%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM130+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:12:26 AM UTC 2026
% Result : Theorem 3.14s 0.71s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 25
% Syntax : Number of formulae : 493 ( 250 unt; 0 typ; 0 def)
% Number of atoms : 4034 (2577 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 8417 (2135 ~;1387 |; 124 &;4643 @)
% ( 0 <=>; 128 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 14 con; 0-3 aty)
% Number of variables : 3029 ( 0 ^;3029 !; 0 ?;3029 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_VT,type,
sK1_VT: $i ).
thf(tp_sK2_SY148,type,
sK2_SY148: $i ).
thf(tp_sK3_SY155,type,
sK3_SY155: $i ).
thf(tp_sK4_SY161,type,
sK4_SY161: $i ).
thf(tp_sK5_SY166,type,
sK5_SY166: $i ).
thf(tp_sK6_SY170,type,
sK6_SY170: $i ).
thf(tp_sK7_SY173,type,
sK7_SY173: $i ).
thf(tp_sK8_SY175,type,
sK8_SY175: $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,
! [VT: $i,VC: $i,Vx: $i,Ve: $i,VT2: $i] :
( ( ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ veabs @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ veabs ) @ VT2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-IH-abs') ).
thf(2,axiom,
! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar') ).
thf(3,axiom,
! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) )
=> ( vtcheck @ VC @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong') ).
thf(4,axiom,
! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak') ).
thf(6,axiom,
! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-app') ).
thf(7,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/sandbox/benchmark/theBenchmark.p','T-abs') ).
thf(8,axiom,
! [VC: $i,Vx: $i,VT: $i] :
( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
=> ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-var') ).
thf(16,axiom,
! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce1) ).
thf(25,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Vx: $i,Ve: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ ( vsubst @ Vx @ Ve @ Ve1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst5) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',subst3) ).
thf(28,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst2) ).
thf(29,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst1) ).
thf(30,axiom,
! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst0) ).
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 @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(33,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/sandbox/benchmark/theBenchmark.p','T-Context-Duplicate') ).
thf(35,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/sandbox/benchmark/theBenchmark.p',lookup2) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',lookup1) ).
thf(42,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
thf(45,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/sandbox/benchmark/theBenchmark.p','EQ-bind') ).
thf(48,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/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
thf(52,axiom,
! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue0) ).
thf(53,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-abs-app') ).
thf(55,axiom,
! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-abs') ).
thf(57,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/sandbox/benchmark/theBenchmark.p','EQ-abs') ).
thf(59,conjecture,
! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,Ve1: $i,VT2: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ Ve1 ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ Ve1 ) ) @ VT2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-1') ).
thf(60,negated_conjecture,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,Ve1: $i,VT2: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ Ve1 ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ Ve1 ) ) @ VT2 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[59]) ).
thf(61,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,Ve1: $i,VT2: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ Ve1 ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ Ve1 ) ) @ VT2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,VT2: $i] :
( ( ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ veabs @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ veabs ) @ VT2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(63,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(64,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) )
=> ( vtcheck @ VC @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(66,plain,
( ( ! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(67,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)],[7]) ).
thf(68,plain,
( ( ! [VC: $i,Vx: $i,VT: $i] :
( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
=> ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(69,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(70,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Vx: $i,Ve: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ ( vsubst @ Vx @ Ve @ Ve1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(71,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)],[27]) ).
thf(72,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(73,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
( ( ! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,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)],[32]) ).
thf(76,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)],[33]) ).
thf(77,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)],[35]) ).
thf(78,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)],[36]) ).
thf(79,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(80,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)],[45]) ).
thf(81,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)],[48]) ).
thf(82,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(83,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(84,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(85,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)],[57]) ).
