%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM141+1 : TPTP v9.3.1. Released v6.4.0.
% 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 : n011.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 10:12:27 AM UTC 2026
% Result : Theorem 2.43s 0.61s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of formulae : 380 ( 199 unt; 0 typ; 0 def)
% Number of atoms : 2856 (1809 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 6023 (1509 ~; 933 |; 90 &;3398 @)
% ( 0 <=>; 93 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 12 con; 0-3 aty)
% Number of variables : 2067 ( 0 ^;2067 !; 0 ?;2067 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Vx,type,
sK1_Vx: $i ).
thf(tp_sK2_SY104,type,
sK2_SY104: $i ).
thf(tp_sK3_SY109,type,
sK3_SY109: $i ).
thf(tp_sK4_SY113,type,
sK4_SY113: $i ).
thf(tp_sK5_SY116,type,
sK5_SY116: $i ).
thf(tp_sK6_SY118,type,
sK6_SY118: $i ).
thf(tp_vabs,type,
vabs: $i > $i > $i > $i ).
thf(tp_vapp,type,
vapp: $i > $i > $i ).
thf(tp_varrow,type,
varrow: $i > $i > $i ).
thf(tp_vbind,type,
vbind: $i > $i > $i > $i ).
thf(tp_veabs,type,
veabs: $i ).
thf(tp_vempty,type,
vempty: $i ).
thf(tp_vgensym,type,
vgensym: $i > $i ).
thf(tp_vgetSomeExp,type,
vgetSomeExp: $i > $i ).
thf(tp_vgetSomeType,type,
vgetSomeType: $i > $i ).
thf(tp_visFreeVar,type,
visFreeVar: $i > $i > $o ).
thf(tp_visSomeExp,type,
visSomeExp: $i > $o ).
thf(tp_visSomeType,type,
visSomeType: $i > $o ).
thf(tp_visValue,type,
visValue: $i > $o ).
thf(tp_vlookup,type,
vlookup: $i > $i > $i ).
thf(tp_vnoExp,type,
vnoExp: $i ).
thf(tp_vnoType,type,
vnoType: $i ).
thf(tp_vreduce,type,
vreduce: $i > $i ).
thf(tp_vsomeExp,type,
vsomeExp: $i > $i ).
thf(tp_vsomeType,type,
vsomeType: $i > $i ).
thf(tp_vsubst,type,
vsubst: $i > $i > $i > $i ).
thf(tp_vtcheck,type,
vtcheck: $i > $i > $i > $o ).
thf(tp_vvar,type,
vvar: $i > $i ).
thf(1,axiom,
! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx = Vy )
& ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-abs-2') ).
thf(2,axiom,
! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx != Vy )
& ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-abs-1') ).
thf(3,axiom,
! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ veabs @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ veabs @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-abs-IH') ).
thf(6,axiom,
! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-abs') ).
thf(26,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst3) ).
thf(31,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(32,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate') ).
thf(34,axiom,
! [VTy: $i,Vy: $i,VVar0: $i,VCtx0: $i,RESULT: $i,Vx: $i,VC: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0
= ( vbind @ Vy @ VTy @ VC ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT
= ( vlookup @ Vx @ VC ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup2) ).
thf(35,axiom,
! [VC: $i,Vx: $i,Vy: $i,VVar0: $i,VCtx0: $i,RESULT: $i,VTy: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0
= ( vbind @ Vy @ VTy @ VC ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT
= ( vsomeType @ VTy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup1) ).
thf(36,axiom,
! [Vx: $i,VVar0: $i,VCtx0: $i,RESULT: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0 = vempty ) )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT = vnoType ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup0) ).
thf(39,axiom,
! [VOptTyp0: $i] :
( ( VOptTyp0 = vnoType )
=> ~ ( visSomeType @ VOptTyp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType0) ).
thf(40,axiom,
! [VTyp0: $i] :
( vnoType
!= ( vsomeType @ VTyp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noType-someType') ).
thf(41,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-empty-bind') ).
thf(43,axiom,
( ( ( vnoType = vnoType )
=> $true )
& ( $true
=> ( vnoType = vnoType ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-noType') ).
thf(44,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i,VVar1: $i,VTyp1: $i,VCtx1: $i] :
( ( ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) )
=> ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-bind') ).
thf(47,axiom,
! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).
thf(51,axiom,
! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0) ).
thf(52,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).
thf(54,axiom,
! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs') ).
thf(56,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-abs') ).
thf(58,conjecture,
! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-abs') ).
thf(59,negated_conjecture,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[58]) ).
thf(60,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $false ),
inference(unfold_def,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx = Vy )
& ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(62,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx != Vy )
& ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(63,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ veabs @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ veabs @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(65,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(66,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(67,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(68,plain,
( ( ! [VTy: $i,Vy: $i,VVar0: $i,VCtx0: $i,RESULT: $i,Vx: $i,VC: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0
= ( vbind @ Vy @ VTy @ VC ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT
= ( vlookup @ Vx @ VC ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(69,plain,
( ( ! [VC: $i,Vx: $i,Vy: $i,VVar0: $i,VCtx0: $i,RESULT: $i,VTy: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0
= ( vbind @ Vy @ VTy @ VC ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT
= ( vsomeType @ VTy ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(70,plain,
( ( ! [Vx: $i,VVar0: $i,VCtx0: $i,RESULT: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0 = vempty ) )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT = vnoType ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(71,plain,
( ( ! [VOptTyp0: $i] :
( ( VOptTyp0 = vnoType )
=> ~ ( visSomeType @ VOptTyp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(72,plain,
( ( ! [VTyp0: $i] :
( vnoType
!= ( vsomeType @ VTyp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(73,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(74,plain,
( ( ( ( vnoType = vnoType )
=> $true )
& ( $true
=> ( vnoType = vnoType ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(75,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i,VVar1: $i,VTyp1: $i,VCtx1: $i] :
( ( ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) )
=> ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(76,plain,
( ( ! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(77,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(79,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(80,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(81,plain,
( ( ! [SY104: $i,SY105: $i,SY106: $i,SY107: $i,SY108: $i] :
( ( ( ( vlookup @ sK1_Vx @ SY105 )
= vnoType )
& ( vtcheck @ SY105 @ ( vabs @ SY106 @ SY107 @ veabs ) @ SY108 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ SY104 @ SY105 ) @ ( vabs @ SY106 @ SY107 @ veabs ) @ SY108 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(82,plain,
( ( ! [SY109: $i,SY110: $i,SY111: $i,SY112: $i] :
( ( ( ( vlookup @ sK1_Vx @ SY109 )
= vnoType )
& ( vtcheck @ SY109 @ ( vabs @ SY110 @ SY111 @ veabs ) @ SY112 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ SY109 ) @ ( vabs @ SY110 @ SY111 @ veabs ) @ SY112 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(83,plain,
( ( ! [SY113: $i,SY114: $i,SY115: $i] :
( ( ( ( vlookup @ sK1_Vx @ sK3_SY109 )
= vnoType )
& ( vtcheck @ sK3_SY109 @ ( vabs @ SY113 @ SY114 @ veabs ) @ SY115 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ SY113 @ SY114 @ veabs ) @ SY115 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(84,plain,
( ( ! [SY116: $i,SY117: $i] :
( ( ( ( vlookup @ sK1_Vx @ sK3_SY109 )
= vnoType )
& ( vtcheck @ sK3_SY109 @ ( vabs @ sK4_SY113 @ SY116 @ veabs ) @ SY117 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ SY116 @ veabs ) @ SY117 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(85,plain,
( ( ! [SY118: $i] :
( ( ( ( vlookup @ sK1_Vx @ sK3_SY109 )
= vnoType )
& ( vtcheck @ sK3_SY109 @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ SY118 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ SY118 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(86,plain,
( ( ( ( ( vlookup @ sK1_Vx @ sK3_SY109 )
= vnoType )
& ( vtcheck @ sK3_SY109 @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(87,plain,
( ( ( vlookup @ sK1_Vx @ sK3_SY109 )
= vnoType )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(88,plain,
( ( vtcheck @ sK3_SY109 @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(89,plain,
( ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 )
= $false ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(90,plain,
( ( ~ ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 ) )
= $true ),
inference(polarity_switch,[status(thm)],[89]) ).
