( ( ! [SY103: a > a > $o] :
~ ~ ( ~ ~ ! [SX4: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SX4 )
| ( SY103
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SX4 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SY103 @ SV2 @ SV3 ) ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV1: a > a > $o] :
( ( ( ~ ~ ( ~ ( sK2_SY18 @ ( sK8_SY102 @ SV1 ) )
| ~ ( sK8_SY102 @ SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(44,plain,
! [SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ~ ~ ( ~ ~ ! [SY110: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY110 )
| ( SV4
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SY110 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SV4 @ SV2 @ SV3 ) ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( ~ ( sK2_SY18 @ ( sK8_SY102 @ SV1 ) )
| ~ ( sK8_SY102 @ SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ~ ( ~ ~ ! [SY110: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY110 )
| ( SV4
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SY110 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SV4 @ SV2 @ SV3 ) ) )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( sK2_SY18 @ ( sK8_SY102 @ SV1 ) )
| ~ ( sK8_SY102 @ SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ~ ~ ! [SY110: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY110 )
| ( SV4
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SY110 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) )
| ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(49,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( sK2_SY18 @ ( sK8_SY102 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV1: a > a > $o] :
( ( ( ~ ( sK8_SY102 @ SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ~ ~ ! [SY110: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY110 )
| ( SV4
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SY110 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV1: a > a > $o] :
( ( ( sK2_SY18 @ ( sK8_SY102 @ SV1 ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV1: a > a > $o] :
( ( ( sK8_SY102 @ SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ~ ! [SY110: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY110 )
| ( SV4
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SY110 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) ) )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV1: a > a > $o] :
( ( ( sK1_PROP @ SV1 )
= $false )
| ( ( sK2_SY18 @ ( sK8_SY102 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV1: a > a > $o] :
( ( ( sK1_PROP @ SV1 )
= $false )
| ( ( sK8_SY102 @ SV1 @ ( sK6_SY80 @ SV1 ) @ ( sK7_SY92 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY35 @ sK4_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ! [SY110: a > a > $o] :
~ ~ ( ~ ( sK2_SY18 @ SY110 )
| ( SV4
!= ( ^ [SX5: a,SX6: a] :
! [SX7: a > a > $o] :
( ~ ~ ( ~ ! [SX8: a,SX9: a] :
( ~ ( SY110 @ SX8 @ SX9 )
| ( SX7 @ SX8 @ SX9 ) )
| ~ ( sK1_PROP @ SX7 ) )
| ( SX7 @ SX5 @ SX6 ) ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ( sK2_SY18 @ SV5 )
| ( SV4
!= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(59,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( ~ ( sK2_SY18 @ SV5 )
| ( SV4
!= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) ) ) )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( sK2_SY18 @ SV5 )
| ( SV4
!= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) ) )
= $true )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(61,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( sK2_SY18 @ SV5 ) )
= $true )
| ( ( SV4
!= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) )
= $true )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4
!= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) )
= $true )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV3: a,SV2: a,SV5: a > a > $o,SV4: a > a > $o] :
( ( ( SV4
= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(64,plain,
! [SV3: a,SV2: a,SV5: a > a > $o,SV4: a > a > $o] :
( ( ( ! [SV6: a] :
( ( SV4 @ SV6 )
= ( ^ [SY121: a] :
! [SY122: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY122 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY122 ) )
| ( SY122 @ SV6 @ SY121 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[63]) ).
thf(65,plain,
! [SV3: a,SV2: a,SV5: a > a > $o,SV4: a > a > $o] :
( ( ( SV4
= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) )
= ( ^ [SY125: a] :
! [SY126: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY126 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY126 ) )
| ( SY126 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ SY125 ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(67,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4
= ( ^ [SY116: a,SY117: a] :
! [SY118: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY118 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY118 ) )
| ( SY118 @ SY116 @ SY117 ) ) ) )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ! [SV7: a] :
( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ SV7 )
= ( ! [SY129: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY129 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY129 ) )
| ( SY129 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ SV7 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[66]) ).
thf(69,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) )
= ( ^ [SY125: a] :
! [SY126: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY126 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY126 ) )
| ( SY126 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ SY125 ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[66]) ).
thf(70,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= ( ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(71,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) )
= ( ^ [SY125: a] :
! [SY126: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY126 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY126 ) )
| ( SY126 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ SY125 ) ) ) )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ~ ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
| ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
| ~ ( ~ ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
| ~ ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[70]) ).