thf(86,plain,
( ( ! [SY148: $i,SY149: $i,SY150: $i,SY151: $i,SY152: $i,SY153: $i,SY154: $i] :
( ( ( SY149 = SY151 )
& ( vtcheck @ SY148 @ SY150 @ sK1_VT )
& ( vtcheck @ ( vbind @ SY149 @ sK1_VT @ SY148 ) @ ( vabs @ SY151 @ SY152 @ SY153 ) @ SY154 ) )
=> ( vtcheck @ SY148 @ ( vsubst @ SY149 @ SY150 @ ( vabs @ SY151 @ SY152 @ SY153 ) ) @ SY154 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(87,plain,
( ( ! [SY155: $i,SY156: $i,SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
( ( ( SY155 = SY157 )
& ( vtcheck @ sK2_SY148 @ SY156 @ sK1_VT )
& ( vtcheck @ ( vbind @ SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ SY157 @ SY158 @ SY159 ) @ SY160 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ SY155 @ SY156 @ ( vabs @ SY157 @ SY158 @ SY159 ) ) @ SY160 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ! [SY161: $i,SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
( ( ( sK3_SY155 = SY162 )
& ( vtcheck @ sK2_SY148 @ SY161 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ SY162 @ SY163 @ SY164 ) @ SY165 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ SY161 @ ( vabs @ SY162 @ SY163 @ SY164 ) ) @ SY165 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ! [SY166: $i,SY167: $i,SY168: $i,SY169: $i] :
( ( ( sK3_SY155 = SY166 )
& ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ SY166 @ SY167 @ SY168 ) @ SY169 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ SY166 @ SY167 @ SY168 ) ) @ SY169 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ( ( sK3_SY155 = sK5_SY166 )
& ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ sK5_SY166 @ SY170 @ SY171 ) @ SY172 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ SY170 @ SY171 ) ) @ SY172 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(91,plain,
( ( ! [SY173: $i,SY174: $i] :
( ( ( sK3_SY155 = sK5_SY166 )
& ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ sK5_SY166 @ sK6_SY170 @ SY173 ) @ SY174 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ SY173 ) ) @ SY174 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(92,plain,
( ( ! [SY175: $i] :
( ( ( sK3_SY155 = sK5_SY166 )
& ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) @ SY175 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) ) @ SY175 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(93,plain,
( ( ( ( sK3_SY155 = sK5_SY166 )
& ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) @ sK8_SY175 ) )
=> ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) ) @ sK8_SY175 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(94,plain,
( ( sK3_SY155 = sK5_SY166 )
= $true ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(95,plain,
( ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
= $true ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(96,plain,
( ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) @ sK8_SY175 )
= $true ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(97,plain,
( ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) ) @ sK8_SY175 )
= $false ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(98,plain,
( ( ~ ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) ) @ sK8_SY175 ) )
= $true ),
inference(polarity_switch,[status(thm)],[97]) ).
thf(99,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)],[85]) ).
thf(100,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(101,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(102,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(103,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)],[81]) ).
thf(104,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)],[80]) ).
thf(105,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(106,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)],[78]) ).
thf(107,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)],[77]) ).
thf(108,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)],[76]) ).
thf(109,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)],[75]) ).
thf(110,plain,
( ( ! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(111,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(112,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(113,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)],[71]) ).
thf(114,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Vx: $i,Ve: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ ( vsubst @ Vx @ Ve @ Ve1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(115,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(116,plain,
( ( ! [VC: $i,Vx: $i,VT: $i] :
( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
=> ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(117,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)],[67]) ).