thf(91,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(92,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(93,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(94,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(95,plain,
( ( ! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(96,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i,VVar1: $i,VTyp1: $i,VCtx1: $i] :
( ( ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) )
=> ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(97,plain,
( ( ( ( vnoType = vnoType )
=> $true )
& ( $true
=> ( vnoType = vnoType ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(98,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(99,plain,
( ( ! [VTyp0: $i] :
( vnoType
!= ( vsomeType @ VTyp0 ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(100,plain,
( ( ! [VOptTyp0: $i] :
( ( VOptTyp0 = vnoType )
=> ~ ( visSomeType @ VOptTyp0 ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(101,plain,
( ( ! [Vx: $i,VVar0: $i,VCtx0: $i,RESULT: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0 = vempty ) )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT = vnoType ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(102,plain,
( ( ! [VC: $i,Vx: $i,Vy: $i,VVar0: $i,VCtx0: $i,RESULT: $i,VTy: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0
= ( vbind @ Vy @ VTy @ VC ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT
= ( vsomeType @ VTy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(103,plain,
( ( ! [VTy: $i,Vy: $i,VVar0: $i,VCtx0: $i,RESULT: $i,Vx: $i,VC: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0
= ( vbind @ Vy @ VTy @ VC ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT
= ( vlookup @ Vx @ VC ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(104,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(105,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(106,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(107,plain,
( ( ! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(108,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ veabs @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ veabs @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(109,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx != Vy )
& ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(110,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx = Vy )
& ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(111,plain,
( ( vtcheck @ sK3_SY109 @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(112,plain,
( ( ( vlookup @ sK1_Vx @ sK3_SY109 )
= vnoType )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(113,plain,
( ( ~ ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ( SX1 != SX4 )
| ( SX2
!= ( vabs @ SX3 @ SX0 @ SX5 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SX3 != SX4 ) )
| ~ ( visFreeVar @ SX4 @ SX5 ) )
| ( visFreeVar @ SX1 @ SX2 ) )
| ~ ( ~ ( visFreeVar @ SX1 @ SX2 )
| ~ ( ~ ( ( SX3 != SX4 ) )
| ~ ( visFreeVar @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( vnoType
!= ( vsomeType @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(118,plain,
( ( ~ ( ~ ( ( vnoType != vnoType )
| $true )
| ~ ( ~ $true
| ( vnoType = vnoType ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vabs @ SX3 @ SX4 @ SX5 ) )
| ~ ( ~ ~ ( ( SX0 != SX3 )
| ( SX1 != SX4 ) )
| ( SX2 != SX5 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SX0 != SX3 )
| ( SX1 != SX4 ) )
| ( SX2 != SX5 ) )
| ( ( vabs @ SX0 @ SX1 @ SX2 )
= ( vabs @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ( SX0 != SX3 )
| ( ( vlookup @ SX0 @ SX2 )
!= vnoType ) )
| ~ ( vtcheck @ SX2 @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( vtcheck @ ( vbind @ SX1 @ SX3 @ SX0 ) @ SX2 @ SX4 )
| ( vtcheck @ SX0 @ ( vabs @ SX1 @ SX3 @ SX2 ) @ ( varrow @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( ( SX2 != SX0 ) )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX3 @ ( vbind @ SX0 @ SX1 @ SX4 ) ) @ SX5 @ SX6 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ ( vbind @ SX2 @ SX3 @ SX4 ) ) @ SX5 @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( vempty
!= ( vbind @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(124,plain,
( ( ! [SX0: $i] :
( ( SX0 != vnoType )
| ~ ( visSomeType @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SX0 != SX3 ) )
| ( ( vlookup @ SX0 @ SX2 )
!= vnoType ) )
| ~ ( vtcheck @ SX2 @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( visValue @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( ( vbind @ SX0 @ SX1 @ SX2 )
!= ( vbind @ SX3 @ SX4 @ SX5 ) )
| ~ ( ~ ~ ( ( SX0 != SX3 )
| ( SX1 != SX4 ) )
| ( SX2 != SX5 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SX0 != SX3 )
| ( SX1 != SX4 ) )
| ( SX2 != SX5 ) )
| ( ( vbind @ SX0 @ SX1 @ SX2 )
= ( vbind @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ( SX1 != SX0 )
| ( SX2 != vempty ) )
| ( SX3
!= ( vlookup @ SX1 @ SX2 ) )
| ( SX3 = vnoType ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX1 )
| ( SX3 != SX0 ) )
| ( SX4
!= ( vabs @ SX6 @ SX7 @ SX8 ) ) )
| ( SX1 != SX6 )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5
= ( vabs @ SX6 @ SX7 @ SX8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ( SX3 != SX1 )
| ( SX4
!= ( vbind @ SX2 @ SX6 @ SX0 ) ) )
| ( SX1 != SX2 )
| ( SX5
!= ( vlookup @ SX3 @ SX4 ) )
| ( SX5
= ( vsomeType @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ( SX2 != SX5 )
| ( SX3
!= ( vbind @ SX1 @ SX0 @ SX6 ) ) )
| ~ ( ( SX5 != SX1 ) )
| ( SX4
!= ( vlookup @ SX2 @ SX3 ) )
| ( SX4
= ( vlookup @ SX5 @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ( SX2 != SX0 )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX3 @ ( vbind @ SX0 @ SX1 @ SX4 ) ) @ SX5 @ SX6 ) )
| ( vtcheck @ ( vbind @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ( ( vlookup @ SX0 @ SX2 )
!= vnoType )
| ~ ( vtcheck @ SX2 @ veabs @ SX3 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ veabs @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(134,plain,
( ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY104 @ sK3_SY109 ) @ ( vabs @ sK4_SY113 @ sK5_SY116 @ veabs ) @ sK6_SY118 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(135,plain,
! [SV1: $i] :
( ( ! [SY119: $i,SY120: $i,SY121: $i] :
( ( vvar @ SV1 )
!= ( vabs @ SY119 @ SY120 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(136,plain,
! [SV2: $i] :
( ( ! [SY122: $i,SY123: $i,SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ( SY122 != SY125 )
| ( SY123
!= ( vabs @ SY124 @ SV2 @ SY126 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY124 != SY125 ) )
| ~ ( visFreeVar @ SY125 @ SY126 ) )
| ( visFreeVar @ SY122 @ SY123 ) )
| ~ ( ~ ( visFreeVar @ SY122 @ SY123 )
| ~ ( ~ ( ( SY124 != SY125 ) )
| ~ ( visFreeVar @ SY125 @ SY126 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(137,plain,
! [SV3: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i,SY130: $i] :
( ( vabs @ SV3 @ SY127 @ SY128 )
!= ( vapp @ SY129 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(138,plain,
! [SV4: $i] :
( ( vnoType
!= ( vsomeType @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(139,plain,
( ( ~ ( ( vnoType != vnoType )
| $true )
| ~ ( ~ $true
| ( vnoType = vnoType ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(140,plain,
! [SV5: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
~ ( ~ ( ( ( vabs @ SV5 @ SY131 @ SY132 )
!= ( vabs @ SY133 @ SY134 @ SY135 ) )
| ~ ( ~ ~ ( ( SV5 != SY133 )
| ( SY131 != SY134 ) )
| ( SY132 != SY135 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SY133 )
| ( SY131 != SY134 ) )
| ( SY132 != SY135 ) )
| ( ( vabs @ SV5 @ SY131 @ SY132 )
= ( vabs @ SY133 @ SY134 @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(141,plain,
! [SV6: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i,SY139: $i,SY140: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY138 )
| ( ( vlookup @ SV6 @ SY137 )
!= vnoType ) )
| ~ ( vtcheck @ SY137 @ ( vabs @ SY138 @ SY139 @ veabs ) @ SY140 ) )
| ( vtcheck @ ( vbind @ SV6 @ SY136 @ SY137 ) @ ( vabs @ SY138 @ SY139 @ veabs ) @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(142,plain,
! [SV7: $i] :
( ( ! [SY141: $i,SY142: $i,SY143: $i,SY144: $i] :
( ~ ( vtcheck @ ( vbind @ SY141 @ SY143 @ SV7 ) @ SY142 @ SY144 )
| ( vtcheck @ SV7 @ ( vabs @ SY141 @ SY143 @ SY142 ) @ ( varrow @ SY143 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(143,plain,
! [SV8: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i,SY148: $i,SY149: $i,SY150: $i] :
( ~ ~ ( ~ ( ( SY146 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SY146 @ SY147 @ ( vbind @ SV8 @ SY145 @ SY148 ) ) @ SY149 @ SY150 ) )
| ( vtcheck @ ( vbind @ SV8 @ SY145 @ ( vbind @ SY146 @ SY147 @ SY148 ) ) @ SY149 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(144,plain,
! [SV9: $i] :
( ( ! [SY151: $i,SY152: $i] :
( vempty
!= ( vbind @ SV9 @ SY151 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(145,plain,
! [SV10: $i] :
( ( ( SV10 != vnoType )
| ~ ( visSomeType @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(146,plain,
! [SV11: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SY155 ) )
| ( ( vlookup @ SV11 @ SY154 )
!= vnoType ) )
| ~ ( vtcheck @ SY154 @ ( vabs @ SY155 @ SY156 @ veabs ) @ SY157 ) )
| ( vtcheck @ ( vbind @ SV11 @ SY153 @ SY154 ) @ ( vabs @ SY155 @ SY156 @ veabs ) @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV12: $i] :
( ( ! [SY158: $i,SY159: $i,SY160: $i] :
( ( SY160
!= ( vabs @ SV12 @ SY158 @ SY159 ) )
| ( visValue @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV13: $i] :