thf(73,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= ( ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ~ ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
| ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
| ~ ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= ( ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) ) )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
| ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ~ ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
| ~ ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(79,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(80,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( ~ ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(81,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV8: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY135: a,SY136: a] :
( ~ ( SV5 @ SY135 @ SY136 )
| ( SV8 @ SY135 @ SY136 ) )
| ~ ( sK1_PROP @ SV8 ) )
| ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(82,plain,
! [SV5: a > a > $o,SV2: a,SV3: a,SV4: a > a > $o] :
( ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( ~ ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV8: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY135: a,SY136: a] :
( ~ ( SV5 @ SY135 @ SY136 )
| ( SV8 @ SY135 @ SY136 ) )
| ~ ( sK1_PROP @ SV8 ) ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV5: a > a > $o] :
( ( ( ! [SY132: a > a > $o] :
( ~ ~ ( ~ ! [SY119: a,SY120: a] :
( ~ ( SV5 @ SY119 @ SY120 )
| ( SY132 @ SY119 @ SY120 ) )
| ~ ( sK1_PROP @ SY132 ) )
| ( SY132 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(85,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV8: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( ~ ! [SY135: a,SY136: a] :
( ~ ( SV5 @ SY135 @ SY136 )
| ( SV8 @ SY135 @ SY136 ) )
| ~ ( sK1_PROP @ SV8 ) ) )
= $false )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(86,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY137: a,SY138: a] :
( ~ ( SV5 @ SY137 @ SY138 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SY137 @ SY138 ) )
| ~ ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) ) )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(87,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV8: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ! [SY135: a,SY136: a] :
( ~ ( SV5 @ SY135 @ SY136 )
| ( SV8 @ SY135 @ SY136 ) )
| ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(88,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ~ ( ~ ! [SY137: a,SY138: a] :
( ~ ( SV5 @ SY137 @ SY138 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SY137 @ SY138 ) )
| ~ ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) ) ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(89,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV8: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ! [SY135: a,SY136: a] :
( ~ ( SV5 @ SY135 @ SY136 )
| ( SV8 @ SY135 @ SY136 ) ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( ~ ! [SY137: a,SY138: a] :
( ~ ( SV5 @ SY137 @ SY138 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SY137 @ SY138 ) )
| ~ ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) ) ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(92,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV4: a > a > $o,SV2: a,SV3: a,SV8: a > a > $o,SV5: a > a > $o] :
( ( ( ! [SY135: a,SY136: a] :
( ~ ( SV5 @ SY135 @ SY136 )
| ( SV8 @ SY135 @ SY136 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ! [SY137: a,SY138: a] :
( ~ ( SV5 @ SY137 @ SY138 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SY137 @ SY138 ) )
| ~ ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV8: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ! [SY139: a] :
( ~ ( SV5 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ SY139 )
| ( SV8 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ SY139 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(96,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ! [SY137: a,SY138: a] :
( ~ ( SV5 @ SY137 @ SY138 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SY137 @ SY138 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(97,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( ~ ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) ) )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(98,plain,
! [SV8: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( SV5 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
| ( SV8 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(99,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ! [SY137: a,SY138: a] :
( ~ ( SV5 @ SY137 @ SY138 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SY137 @ SY138 ) ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(100,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(101,plain,
! [SV8: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( ~ ( SV5 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(102,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o,SV8: a > a > $o] :
( ( ( SV8 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
= $false )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(103,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV9: a,SV5: a > a > $o] :
( ( ( ! [SY140: a] :
( ~ ( SV5 @ SV9 @ SY140 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SV9 @ SY140 ) ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK1_PROP @ ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV8: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o] :
( ( ( SV5 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
= $true )
| ( ( ~ ( sK1_PROP @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
! [SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o,SV8: a > a > $o] :
( ( ( sK1_PROP @ SV8 )
= $false )
| ( ( SV8 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
= $false )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV10: a,SV9: a,SV5: a > a > $o] :
( ( ( ~ ( SV5 @ SV9 @ SV10 )
| ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SV9 @ SV10 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV5: a > a > $o,SV8: a > a > $o] :
( ( ( sK1_PROP @ SV8 )
= $false )
| ( ( SV5 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(109,plain,
! [SV8: a > a > $o,SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV8 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
= $false )
| ( ( sK1_PROP @ SV8 )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV10: a,SV9: a,SV5: a > a > $o] :
( ( ( ~ ( SV5 @ SV9 @ SV10 ) )
= $true )
| ( ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SV9 @ SV10 )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(111,plain,
! [SV8: a > a > $o,SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV8 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( SV5 @ ( sK12_SY135 @ SV4 @ SV2 @ SV3 @ SV8 @ SV5 ) @ ( sK13_SY139 @ SV8 @ SV3 @ SV2 @ SV4 @ SV5 ) )
= $true )
| ( ( sK1_PROP @ SV8 )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV3: a,SV2: a,SV4: a > a > $o,SV10: a,SV9: a,SV5: a > a > $o] :
( ( ( SV5 @ SV9 @ SV10 )
= $false )
| ( ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SV9 @ SV10 )
= $true )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( ~ ( SV4 @ SV2 @ SV3 ) )
= $true )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(113,plain,
! [SV10: a,SV9: a,SV5: a > a > $o,SV3: a,SV2: a,SV4: a > a > $o] :
( ( ( SV4 @ SV2 @ SV3 )
= $false )
| ( ( sK2_SY18 @ SV5 )
= $false )
| ( ( SV4 @ ( sK9_SV6 @ SV3 @ SV2 @ SV5 @ SV4 ) @ ( sK10_SV7 @ SV5 @ SV2 @ SV3 @ SV4 ) )
= $false )
| ( ( sK11_SY132 @ SV4 @ SV2 @ SV3 @ SV5 @ SV9 @ SV10 )
= $true )
| ( ( SV5 @ SV9 @ SV10 )
= $false )
| ( ( sK5_SX0 @ SV2 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(114,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,113,111,109,104,92,76,71,67,56,55,39,30]) ).
thf(115,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV124^5 : 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
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:43:42 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.92/0.43
% 0.92/0.43 No.of.Axioms: 0
% 0.92/0.43
% 0.92/0.43 Length.of.Defs: 0
% 0.92/0.43
% 0.92/0.43 Contains.Choice.Funs: false
% 0.92/0.43 ....
% 0.92/0.43
% 0.92/0.43 ********************************
% 0.92/0.43 * All subproblems solved! *
% 0.92/0.43 ********************************
% 0.92/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:114,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.92/0.43
% 0.92/0.43 %**** Beginning of derivation protocol ****
% 0.92/0.43 % SZS output start CNFRefutation
% See solution above
% 0.92/0.44
% 0.92/0.44 %**** End of derivation protocol ****
% 0.92/0.44 %**** no. of clauses in derivation: 115 ****
% 0.92/0.44 %**** clause counter: 114 ****
% 0.92/0.44
% 0.92/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:114,loop_count:0,foatp_calls:1,translation:fof_full)
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