thf(118,plain,
( ( ! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(119,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(120,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) )
=> ( vtcheck @ VC @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(121,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(122,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,VT2: $i] :
( ( ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ veabs @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ veabs ) @ VT2 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(123,plain,
( ( vtcheck @ ( vbind @ sK3_SY155 @ sK1_VT @ sK2_SY148 ) @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) @ sK8_SY175 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(124,plain,
( ( vtcheck @ sK2_SY148 @ sK4_SY161 @ sK1_VT )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(125,plain,
( ( sK3_SY155 = sK5_SY166 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(126,plain,
( ( ~ ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) ) @ sK8_SY175 ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( SX4
!= ( vreduce @ SX3 ) )
| ( SX4 = vnoExp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ( ( vlookup @ SX0 @ SX2 )
!= vnoType )
| ~ ( vtcheck @ SX2 @ SX3 @ SX4 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ( SX0 != SX6 )
| ( SX1 != SX7 ) )
| ( SX2
!= ( vabs @ SX4 @ SX5 @ SX8 ) ) )
| ~ ~ ( ~ ( ( SX6 != SX4 ) )
| ~ ~ ( visFreeVar @ SX4 @ SX7 ) )
| ( SX3
!= ( vsubst @ SX0 @ SX1 @ SX2 ) )
| ( SX3
= ( vabs @ SX4 @ SX5 @ ( vsubst @ SX6 @ SX7 @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(130,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)],[99]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SX0 @ SX3 )
| ~ ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ SX3 @ SX4 ) )
| ( vtcheck @ SX2 @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ~ ( ~ ~ ( ( SX0 != SX5 )
| ( SX1 != SX6 ) )
| ( SX2
!= ( vapp @ SX4 @ SX7 ) ) )
| ( SX3
!= ( vsubst @ SX0 @ SX1 @ SX2 ) )
| ( SX3
= ( vapp @ ( vsubst @ SX5 @ SX6 @ SX4 ) @ ( vsubst @ SX5 @ SX6 @ SX7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(133,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)],[113]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( vlookup @ SX1 @ SX0 )
!= ( vsomeType @ SX2 ) )
| ( vtcheck @ SX0 @ ( vvar @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX0 )
| ( SX3 != SX6 ) )
| ( SX4
!= ( vvar @ SX1 ) ) )
| ( SX0 != SX1 )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5 = SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(136,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)],[117]) ).
thf(137,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)],[107]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( vempty
!= ( vbind @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( vtcheck @ SX1 @ SX3 @ SX0 )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX0 @ SX1 ) @ veabs @ SX4 ) )
| ( vtcheck @ SX1 @ ( vsubst @ SX2 @ SX3 @ veabs ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(141,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)],[109]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( vtcheck @ SX1 @ SX2 @ ( varrow @ SX0 @ SX4 ) )
| ~ ( vtcheck @ SX1 @ SX3 @ SX0 ) )
| ( vtcheck @ SX1 @ ( vapp @ SX2 @ SX3 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SX0 @ SX3 )
| ~ ( vtcheck @ SX2 @ SX3 @ SX4 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX1 )
| ( SX3 != SX0 ) )
| ( SX4
!= ( vvar @ SX6 ) ) )
| ~ ( ( SX1 != SX6 ) )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5