( ( ! [SY161: $i,SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
~ ( ~ ( ( ( vbind @ SV13 @ SY161 @ SY162 )
!= ( vbind @ SY163 @ SY164 @ SY165 ) )
| ~ ( ~ ~ ( ( SV13 != SY163 )
| ( SY161 != SY164 ) )
| ( SY162 != SY165 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SY163 )
| ( SY161 != SY164 ) )
| ( SY162 != SY165 ) )
| ( ( vbind @ SV13 @ SY161 @ SY162 )
= ( vbind @ SY163 @ SY164 @ SY165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV14: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ( SY166 != SV14 )
| ( SY167 != vempty ) )
| ( SY168
!= ( vlookup @ SY166 @ SY167 ) )
| ( SY168 = vnoType ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV15: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i,SY173: $i,SY174: $i,SY175: $i,SY176: $i] :
( ~ ~ ( ~ ~ ( ( SY170 != SY169 )
| ( SY171 != SV15 ) )
| ( SY172
!= ( vabs @ SY174 @ SY175 @ SY176 ) ) )
| ( SY169 != SY174 )
| ( SY173
!= ( vsubst @ SY170 @ SY171 @ SY172 ) )
| ( SY173
= ( vabs @ SY174 @ SY175 @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV16: $i] :
( ( ! [SY177: $i,SY178: $i,SY179: $i,SY180: $i,SY181: $i,SY182: $i] :
( ~ ~ ( ( SY179 != SY177 )
| ( SY180
!= ( vbind @ SY178 @ SY182 @ SV16 ) ) )
| ( SY177 != SY178 )
| ( SY181
!= ( vlookup @ SY179 @ SY180 ) )
| ( SY181
= ( vsomeType @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV17: $i] :
( ( ! [SY183: $i,SY184: $i,SY185: $i,SY186: $i,SY187: $i,SY188: $i] :
( ~ ~ ( ( SY184 != SY187 )
| ( SY185
!= ( vbind @ SY183 @ SV17 @ SY188 ) ) )
| ~ ( ( SY187 != SY183 ) )
| ( SY186
!= ( vlookup @ SY184 @ SY185 ) )
| ( SY186
= ( vlookup @ SY187 @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV18: $i] :
( ( ! [SY189: $i,SY190: $i,SY191: $i,SY192: $i,SY193: $i,SY194: $i] :
( ~ ~ ( ( SY190 != SV18 )
| ~ ( vtcheck @ ( vbind @ SY190 @ SY191 @ ( vbind @ SV18 @ SY189 @ SY192 ) ) @ SY193 @ SY194 ) )
| ( vtcheck @ ( vbind @ SY190 @ SY191 @ SY192 ) @ SY193 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV19: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ~ ~ ( ( ( vlookup @ SV19 @ SY196 )
!= vnoType )
| ~ ( vtcheck @ SY196 @ veabs @ SY197 ) )
| ( vtcheck @ ( vbind @ SV19 @ SY195 @ SY196 ) @ veabs @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV20: $i,SV1: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ( vvar @ SV1 )
!= ( vabs @ SV20 @ SY198 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(156,plain,
! [SV2: $i,SV21: $i] :
( ( ! [SY200: $i,SY201: $i,SY202: $i,SY203: $i] :
( ~ ~ ( ( SV21 != SY202 )
| ( SY200
!= ( vabs @ SY201 @ SV2 @ SY203 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY201 != SY202 ) )
| ~ ( visFreeVar @ SY202 @ SY203 ) )
| ( visFreeVar @ SV21 @ SY200 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SY200 )
| ~ ( ~ ( ( SY201 != SY202 ) )
| ~ ( visFreeVar @ SY202 @ SY203 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(157,plain,
! [SV22: $i,SV3: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i] :
( ( vabs @ SV3 @ SV22 @ SY204 )
!= ( vapp @ SY205 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(158,plain,
! [SV4: $i] :
( ( vnoType
= ( vsomeType @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(159,plain,
( ( ~ ( ( vnoType != vnoType )
| $true ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(160,plain,
( ( ~ ( ~ $true
| ( vnoType = vnoType ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(161,plain,
! [SV23: $i,SV5: $i] :
( ( ! [SY207: $i,SY208: $i,SY209: $i,SY210: $i] :
~ ( ~ ( ( ( vabs @ SV5 @ SV23 @ SY207 )
!= ( vabs @ SY208 @ SY209 @ SY210 ) )
| ~ ( ~ ~ ( ( SV5 != SY208 )
| ( SV23 != SY209 ) )
| ( SY207 != SY210 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SY208 )
| ( SV23 != SY209 ) )
| ( SY207 != SY210 ) )
| ( ( vabs @ SV5 @ SV23 @ SY207 )
= ( vabs @ SY208 @ SY209 @ SY210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(162,plain,
! [SV24: $i,SV6: $i] :
( ( ! [SY211: $i,SY212: $i,SY213: $i,SY214: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY212 )
| ( ( vlookup @ SV6 @ SY211 )
!= vnoType ) )
| ~ ( vtcheck @ SY211 @ ( vabs @ SY212 @ SY213 @ veabs ) @ SY214 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV24 @ SY211 ) @ ( vabs @ SY212 @ SY213 @ veabs ) @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(163,plain,
! [SV7: $i,SV25: $i] :
( ( ! [SY215: $i,SY216: $i,SY217: $i] :
( ~ ( vtcheck @ ( vbind @ SV25 @ SY216 @ SV7 ) @ SY215 @ SY217 )
| ( vtcheck @ SV7 @ ( vabs @ SV25 @ SY216 @ SY215 ) @ ( varrow @ SY216 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(164,plain,
! [SV26: $i,SV8: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i,SY221: $i,SY222: $i] :
( ~ ~ ( ~ ( ( SY218 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SY218 @ SY219 @ ( vbind @ SV8 @ SV26 @ SY220 ) ) @ SY221 @ SY222 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SY218 @ SY219 @ SY220 ) ) @ SY221 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(165,plain,
! [SV27: $i,SV9: $i] :
( ( ! [SY223: $i] :
( vempty
!= ( vbind @ SV9 @ SV27 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(166,plain,
! [SV10: $i] :
( ( ( SV10 != vnoType )
= $true )
| ( ( ~ ( visSomeType @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(167,plain,
! [SV28: $i,SV11: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i,SY227: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SY225 ) )
| ( ( vlookup @ SV11 @ SY224 )
!= vnoType ) )
| ~ ( vtcheck @ SY224 @ ( vabs @ SY225 @ SY226 @ veabs ) @ SY227 ) )
| ( vtcheck @ ( vbind @ SV11 @ SV28 @ SY224 ) @ ( vabs @ SY225 @ SY226 @ veabs ) @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV29: $i,SV12: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ( SY229
!= ( vabs @ SV12 @ SV29 @ SY228 ) )
| ( visValue @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV30: $i,SV13: $i] :
( ( ! [SY230: $i,SY231: $i,SY232: $i,SY233: $i] :
~ ( ~ ( ( ( vbind @ SV13 @ SV30 @ SY230 )
!= ( vbind @ SY231 @ SY232 @ SY233 ) )
| ~ ( ~ ~ ( ( SV13 != SY231 )
| ( SV30 != SY232 ) )
| ( SY230 != SY233 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SY231 )
| ( SV30 != SY232 ) )
| ( SY230 != SY233 ) )
| ( ( vbind @ SV13 @ SV30 @ SY230 )
= ( vbind @ SY231 @ SY232 @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV14: $i,SV31: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ~ ~ ( ( SV31 != SV14 )
| ( SY234 != vempty ) )
| ( SY235
!= ( vlookup @ SV31 @ SY234 ) )
| ( SY235 = vnoType ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(171,plain,
! [SV15: $i,SV32: $i] :
( ( ! [SY236: $i,SY237: $i,SY238: $i,SY239: $i,SY240: $i,SY241: $i,SY242: $i] :
( ~ ~ ( ~ ~ ( ( SY236 != SV32 )
| ( SY237 != SV15 ) )
| ( SY238
!= ( vabs @ SY240 @ SY241 @ SY242 ) ) )
| ( SV32 != SY240 )
| ( SY239
!= ( vsubst @ SY236 @ SY237 @ SY238 ) )
| ( SY239
= ( vabs @ SY240 @ SY241 @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(172,plain,
! [SV16: $i,SV33: $i] :
( ( ! [SY243: $i,SY244: $i,SY245: $i,SY246: $i,SY247: $i] :
( ~ ~ ( ( SY244 != SV33 )
| ( SY245
!= ( vbind @ SY243 @ SY247 @ SV16 ) ) )
| ( SV33 != SY243 )
| ( SY246
!= ( vlookup @ SY244 @ SY245 ) )
| ( SY246
= ( vsomeType @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(173,plain,
! [SV17: $i,SV34: $i] :
( ( ! [SY248: $i,SY249: $i,SY250: $i,SY251: $i,SY252: $i] :
( ~ ~ ( ( SY248 != SY251 )
| ( SY249
!= ( vbind @ SV34 @ SV17 @ SY252 ) ) )
| ~ ( ( SY251 != SV34 ) )
| ( SY250
!= ( vlookup @ SY248 @ SY249 ) )
| ( SY250
= ( vlookup @ SY251 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(174,plain,
! [SV35: $i,SV18: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i,SY256: $i,SY257: $i] :
( ~ ~ ( ( SY253 != SV18 )
| ~ ( vtcheck @ ( vbind @ SY253 @ SY254 @ ( vbind @ SV18 @ SV35 @ SY255 ) ) @ SY256 @ SY257 ) )
| ( vtcheck @ ( vbind @ SY253 @ SY254 @ SY255 ) @ SY256 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(175,plain,
! [SV36: $i,SV19: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ~ ( ( ( vlookup @ SV19 @ SY258 )
!= vnoType )
| ~ ( vtcheck @ SY258 @ veabs @ SY259 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV36 @ SY258 ) @ veabs @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(176,plain,
! [SV37: $i,SV20: $i,SV1: $i] :
( ( ! [SY260: $i] :
( ( vvar @ SV1 )
!= ( vabs @ SV20 @ SV37 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV2: $i,SV38: $i,SV21: $i] :
( ( ! [SY261: $i,SY262: $i,SY263: $i] :
( ~ ~ ( ( SV21 != SY262 )
| ( SV38
!= ( vabs @ SY261 @ SV2 @ SY263 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY261 != SY262 ) )
| ~ ( visFreeVar @ SY262 @ SY263 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SY261 != SY262 ) )
| ~ ( visFreeVar @ SY262 @ SY263 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(178,plain,
! [SV39: $i,SV22: $i,SV3: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ( vabs @ SV3 @ SV22 @ SV39 )
!= ( vapp @ SY264 @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(179,plain,
( ( ( vnoType != vnoType )
| $true )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(180,plain,
( ( ~ $true
| ( vnoType = vnoType ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(181,plain,
! [SV40: $i,SV23: $i,SV5: $i] :
( ( ! [SY266: $i,SY267: $i,SY268: $i] :
~ ( ~ ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SY266 @ SY267 @ SY268 ) )
| ~ ( ~ ~ ( ( SV5 != SY266 )
| ( SV23 != SY267 ) )
| ( SV40 != SY268 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SY266 )
| ( SV23 != SY267 ) )
| ( SV40 != SY268 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SY266 @ SY267 @ SY268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(182,plain,