= ( vvar @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(146,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)],[106]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( visValue @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(148,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)],[103]) ).
thf(149,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)],[104]) ).
thf(150,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)],[108]) ).
thf(151,plain,
( ( vtcheck @ sK2_SY148 @ ( vsubst @ sK3_SY155 @ sK4_SY161 @ ( vabs @ sK5_SY166 @ sK6_SY170 @ sK7_SY173 ) ) @ sK8_SY175 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(152,plain,
! [SV1: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( SY178
!= ( vabs @ SV1 @ SY176 @ SY177 ) )
| ( SY179
!= ( vreduce @ SY178 ) )
| ( SY179 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(153,plain,
! [SV2: $i] :
( ( ! [SY180: $i,SY181: $i,SY182: $i,SY183: $i] :
( ~ ~ ( ( ( vlookup @ SV2 @ SY181 )
!= vnoType )
| ~ ( vtcheck @ SY181 @ SY182 @ SY183 ) )
| ( vtcheck @ ( vbind @ SV2 @ SY180 @ SY181 ) @ SY182 @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(154,plain,
! [SV3: $i] :
( ( ! [SY184: $i,SY185: $i,SY186: $i,SY187: $i,SY188: $i,SY189: $i,SY190: $i,SY191: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SY189 )
| ( SY184 != SY190 ) )
| ( SY185
!= ( vabs @ SY187 @ SY188 @ SY191 ) ) )
| ~ ~ ( ~ ( ( SY189 != SY187 ) )
| ~ ~ ( visFreeVar @ SY187 @ SY190 ) )
| ( SY186
!= ( vsubst @ SV3 @ SY184 @ SY185 ) )
| ( SY186
= ( vabs @ SY187 @ SY188 @ ( vsubst @ SY189 @ SY190 @ SY191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(155,plain,
! [SV4: $i] :
( ( ! [SY192: $i,SY193: $i,SY194: $i,SY195: $i,SY196: $i] :
~ ( ~ ( ( ( vabs @ SV4 @ SY192 @ SY193 )
!= ( vabs @ SY194 @ SY195 @ SY196 ) )
| ~ ( ~ ~ ( ( SV4 != SY194 )
| ( SY192 != SY195 ) )
| ( SY193 != SY196 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SY194 )
| ( SY192 != SY195 ) )
| ( SY193 != SY196 ) )
| ( ( vabs @ SV4 @ SY192 @ SY193 )
= ( vabs @ SY194 @ SY195 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(156,plain,
! [SV5: $i] :
( ( ! [SY197: $i,SY198: $i,SY199: $i,SY200: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV5 @ SY199 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SY197 @ SY198 ) @ SY199 @ SY200 ) )
| ( vtcheck @ SY198 @ SY199 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(157,plain,
! [SV6: $i] :
( ( ! [SY201: $i,SY202: $i,SY203: $i,SY204: $i,SY205: $i,SY206: $i,SY207: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY205 )
| ( SY201 != SY206 ) )
| ( SY202
!= ( vapp @ SY204 @ SY207 ) ) )
| ( SY203
!= ( vsubst @ SV6 @ SY201 @ SY202 ) )
| ( SY203
= ( vapp @ ( vsubst @ SY205 @ SY206 @ SY204 ) @ ( vsubst @ SY205 @ SY206 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(158,plain,
! [SV7: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i,SY211: $i,SY212: $i,SY213: $i,SY214: $i,SY215: $i] :
( ~ ~ ( ~ ~ ( ( SY209 != SY208 )
| ( SY210 != SV7 ) )
| ( SY211
!= ( vabs @ SY213 @ SY214 @ SY215 ) ) )
| ( SY208 != SY213 )
| ( SY212
!= ( vsubst @ SY209 @ SY210 @ SY211 ) )
| ( SY212
= ( vabs @ SY213 @ SY214 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(159,plain,
! [SV8: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ( ( vlookup @ SY216 @ SV8 )
!= ( vsomeType @ SY217 ) )
| ( vtcheck @ SV8 @ ( vvar @ SY216 ) @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(160,plain,
! [SV9: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i,SY221: $i,SY222: $i,SY223: $i] :
( ~ ~ ( ~ ~ ( ( SY219 != SV9 )
| ( SY220 != SY223 ) )
| ( SY221
!= ( vvar @ SY218 ) ) )
| ( SV9 != SY218 )
| ( SY222
!= ( vsubst @ SY219 @ SY220 @ SY221 ) )
| ( SY222 = SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(161,plain,