! [SV24: $i,SV41: $i,SV6: $i] :
( ( ! [SY269: $i,SY270: $i,SY271: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY269 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SY269 @ SY270 @ veabs ) @ SY271 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SY269 @ SY270 @ veabs ) @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV42: $i,SV7: $i,SV25: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( vtcheck @ ( vbind @ SV25 @ SY272 @ SV7 ) @ SV42 @ SY273 )
| ( vtcheck @ SV7 @ ( vabs @ SV25 @ SY272 @ SV42 ) @ ( varrow @ SY272 @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(184,plain,
! [SV26: $i,SV8: $i,SV43: $i] :
( ( ! [SY274: $i,SY275: $i,SY276: $i,SY277: $i] :
( ~ ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SY274 @ ( vbind @ SV8 @ SV26 @ SY275 ) ) @ SY276 @ SY277 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SY274 @ SY275 ) ) @ SY276 @ SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(185,plain,
! [SV44: $i,SV27: $i,SV9: $i] :
( ( vempty
!= ( vbind @ SV9 @ SV27 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(186,plain,
! [SV10: $i] :
( ( ( SV10 = vnoType )
= $false )
| ( ( ~ ( visSomeType @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(187,plain,
! [SV28: $i,SV45: $i,SV11: $i] :
( ( ! [SY278: $i,SY279: $i,SY280: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SY278 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SY278 @ SY279 @ veabs ) @ SY280 ) )
| ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SY278 @ SY279 @ veabs ) @ SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(188,plain,
! [SV46: $i,SV29: $i,SV12: $i] :
( ( ! [SY281: $i] :
( ( SY281
!= ( vabs @ SV12 @ SV29 @ SV46 ) )
| ( visValue @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(189,plain,
! [SV47: $i,SV30: $i,SV13: $i] :
( ( ! [SY282: $i,SY283: $i,SY284: $i] :
~ ( ~ ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SY282 @ SY283 @ SY284 ) )
| ~ ( ~ ~ ( ( SV13 != SY282 )
| ( SV30 != SY283 ) )
| ( SV47 != SY284 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SY282 )
| ( SV30 != SY283 ) )
| ( SV47 != SY284 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SY282 @ SY283 @ SY284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(190,plain,
! [SV48: $i,SV14: $i,SV31: $i] :
( ( ! [SY285: $i] :
( ~ ~ ( ( SV31 != SV14 )
| ( SV48 != vempty ) )
| ( SY285
!= ( vlookup @ SV31 @ SV48 ) )
| ( SY285 = vnoType ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(191,plain,
! [SV15: $i,SV32: $i,SV49: $i] :
( ( ! [SY286: $i,SY287: $i,SY288: $i,SY289: $i,SY290: $i,SY291: $i] :
( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SY286 != SV15 ) )
| ( SY287
!= ( vabs @ SY289 @ SY290 @ SY291 ) ) )
| ( SV32 != SY289 )
| ( SY288
!= ( vsubst @ SV49 @ SY286 @ SY287 ) )
| ( SY288
= ( vabs @ SY289 @ SY290 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(192,plain,
! [SV16: $i,SV50: $i,SV33: $i] :
( ( ! [SY292: $i,SY293: $i,SY294: $i,SY295: $i] :
( ~ ~ ( ( SY292 != SV33 )
| ( SY293
!= ( vbind @ SV50 @ SY295 @ SV16 ) ) )
| ( SV33 != SV50 )
| ( SY294
!= ( vlookup @ SY292 @ SY293 ) )
| ( SY294
= ( vsomeType @ SY295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(193,plain,
! [SV17: $i,SV34: $i,SV51: $i] :
( ( ! [SY296: $i,SY297: $i,SY298: $i,SY299: $i] :
( ~ ~ ( ( SV51 != SY298 )
| ( SY296
!= ( vbind @ SV34 @ SV17 @ SY299 ) ) )
| ~ ( ( SY298 != SV34 ) )
| ( SY297
!= ( vlookup @ SV51 @ SY296 ) )
| ( SY297
= ( vlookup @ SY298 @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(194,plain,
! [SV35: $i,SV18: $i,SV52: $i] :
( ( ! [SY300: $i,SY301: $i,SY302: $i,SY303: $i] :
( ~ ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SY300 @ ( vbind @ SV18 @ SV35 @ SY301 ) ) @ SY302 @ SY303 ) )
| ( vtcheck @ ( vbind @ SV52 @ SY300 @ SY301 ) @ SY302 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(195,plain,
! [SV36: $i,SV53: $i,SV19: $i] :
( ( ! [SY304: $i] :
( ~ ~ ( ( ( vlookup @ SV19 @ SV53 )
!= vnoType )
| ~ ( vtcheck @ SV53 @ veabs @ SY304 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(196,plain,
! [SV54: $i,SV37: $i,SV20: $i,SV1: $i] :
( ( ( vvar @ SV1 )
!= ( vabs @ SV20 @ SV37 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(197,plain,
! [SV2: $i,SV55: $i,SV38: $i,SV21: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ~ ( ( SV21 != SY305 )
| ( SV38
!= ( vabs @ SV55 @ SV2 @ SY306 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SY305 ) )
| ~ ( visFreeVar @ SY305 @ SY306 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SY305 ) )
| ~ ( visFreeVar @ SY305 @ SY306 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(198,plain,
! [SV56: $i,SV39: $i,SV22: $i,SV3: $i] :
( ( ! [SY307: $i] :
( ( vabs @ SV3 @ SV22 @ SV39 )
!= ( vapp @ SV56 @ SY307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(199,plain,
( ( ( vnoType != vnoType )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(200,plain,
( ( ( ~ $true ) = $true )
| ( ( vnoType = vnoType )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(201,plain,
! [SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ! [SY308: $i,SY309: $i] :
~ ( ~ ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SY308 @ SY309 ) )
| ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SY308 ) )
| ( SV40 != SY309 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SY308 ) )
| ( SV40 != SY309 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SY308 @ SY309 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(202,plain,
! [SV24: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SY310 @ veabs ) @ SY311 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SY310 @ veabs ) @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(203,plain,
! [SV42: $i,SV7: $i,SV59: $i,SV25: $i] :
( ( ! [SY312: $i] :
( ~ ( vtcheck @ ( vbind @ SV25 @ SV59 @ SV7 ) @ SV42 @ SY312 )
| ( vtcheck @ SV7 @ ( vabs @ SV25 @ SV59 @ SV42 ) @ ( varrow @ SV59 @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(204,plain,
! [SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i] :
( ~ ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SY313 ) ) @ SY314 @ SY315 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SY313 ) ) @ SY314 @ SY315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(205,plain,
! [SV44: $i,SV27: $i,SV9: $i] :
( ( vempty
= ( vbind @ SV9 @ SV27 @ SV44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(206,plain,
! [SV10: $i] :
( ( ( visSomeType @ SV10 )
= $false )
| ( ( SV10 = vnoType )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(207,plain,
! [SV28: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SY316 @ veabs ) @ SY317 ) )
| ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SY316 @ veabs ) @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(208,plain,
! [SV46: $i,SV29: $i,SV12: $i,SV62: $i] :
( ( ( SV62
!= ( vabs @ SV12 @ SV29 @ SV46 ) )
| ( visValue @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(209,plain,
! [SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ! [SY318: $i,SY319: $i] :
~ ( ~ ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SY318 @ SY319 ) )
| ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SY318 ) )
| ( SV47 != SY319 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SY318 ) )
| ( SV47 != SY319 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SY318 @ SY319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV64: $i,SV48: $i,SV14: $i,SV31: $i] :
( ( ~ ~ ( ( SV31 != SV14 )
| ( SV48 != vempty ) )
| ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ! [SY320: $i,SY321: $i,SY322: $i,SY323: $i,SY324: $i] :
( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SY320
!= ( vabs @ SY322 @ SY323 @ SY324 ) ) )
| ( SV32 != SY322 )
| ( SY321
!= ( vsubst @ SV49 @ SV65 @ SY320 ) )
| ( SY321
= ( vabs @ SY322 @ SY323 @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(212,plain,
! [SV16: $i,SV50: $i,SV33: $i,SV66: $i] :
( ( ! [SY325: $i,SY326: $i,SY327: $i] :
( ~ ~ ( ( SV66 != SV33 )
| ( SY325
!= ( vbind @ SV50 @ SY327 @ SV16 ) ) )
| ( SV33 != SV50 )
| ( SY326
!= ( vlookup @ SV66 @ SY325 ) )
| ( SY326
= ( vsomeType @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(213,plain,
! [SV17: $i,SV34: $i,SV67: $i,SV51: $i] :
( ( ! [SY328: $i,SY329: $i,SY330: $i] :
( ~ ~ ( ( SV51 != SY329 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SY330 ) ) )
| ~ ( ( SY329 != SV34 ) )
| ( SY328
!= ( vlookup @ SV51 @ SV67 ) )
| ( SY328
= ( vlookup @ SY329 @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(214,plain,
! [SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ! [SY331: $i,SY332: $i,SY333: $i] :
( ~ ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SY331 ) ) @ SY332 @ SY333 ) )
| ( vtcheck @ ( vbind @ SV52 @ SV68 @ SY331 ) @ SY332 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(215,plain,
! [SV36: $i,SV69: $i,SV53: $i,SV19: $i] :
( ( ~ ~ ( ( ( vlookup @ SV19 @ SV53 )
!= vnoType )
| ~ ( vtcheck @ SV53 @ veabs @ SV69 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(216,plain,
! [SV54: $i,SV37: $i,SV20: $i,SV1: $i] :
( ( ( vvar @ SV1 )
= ( vabs @ SV20 @ SV37 @ SV54 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(217,plain,
! [SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ! [SY334: $i] :
( ~ ~ ( ( SV21 != SV70 )
| ( SV38
!= ( vabs @ SV55 @ SV2 @ SY334 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SY334 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SY334 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(218,plain,
! [SV71: $i,SV56: $i,SV39: $i,SV22: $i,SV3: $i] :
( ( ( vabs @ SV3 @ SV22 @ SV39 )
!= ( vapp @ SV56 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(219,plain,
( ( ( vnoType = vnoType )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(220,plain,
( ( $true = $false )
| ( ( vnoType = vnoType )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ! [SY335: $i] :
~ ( ~ ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SV72 @ SY335 ) )
| ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SY335 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SY335 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SY335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV24: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ! [SY336: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SY336 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(223,plain,
! [SV74: $i,SV42: $i,SV7: $i,SV59: $i,SV25: $i] :
( ( ~ ( vtcheck @ ( vbind @ SV25 @ SV59 @ SV7 ) @ SV42 @ SV74 )
| ( vtcheck @ SV7 @ ( vabs @ SV25 @ SV59 @ SV42 ) @ ( varrow @ SV59 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(224,plain,
! [SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ~ ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SY337 @ SY338 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SY337 @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(225,plain,
! [SV28: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ! [SY339: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SY339 ) )
| ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(226,plain,
! [SV46: $i,SV29: $i,SV12: $i,SV62: $i] :
( ( ( SV62
!= ( vabs @ SV12 @ SV29 @ SV46 ) )
= $true )
| ( ( visValue @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ! [SY340: $i] :
~ ( ~ ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SV77 @ SY340 ) )
| ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SY340 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SY340 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(228,plain,
! [SV64: $i,SV48: $i,SV14: $i,SV31: $i] :
( ( ( ~ ~ ( ( SV31 != SV14 )
| ( SV48 != vempty ) ) )
= $true )
| ( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ! [SY341: $i,SY342: $i,SY343: $i,SY344: $i] :
( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SY342 @ SY343 @ SY344 ) ) )
| ( SV32 != SY342 )
| ( SY341
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SY341
= ( vabs @ SY342 @ SY343 @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(230,plain,
! [SV16: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ~ ~ ( ( SV66 != SV33 )
| ( SV79
!= ( vbind @ SV50 @ SY346 @ SV16 ) ) )
| ( SV33 != SV50 )
| ( SY345
!= ( vlookup @ SV66 @ SV79 ) )
| ( SY345
= ( vsomeType @ SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(231,plain,
! [SV80: $i,SV17: $i,SV34: $i,SV67: $i,SV51: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ~ ~ ( ( SV51 != SY347 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SY348 ) ) )
| ~ ( ( SY347 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SY347 @ SY348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(232,plain,
! [SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ! [SY349: $i,SY350: $i] :
( ~ ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SY349 @ SY350 ) )
| ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SY349 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(233,plain,
! [SV36: $i,SV69: $i,SV53: $i,SV19: $i] :
( ( ( ~ ~ ( ( ( vlookup @ SV19 @ SV53 )
!= vnoType )
| ~ ( vtcheck @ SV53 @ veabs @ SV69 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(234,plain,
! [SV82: $i,SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ~ ~ ( ( SV21 != SV70 )
| ( SV38
!= ( vabs @ SV55 @ SV2 @ SV82 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV71: $i,SV56: $i,SV39: $i,SV22: $i,SV3: $i] :
( ( ( vabs @ SV3 @ SV22 @ SV39 )
= ( vapp @ SV56 @ SV71 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV83: $i,SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ~ ( ~ ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SV72 @ SV83 ) )
| ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(238,plain,
! [SV74: $i,SV42: $i,SV7: $i,SV59: $i,SV25: $i] :
( ( ( ~ ( vtcheck @ ( vbind @ SV25 @ SV59 @ SV7 ) @ SV42 @ SV74 ) )
= $true )
| ( ( vtcheck @ SV7 @ ( vabs @ SV25 @ SV59 @ SV42 ) @ ( varrow @ SV59 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ! [SY351: $i] :
( ~ ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SY351 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(240,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
| ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(241,plain,
! [SV46: $i,SV29: $i,SV12: $i,SV62: $i] :
( ( ( SV62
= ( vabs @ SV12 @ SV29 @ SV46 ) )
= $false )
| ( ( visValue @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV87: $i,SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ~ ( ~ ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SV77 @ SV87 ) )
| ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV64: $i,SV48: $i,SV14: $i,SV31: $i] :
( ( ( ~ ( ( SV31 != SV14 )
| ( SV48 != vempty ) ) )
= $false )
| ( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV88: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ! [SY352: $i,SY353: $i,SY354: $i] :
( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SY352 @ SY353 @ SY354 ) ) )
| ( SV32 != SY352 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SY352 @ SY353 @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV89: $i,SV16: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ! [SY355: $i] :
( ~ ~ ( ( SV66 != SV33 )
| ( SV79
!= ( vbind @ SV50 @ SY355 @ SV16 ) ) )
| ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SY355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV80: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ! [SY356: $i] :
( ~ ~ ( ( SV51 != SV90 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SY356 ) ) )
| ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(247,plain,
! [SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ! [SY357: $i] :
( ~ ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SY357 ) )
| ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SY357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV36: $i,SV69: $i,SV53: $i,SV19: $i] :
( ( ( ~ ( ( ( vlookup @ SV19 @ SV53 )
!= vnoType )
| ~ ( vtcheck @ SV53 @ veabs @ SV69 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV82: $i,SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ( ~ ~ ( ( SV21 != SV70 )
| ( SV38
!= ( vabs @ SV55 @ SV2 @ SV82 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(250,plain,
! [SV83: $i,SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ~ ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SV72 @ SV83 ) )
| ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(251,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(252,plain,
! [SV74: $i,SV42: $i,SV7: $i,SV59: $i,SV25: $i] :
( ( ( vtcheck @ ( vbind @ SV25 @ SV59 @ SV7 ) @ SV42 @ SV74 )
= $false )
| ( ( vtcheck @ SV7 @ ( vabs @ SV25 @ SV59 @ SV42 ) @ ( varrow @ SV59 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(253,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ~ ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(254,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(255,plain,
! [SV87: $i,SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ~ ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SV77 @ SV87 ) )
| ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(256,plain,
! [SV64: $i,SV48: $i,SV14: $i,SV31: $i] :
( ( ( ( SV31 != SV14 )
| ( SV48 != vempty ) )
= $true )
| ( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(257,plain,
! [SV88: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ! [SY358: $i,SY359: $i] :
( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SV93 @ SY358 @ SY359 ) ) )
| ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SY358 @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(258,plain,
! [SV89: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ~ ~ ( ( SV66 != SV33 )
| ( SV79
!= ( vbind @ SV50 @ SV94 @ SV16 ) ) )
| ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(259,plain,
! [SV80: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ~ ~ ( ( SV51 != SV90 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SV95 ) ) )
| ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(260,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ~ ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 ) )
| ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(261,plain,
! [SV36: $i,SV69: $i,SV53: $i,SV19: $i] :
( ( ( ( ( vlookup @ SV19 @ SV53 )
!= vnoType )
| ~ ( vtcheck @ SV53 @ veabs @ SV69 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(262,plain,
! [SV82: $i,SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ( ~ ( ( SV21 != SV70 )
| ( SV38
!= ( vabs @ SV55 @ SV2 @ SV82 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(263,plain,
! [SV83: $i,SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ~ ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SV72 @ SV83 ) )
| ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(264,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(265,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(266,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(267,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV87: $i,SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ~ ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SV77 @ SV87 ) )
| ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(269,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(270,plain,
! [SV64: $i,SV48: $i,SV14: $i,SV31: $i] :
( ( ( SV31 != SV14 )
= $true )
| ( ( SV48 != vempty )
= $true )
| ( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(271,plain,
! [SV88: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ! [SY360: $i] :
( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SV93 @ SV97 @ SY360 ) ) )
| ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(272,plain,
! [SV89: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ( ~ ~ ( ( SV66 != SV33 )
| ( SV79
!= ( vbind @ SV50 @ SV94 @ SV16 ) ) ) )
= $true )
| ( ( ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(273,plain,
! [SV80: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ( ~ ~ ( ( SV51 != SV90 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(274,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ( ~ ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(275,plain,
! [SV36: $i,SV69: $i,SV53: $i,SV19: $i] :
( ( ( ( vlookup @ SV19 @ SV53 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV53 @ veabs @ SV69 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(276,plain,
! [SV82: $i,SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ( ( SV21 != SV70 )
| ( SV38
!= ( vabs @ SV55 @ SV2 @ SV82 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(277,plain,
! [SV83: $i,SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SV72 @ SV83 ) )
| ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(278,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) )
| ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(279,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
| ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(280,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ( ~ ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(282,plain,
! [SV87: $i,SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SV77 @ SV87 ) )
| ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(283,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) )
| ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(284,plain,
! [SV64: $i,SV48: $i,SV14: $i,SV31: $i] :
( ( ( SV31 = SV14 )
= $false )
| ( ( SV48 != vempty )
= $true )
| ( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(285,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
| ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(286,plain,
! [SV89: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( ( SV66 != SV33 )
| ( SV79
!= ( vbind @ SV50 @ SV94 @ SV16 ) ) ) )
= $false )
| ( ( ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(287,plain,
! [SV80: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ( ~ ( ( SV51 != SV90 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(288,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ( ~ ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(289,plain,
! [SV36: $i,SV69: $i,SV53: $i,SV19: $i] :
( ( ( ( vlookup @ SV19 @ SV53 )
= vnoType )
= $false )
| ( ( ~ ( vtcheck @ SV53 @ veabs @ SV69 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(290,plain,
! [SV82: $i,SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ( SV21 != SV70 )
= $true )
| ( ( SV38
!= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(291,plain,
! [SV83: $i,SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ( ( vabs @ SV5 @ SV23 @ SV40 )
!= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(292,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(293,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( ~ ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(294,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ( ~ ( ( SV43 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(295,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(296,plain,
! [SV87: $i,SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ( ( vbind @ SV13 @ SV30 @ SV47 )
!= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(297,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV64: $i,SV14: $i,SV31: $i,SV48: $i] :
( ( ( SV48 = vempty )
= $false )
| ( ( SV31 = SV14 )
= $false )
| ( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
| ( SV64 = vnoType ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(299,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) ) ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(300,plain,
! [SV89: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ( ( SV66 != SV33 )
| ( SV79
!= ( vbind @ SV50 @ SV94 @ SV16 ) ) )
= $true )
| ( ( ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(301,plain,
! [SV80: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ( ( SV51 != SV90 )
| ( SV67
!= ( vbind @ SV34 @ SV17 @ SV95 ) ) )
= $true )
| ( ( ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(302,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ( ( SV52 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(303,plain,
! [SV36: $i,SV19: $i,SV69: $i,SV53: $i] :
( ( ( vtcheck @ SV53 @ veabs @ SV69 )
= $false )
| ( ( ( vlookup @ SV19 @ SV53 )
= vnoType )
= $false )
| ( ( vtcheck @ ( vbind @ SV19 @ SV36 @ SV53 ) @ veabs @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(304,plain,
! [SV82: $i,SV2: $i,SV55: $i,SV38: $i,SV70: $i,SV21: $i] :
( ( ( SV21 = SV70 )
= $false )
| ( ( SV38
!= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV83: $i,SV72: $i,SV57: $i,SV40: $i,SV23: $i,SV5: $i] :
( ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(306,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) ) )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(307,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( ~ ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) ) )
= $false )
| ( ( ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(308,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ( ~ ( ( SV43 != SV8 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(309,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) ) )
= $false )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(310,plain,
! [SV87: $i,SV77: $i,SV63: $i,SV47: $i,SV30: $i,SV13: $i] :
( ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(311,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) ) )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(312,plain,
! [SV14: $i,SV48: $i,SV31: $i,SV64: $i] :
( ( ( SV64
!= ( vlookup @ SV31 @ SV48 ) )
= $true )
| ( ( SV64 = vnoType )
= $true )
| ( ( SV31 = SV14 )
= $false )
| ( ( SV48 = vempty )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(313,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) ) ) )
= $false )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(314,plain,
! [SV89: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ( SV66 != SV33 )
= $true )
| ( ( SV79
!= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $true )
| ( ( ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(315,plain,
! [SV80: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ( SV51 != SV90 )
= $true )
| ( ( SV67
!= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $true )
| ( ( ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(316,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ( SV52 != SV18 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(317,plain,
! [SV70: $i,SV21: $i,SV82: $i,SV2: $i,SV55: $i,SV38: $i] :
( ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(318,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(319,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
| ( SV40 != SV83 ) )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(320,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( ( SV6 != SV58 )
| ( ( vlookup @ SV6 @ SV41 )
!= vnoType ) )
= $true )
| ( ( ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(321,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ( SV43 != SV8 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(322,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ( ( SV11 != SV61 ) )
| ( ( vlookup @ SV11 @ SV45 )
!= vnoType ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(323,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(324,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
| ( SV47 != SV87 ) )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(325,plain,
! [SV14: $i,SV48: $i,SV31: $i,SV64: $i] :
( ( ( SV64
= ( vlookup @ SV31 @ SV48 ) )
= $false )
| ( ( SV64 = vnoType )
= $true )
| ( ( SV31 = SV14 )
= $false )
| ( ( SV48 = vempty )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(326,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
| ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(327,plain,
! [SV89: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i,SV33: $i,SV66: $i] :
( ( ( SV66 = SV33 )
= $false )
| ( ( SV79
!= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $true )
| ( ( ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(328,plain,
! [SV80: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i,SV90: $i,SV51: $i] :
( ( ( SV51 = SV90 )
= $false )
| ( ( SV67
!= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $true )
| ( ( ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(329,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV68: $i,SV18: $i,SV52: $i] :
( ( ( SV52 = SV18 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(330,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
| ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(331,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) ) )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(332,plain,