! [SV10: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i,SY227: $i] :
( ~ ( vtcheck @ ( vbind @ SY224 @ SY226 @ SV10 ) @ SY225 @ SY227 )
| ( vtcheck @ SV10 @ ( vabs @ SY224 @ SY226 @ SY225 ) @ ( varrow @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(162,plain,
! [SV11: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i,SY231: $i,SY232: $i,SY233: $i] :
( ~ ~ ( ( SY229 != SY232 )
| ( SY230
!= ( vbind @ SY228 @ SV11 @ SY233 ) ) )
| ~ ( ( SY232 != SY228 ) )
| ( SY231
!= ( vlookup @ SY229 @ SY230 ) )
| ( SY231
= ( vlookup @ SY232 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(163,plain,
! [SV12: $i] :
( ( ! [SY234: $i,SY235: $i] :
( vempty
!= ( vbind @ SV12 @ SY234 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(164,plain,
! [SV13: $i] :
( ( ! [SY236: $i,SY237: $i,SY238: $i] :
( ( vvar @ SV13 )
!= ( vabs @ SY236 @ SY237 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(165,plain,
! [SV14: $i] :
( ( ! [SY239: $i,SY240: $i,SY241: $i,SY242: $i] :
( ~ ~ ( ~ ( vtcheck @ SY239 @ SY241 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SY240 @ SV14 @ SY239 ) @ veabs @ SY242 ) )
| ( vtcheck @ SY239 @ ( vsubst @ SY240 @ SY241 @ veabs ) @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(166,plain,
! [SV15: $i] :
( ( ! [SY243: $i,SY244: $i,SY245: $i,SY246: $i,SY247: $i,SY248: $i] :
( ~ ~ ( ~ ( ( SY244 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SY244 @ SY245 @ ( vbind @ SV15 @ SY243 @ SY246 ) ) @ SY247 @ SY248 ) )
| ( vtcheck @ ( vbind @ SV15 @ SY243 @ ( vbind @ SY244 @ SY245 @ SY246 ) ) @ SY247 @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(167,plain,
! [SV16: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i,SY252: $i] :
( ~ ~ ( ~ ( vtcheck @ SY249 @ SY250 @ ( varrow @ SV16 @ SY252 ) )
| ~ ( vtcheck @ SY249 @ SY251 @ SV16 ) )
| ( vtcheck @ SY249 @ ( vapp @ SY250 @ SY251 ) @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(168,plain,
! [SV17: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i,SY256: $i] :
( ( vabs @ SV17 @ SY253 @ SY254 )
!= ( vapp @ SY255 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(169,plain,
! [SV18: $i] :
( ( ! [SY257: $i,SY258: $i,SY259: $i,SY260: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV18 @ SY259 )
| ~ ( vtcheck @ SY258 @ SY259 @ SY260 ) )
| ( vtcheck @ ( vbind @ SV18 @ SY257 @ SY258 ) @ SY259 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(170,plain,
! [SV19: $i] :
( ( ! [SY261: $i,SY262: $i,SY263: $i,SY264: $i,SY265: $i,SY266: $i] :
( ~ ~ ( ~ ~ ( ( SY262 != SY261 )
| ( SY263 != SV19 ) )
| ( SY264
!= ( vvar @ SY266 ) ) )
| ~ ( ( SY261 != SY266 ) )
| ( SY265
!= ( vsubst @ SY262 @ SY263 @ SY264 ) )
| ( SY265
= ( vvar @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(171,plain,
! [SV20: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i,SY270: $i,SY271: $i,SY272: $i] :
( ~ ~ ( ( SY269 != SY267 )
| ( SY270
!= ( vbind @ SY268 @ SY272 @ SV20 ) ) )
| ( SY267 != SY268 )
| ( SY271
!= ( vlookup @ SY269 @ SY270 ) )
| ( SY271
= ( vsomeType @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(172,plain,
! [SV21: $i] :
( ( ! [SY273: $i,SY274: $i,SY275: $i] :
( ( SY275
!= ( vabs @ SV21 @ SY273 @ SY274 ) )
| ( visValue @ SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(173,plain,
! [SV22: $i] :
( ( ! [SY276: $i,SY277: $i,SY278: $i,SY279: $i,SY280: $i] :
( ~ ~ ( ( SY276 != SY279 )
| ( SY277
!= ( vabs @ SY278 @ SV22 @ SY280 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY278 != SY279 ) )
| ~ ( visFreeVar @ SY279 @ SY280 ) )
| ( visFreeVar @ SY276 @ SY277 ) )
| ~ ( ~ ( visFreeVar @ SY276 @ SY277 )
| ~ ( ~ ( ( SY278 != SY279 ) )