! [SV72: $i,SV57: $i,SV23: $i,SV5: $i,SV83: $i,SV40: $i] :
( ( ( SV40 != SV83 )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(333,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) ) )
= $true )
| ( ( SV40 != SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(334,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( SV6 != SV58 )
= $true )
| ( ( ( vlookup @ SV6 @ SV41 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(335,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV60: $i,SV8: $i,SV43: $i] :
( ( ( SV43 = SV8 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(336,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( ~ ( ( SV11 != SV61 ) ) )
= $true )
| ( ( ( vlookup @ SV11 @ SV45 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(337,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) ) )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(338,plain,
! [SV77: $i,SV63: $i,SV30: $i,SV13: $i,SV87: $i,SV47: $i] :
( ( ( SV47 != SV87 )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(339,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) ) )
= $true )
| ( ( SV47 != SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(340,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( ~ ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) ) )
= $true )
| ( ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(341,plain,
! [SV89: $i,SV33: $i,SV66: $i,SV16: $i,SV94: $i,SV50: $i,SV79: $i] :
( ( ( SV79
= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $false )
| ( ( SV66 = SV33 )
= $false )
| ( ( ( SV33 != SV50 )
| ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(342,plain,
! [SV80: $i,SV90: $i,SV51: $i,SV95: $i,SV17: $i,SV34: $i,SV67: $i] :
( ( ( SV67
= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $false )
| ( ( SV51 = SV90 )
= $false )
| ( ( ~ ( ( SV90 != SV34 ) )
| ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(343,plain,
! [SV96: $i,SV91: $i,SV81: $i,SV35: $i,SV18: $i,SV68: $i,SV52: $i] :
( ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ ( vbind @ SV18 @ SV35 @ SV81 ) ) @ SV91 @ SV96 )
= $false )
| ( ( SV52 = SV18 )
= $false )
| ( ( vtcheck @ ( vbind @ SV52 @ SV68 @ SV81 ) @ SV91 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(344,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) ) )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(345,plain,
! [SV2: $i,SV82: $i,SV70: $i,SV55: $i,SV38: $i,SV21: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) ) )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(346,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) ) )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(347,plain,
! [SV72: $i,SV57: $i,SV23: $i,SV5: $i,SV83: $i,SV40: $i] :
( ( ( SV40 = SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(348,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV57 )
| ( SV23 != SV72 ) ) )
= $false )
| ( ( SV40 != SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(349,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV41: $i,SV58: $i,SV6: $i] :
( ( ( SV6 = SV58 )
= $false )
| ( ( ( vlookup @ SV6 @ SV41 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(350,plain,
! [SV92: $i,SV85: $i,SV75: $i,SV26: $i,SV8: $i,SV60: $i,SV43: $i] :
( ( ( vtcheck @ ( vbind @ SV43 @ SV60 @ ( vbind @ SV8 @ SV26 @ SV75 ) ) @ SV85 @ SV92 )
= $false )
| ( ( SV43 = SV8 )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV26 @ ( vbind @ SV43 @ SV60 @ SV75 ) ) @ SV85 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(351,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( SV11 != SV61 )
= $false )
| ( ( ( vlookup @ SV11 @ SV45 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(352,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) ) )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(353,plain,
! [SV77: $i,SV63: $i,SV30: $i,SV13: $i,SV87: $i,SV47: $i] :
( ( ( SV47 = SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(354,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ~ ( ( SV13 != SV63 )
| ( SV30 != SV77 ) ) )
= $false )
| ( ( SV47 != SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(355,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( ~ ( ( SV49 != SV32 )
| ( SV65 != SV15 ) ) )
= $false )
| ( ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(356,plain,
! [SV16: $i,SV94: $i,SV79: $i,SV66: $i,SV89: $i,SV50: $i,SV33: $i] :
( ( ( SV33 != SV50 )
= $true )
| ( ( ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true )
| ( ( SV66 = SV33 )
= $false )
| ( ( SV79
= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(357,plain,
! [SV17: $i,SV95: $i,SV67: $i,SV51: $i,SV80: $i,SV34: $i,SV90: $i] :
( ( ( ~ ( ( SV90 != SV34 ) ) )
= $true )
| ( ( ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true )
| ( ( SV51 = SV90 )
= $false )
| ( ( SV67
= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(358,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
| ( visFreeVar @ SV21 @ SV38 ) )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(359,plain,
! [SV2: $i,SV82: $i,SV70: $i,SV55: $i,SV38: $i,SV21: $i] :
( ( ( ~ ( visFreeVar @ SV21 @ SV38 )
| ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(360,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(361,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( ( SV5 != SV57 )
| ( SV23 != SV72 ) )
= $true )
| ( ( SV40 != SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(362,plain,
! [SV24: $i,SV84: $i,SV73: $i,SV58: $i,SV41: $i,SV6: $i] :
( ( ( ( vlookup @ SV6 @ SV41 )
= vnoType )
= $false )
| ( ( SV6 = SV58 )
= $false )
| ( ( ~ ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(363,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV45: $i,SV61: $i,SV11: $i] :
( ( ( SV11 = SV61 )
= $true )
| ( ( ( vlookup @ SV11 @ SV45 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(364,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(365,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( ( SV13 != SV63 )
| ( SV30 != SV77 ) )
= $true )
| ( ( SV47 != SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(366,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( ( SV49 != SV32 )
| ( SV65 != SV15 ) )
= $true )
| ( ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(367,plain,
! [SV16: $i,SV94: $i,SV79: $i,SV66: $i,SV89: $i,SV50: $i,SV33: $i] :
( ( ( SV33 = SV50 )
= $false )
| ( ( ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
| ( SV89
= ( vsomeType @ SV94 ) ) )
= $true )
| ( ( SV66 = SV33 )
= $false )
| ( ( SV79
= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV17: $i,SV95: $i,SV67: $i,SV51: $i,SV80: $i,SV34: $i,SV90: $i] :
( ( ( SV90 != SV34 )
= $false )
| ( ( ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true )
| ( ( SV51 = SV90 )
= $false )
| ( ( SV67
= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(369,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(370,plain,
! [SV2: $i,SV82: $i,SV70: $i,SV55: $i,SV38: $i,SV21: $i] :
( ( ( ~ ( visFreeVar @ SV21 @ SV38 ) )
= $true )
| ( ( ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(371,plain,
! [SV83: $i,SV72: $i,SV40: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( SV5 != SV57 )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(372,plain,
! [SV83: $i,SV57: $i,SV40: $i,SV5: $i,SV72: $i,SV23: $i] :
( ( ( SV23 != SV72 )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(373,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( SV5 != SV57 )
= $true )
| ( ( SV23 != SV72 )
= $true )
| ( ( SV40 != SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(374,plain,
! [SV24: $i,SV6: $i,SV84: $i,SV73: $i,SV58: $i,SV41: $i] :
( ( ( vtcheck @ SV41 @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $false )
| ( ( SV6 = SV58 )
= $false )
| ( ( ( vlookup @ SV6 @ SV41 )
= vnoType )
= $false )
| ( ( vtcheck @ ( vbind @ SV6 @ SV24 @ SV41 ) @ ( vabs @ SV58 @ SV73 @ veabs ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(375,plain,
! [SV28: $i,SV86: $i,SV76: $i,SV61: $i,SV45: $i,SV11: $i] :
( ( ( ( vlookup @ SV11 @ SV45 )
= vnoType )
= $false )
| ( ( SV11 = SV61 )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(376,plain,
! [SV87: $i,SV77: $i,SV47: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( SV13 != SV63 )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(377,plain,
! [SV87: $i,SV63: $i,SV47: $i,SV13: $i,SV77: $i,SV30: $i] :
( ( ( SV30 != SV77 )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(378,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( SV13 != SV63 )
= $true )
| ( ( SV30 != SV77 )
= $true )
| ( ( SV47 != SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(379,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( SV49 != SV32 )
= $true )
| ( ( SV65 != SV15 )
= $true )
| ( ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(380,plain,
! [SV16: $i,SV50: $i,SV33: $i,SV94: $i,SV79: $i,SV66: $i,SV89: $i] :
( ( ( SV89
!= ( vlookup @ SV66 @ SV79 ) )
= $true )
| ( ( SV89
= ( vsomeType @ SV94 ) )
= $true )
| ( ( SV33 = SV50 )
= $false )
| ( ( SV66 = SV33 )
= $false )
| ( ( SV79
= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(381,plain,
! [SV17: $i,SV95: $i,SV67: $i,SV51: $i,SV80: $i,SV34: $i,SV90: $i] :
( ( ( SV90 = SV34 )
= $true )
| ( ( ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
| ( SV80
= ( vlookup @ SV90 @ SV95 ) ) )
= $true )
| ( ( SV51 = SV90 )
= $false )
| ( ( SV67
= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(382,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) )
= $false )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(383,plain,
! [SV2: $i,SV82: $i,SV70: $i,SV55: $i,SV38: $i,SV21: $i] :
( ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( ~ ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) ) )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(384,plain,
! [SV83: $i,SV72: $i,SV40: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( SV5 = SV57 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(385,plain,
! [SV83: $i,SV57: $i,SV40: $i,SV5: $i,SV72: $i,SV23: $i] :
( ( ( SV23 = SV72 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(386,plain,
! [SV83: $i,SV40: $i,SV72: $i,SV23: $i,SV57: $i,SV5: $i] :
( ( ( SV5 = SV57 )
= $false )
| ( ( SV23 != SV72 )
= $true )
| ( ( SV40 != SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(387,plain,
! [SV28: $i,SV11: $i,SV86: $i,SV76: $i,SV61: $i,SV45: $i] :
( ( ( vtcheck @ SV45 @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $false )
| ( ( SV11 = SV61 )
= $true )
| ( ( ( vlookup @ SV11 @ SV45 )
= vnoType )
= $false )
| ( ( vtcheck @ ( vbind @ SV11 @ SV28 @ SV45 ) @ ( vabs @ SV61 @ SV76 @ veabs ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(388,plain,
! [SV87: $i,SV77: $i,SV47: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( SV13 = SV63 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(389,plain,
! [SV87: $i,SV63: $i,SV47: $i,SV13: $i,SV77: $i,SV30: $i] :
( ( ( SV30 = SV77 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(390,plain,
! [SV87: $i,SV47: $i,SV77: $i,SV30: $i,SV63: $i,SV13: $i] :
( ( ( SV13 = SV63 )
= $false )
| ( ( SV30 != SV77 )
= $true )
| ( ( SV47 != SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(391,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i] :
( ( ( SV49 = SV32 )
= $false )
| ( ( SV65 != SV15 )
= $true )
| ( ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(392,plain,
! [SV16: $i,SV50: $i,SV33: $i,SV94: $i,SV79: $i,SV66: $i,SV89: $i] :
( ( ( SV89
= ( vlookup @ SV66 @ SV79 ) )
= $false )
| ( ( SV89
= ( vsomeType @ SV94 ) )
= $true )
| ( ( SV33 = SV50 )
= $false )
| ( ( SV66 = SV33 )
= $false )
| ( ( SV79
= ( vbind @ SV50 @ SV94 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(393,plain,
! [SV17: $i,SV34: $i,SV95: $i,SV90: $i,SV67: $i,SV51: $i,SV80: $i] :
( ( ( SV80
!= ( vlookup @ SV51 @ SV67 ) )
= $true )
| ( ( SV80
= ( vlookup @ SV90 @ SV95 ) )
= $true )
| ( ( SV90 = SV34 )
= $true )
| ( ( SV51 = SV90 )
= $false )
| ( ( SV67
= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(394,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(395,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV70 ) )
| ~ ( visFreeVar @ SV70 @ SV82 ) )
= $false )
| ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(396,plain,
! [SV83: $i,SV40: $i,SV57: $i,SV5: $i,SV72: $i,SV23: $i] :
( ( ( SV23 = SV72 )
= $false )
| ( ( SV5 = SV57 )
= $false )
| ( ( SV40 != SV83 )
= $true )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(397,plain,
! [SV87: $i,SV47: $i,SV63: $i,SV13: $i,SV77: $i,SV30: $i] :
( ( ( SV30 = SV77 )
= $false )
| ( ( SV13 = SV63 )
= $false )
| ( ( SV47 != SV87 )
= $true )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(398,plain,
! [SV88: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV32: $i,SV49: $i,SV15: $i,SV65: $i] :
( ( ( SV65 = SV15 )
= $false )
| ( ( SV49 = SV32 )
= $false )
| ( ( SV78
!= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(399,plain,
! [SV17: $i,SV34: $i,SV95: $i,SV90: $i,SV67: $i,SV51: $i,SV80: $i] :
( ( ( SV80
= ( vlookup @ SV51 @ SV67 ) )
= $false )
| ( ( SV80
= ( vlookup @ SV90 @ SV95 ) )
= $true )
| ( ( SV90 = SV34 )
= $true )
| ( ( SV51 = SV90 )
= $false )
| ( ( SV67
= ( vbind @ SV34 @ SV17 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(400,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV70 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV70 @ SV82 ) )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(401,plain,
! [SV82: $i,SV2: $i,SV38: $i,SV21: $i,SV70: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV70 ) ) )
= $false )
| ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(402,plain,
! [SV2: $i,SV55: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i] :
( ( ( ~ ( visFreeVar @ SV70 @ SV82 ) )
= $false )
| ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(403,plain,
! [SV72: $i,SV23: $i,SV57: $i,SV5: $i,SV83: $i,SV40: $i] :
( ( ( SV40 = SV83 )
= $false )
| ( ( SV5 = SV57 )
= $false )
| ( ( SV23 = SV72 )
= $false )
| ( ( ( vabs @ SV5 @ SV23 @ SV40 )
= ( vabs @ SV57 @ SV72 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(404,plain,
! [SV77: $i,SV30: $i,SV63: $i,SV13: $i,SV87: $i,SV47: $i] :
( ( ( SV47 = SV87 )
= $false )
| ( ( SV13 = SV63 )
= $false )
| ( ( SV30 = SV77 )
= $false )
| ( ( ( vbind @ SV13 @ SV30 @ SV47 )
= ( vbind @ SV63 @ SV77 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(405,plain,
! [SV88: $i,SV15: $i,SV65: $i,SV32: $i,SV49: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i] :
( ( ( SV78
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $false )
| ( ( SV49 = SV32 )
= $false )
| ( ( SV65 = SV15 )
= $false )
| ( ( ( SV32 != SV93 )
| ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(406,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( SV55 != SV70 )
= $false )
| ( ( ~ ( visFreeVar @ SV70 @ SV82 ) )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(407,plain,
! [SV82: $i,SV2: $i,SV38: $i,SV21: $i,SV70: $i,SV55: $i] :
( ( ( SV55 != SV70 )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(408,plain,
! [SV2: $i,SV55: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i] :
( ( ( visFreeVar @ SV70 @ SV82 )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(409,plain,
! [SV15: $i,SV98: $i,SV97: $i,SV78: $i,SV65: $i,SV49: $i,SV88: $i,SV93: $i,SV32: $i] :
( ( ( SV32 != SV93 )
= $true )
| ( ( ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true )
| ( ( SV65 = SV15 )
= $false )
| ( ( SV49 = SV32 )
= $false )
| ( ( SV78
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(410,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV82: $i,SV70: $i,SV55: $i] :
( ( ( SV55 = SV70 )
= $true )
| ( ( ~ ( visFreeVar @ SV70 @ SV82 ) )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(411,plain,
! [SV82: $i,SV2: $i,SV38: $i,SV21: $i,SV70: $i,SV55: $i] :
( ( ( SV55 = SV70 )
= $false )
| ( ( visFreeVar @ SV21 @ SV38 )
= $false )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(412,plain,
! [SV15: $i,SV98: $i,SV97: $i,SV78: $i,SV65: $i,SV49: $i,SV88: $i,SV93: $i,SV32: $i] :
( ( ( SV32 = SV93 )
= $false )
| ( ( ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
| ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) ) )
= $true )
| ( ( SV65 = SV15 )
= $false )
| ( ( SV49 = SV32 )
= $false )
| ( ( SV78
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(413,plain,
! [SV2: $i,SV38: $i,SV21: $i,SV55: $i,SV82: $i,SV70: $i] :
( ( ( visFreeVar @ SV70 @ SV82 )
= $false )
| ( ( SV55 = SV70 )
= $true )
| ( ( visFreeVar @ SV21 @ SV38 )
= $true )
| ( ( SV21 = SV70 )
= $false )
| ( ( SV38
= ( vabs @ SV55 @ SV2 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(414,plain,
! [SV15: $i,SV32: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV65: $i,SV49: $i,SV88: $i] :
( ( ( SV88
!= ( vsubst @ SV49 @ SV65 @ SV78 ) )
= $true )
| ( ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( SV32 = SV93 )
= $false )
| ( ( SV65 = SV15 )
= $false )
| ( ( SV49 = SV32 )
= $false )
| ( ( SV78
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(415,plain,
! [SV15: $i,SV32: $i,SV98: $i,SV97: $i,SV93: $i,SV78: $i,SV65: $i,SV49: $i,SV88: $i] :
( ( ( SV88
= ( vsubst @ SV49 @ SV65 @ SV78 ) )
= $false )
| ( ( SV88
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $true )
| ( ( SV32 = SV93 )
= $false )
| ( ( SV65 = SV15 )
= $false )
| ( ( SV49 = SV32 )
= $false )
| ( ( SV78
= ( vabs @ SV93 @ SV97 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(416,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[111,415,413,411,408,404,403,399,392,389,388,387,385,384,374,353,350,347,343,325,303,252,241,235,220,219,216,206,205,158,134,112]) ).
thf(417,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM141+1 : TPTP v9.3.1. Released v6.4.0.
% 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
% 0.04/0.17 % Computer : n011.cluster.edu
% 0.04/0.17 % Model : x86_64 x86_64
% 0.04/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.17 % Memory : 8046.5625MB
% 0.04/0.17 % OS : Linux 6.8.0-71-generic
% 0.04/0.17 % CPULimit : 300
% 0.04/0.17 % WCLimit : 300
% 0.04/0.18 % DateTime : Tue Oct 6 18:39:15 UTC 2026
% 0.04/0.18 % CPUTime :
% 0.04/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.43/0.61
% 2.43/0.61 No.of.Axioms: 20
% 2.43/0.61
% 2.43/0.61 Length.of.Defs: 0
% 2.43/0.61
% 2.43/0.61 Contains.Choice.Funs: false
% 2.43/0.61 ...................
% 2.43/0.61
% 2.43/0.61 ********************************
% 2.43/0.61 * All subproblems solved! *
% 2.43/0.61 ********************************
% 2.43/0.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:416,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.43/0.61
% 2.43/0.61 %**** Beginning of derivation protocol ****
% 2.43/0.61 % SZS output start CNFRefutation
% See solution above
% 2.43/0.62
% 2.43/0.62 %**** End of derivation protocol ****
% 2.43/0.62 %**** no. of clauses in derivation: 380 ****
% 2.43/0.62 %**** clause counter: 416 ****
% 2.43/0.62
% 2.43/0.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:22,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:416,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------