| ~ ( visFreeVar @ SY279 @ SY280 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(174,plain,
! [SV23: $i] :
( ( ! [SY281: $i,SY282: $i,SY283: $i,SY284: $i,SY285: $i] :
~ ( ~ ( ( ( vbind @ SV23 @ SY281 @ SY282 )
!= ( vbind @ SY283 @ SY284 @ SY285 ) )
| ~ ( ~ ~ ( ( SV23 != SY283 )
| ( SY281 != SY284 ) )
| ( SY282 != SY285 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SY283 )
| ( SY281 != SY284 ) )
| ( SY282 != SY285 ) )
| ( ( vbind @ SV23 @ SY281 @ SY282 )
= ( vbind @ SY283 @ SY284 @ SY285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(175,plain,
! [SV24: $i] :
( ( ! [SY286: $i,SY287: $i,SY288: $i,SY289: $i,SY290: $i,SY291: $i] :
( ~ ~ ( ( SY287 != SV24 )
| ~ ( vtcheck @ ( vbind @ SY287 @ SY288 @ ( vbind @ SV24 @ SY286 @ SY289 ) ) @ SY290 @ SY291 ) )
| ( vtcheck @ ( vbind @ SY287 @ SY288 @ SY289 ) @ SY290 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(176,plain,
! [SV25: $i,SV1: $i] :
( ( ! [SY292: $i,SY293: $i,SY294: $i] :
( ( SY293
!= ( vabs @ SV1 @ SV25 @ SY292 ) )
| ( SY294
!= ( vreduce @ SY293 ) )
| ( SY294 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(177,plain,
! [SV26: $i,SV2: $i] :
( ( ! [SY295: $i,SY296: $i,SY297: $i] :
( ~ ~ ( ( ( vlookup @ SV2 @ SY295 )
!= vnoType )
| ~ ( vtcheck @ SY295 @ SY296 @ SY297 ) )
| ( vtcheck @ ( vbind @ SV2 @ SV26 @ SY295 ) @ SY296 @ SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(178,plain,
! [SV27: $i,SV3: $i] :
( ( ! [SY298: $i,SY299: $i,SY300: $i,SY301: $i,SY302: $i,SY303: $i,SY304: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SY302 )
| ( SV27 != SY303 ) )
| ( SY298
!= ( vabs @ SY300 @ SY301 @ SY304 ) ) )
| ~ ~ ( ~ ( ( SY302 != SY300 ) )
| ~ ~ ( visFreeVar @ SY300 @ SY303 ) )
| ( SY299
!= ( vsubst @ SV3 @ SV27 @ SY298 ) )
| ( SY299
= ( vabs @ SY300 @ SY301 @ ( vsubst @ SY302 @ SY303 @ SY304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(179,plain,
! [SV28: $i,SV4: $i] :
( ( ! [SY305: $i,SY306: $i,SY307: $i,SY308: $i] :
~ ( ~ ( ( ( vabs @ SV4 @ SV28 @ SY305 )
!= ( vabs @ SY306 @ SY307 @ SY308 ) )
| ~ ( ~ ~ ( ( SV4 != SY306 )
| ( SV28 != SY307 ) )
| ( SY305 != SY308 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SY306 )
| ( SV28 != SY307 ) )
| ( SY305 != SY308 ) )
| ( ( vabs @ SV4 @ SV28 @ SY305 )
= ( vabs @ SY306 @ SY307 @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(180,plain,
! [SV29: $i,SV5: $i] :
( ( ! [SY309: $i,SY310: $i,SY311: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV5 @ SY310 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SY309 ) @ SY310 @ SY311 ) )
| ( vtcheck @ SY309 @ SY310 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(181,plain,
! [SV30: $i,SV6: $i] :
( ( ! [SY312: $i,SY313: $i,SY314: $i,SY315: $i,SY316: $i,SY317: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY315 )
| ( SV30 != SY316 ) )
| ( SY312
!= ( vapp @ SY314 @ SY317 ) ) )
| ( SY313
!= ( vsubst @ SV6 @ SV30 @ SY312 ) )
| ( SY313
= ( vapp @ ( vsubst @ SY315 @ SY316 @ SY314 ) @ ( vsubst @ SY315 @ SY316 @ SY317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(182,plain,
! [SV7: $i,SV31: $i] :
( ( ! [SY318: $i,SY319: $i,SY320: $i,SY321: $i,SY322: $i,SY323: $i,SY324: $i] :
( ~ ~ ( ~ ~ ( ( SY318 != SV31 )
| ( SY319 != SV7 ) )
| ( SY320
!= ( vabs @ SY322 @ SY323 @ SY324 ) ) )
| ( SV31 != SY322 )
| ( SY321
!= ( vsubst @ SY318 @ SY319 @ SY320 ) )
| ( SY321
= ( vabs @ SY322 @ SY323 @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(183,plain,
! [SV8: $i,SV32: $i] :
( ( ! [SY325: $i] :
( ( ( vlookup @ SV32 @ SV8 )
!= ( vsomeType @ SY325 ) )
| ( vtcheck @ SV8 @ ( vvar @ SV32 ) @ SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(184,plain,
! [SV33: $i,SV9: $i] :
( ( ! [SY326: $i,SY327: $i,SY328: $i,SY329: $i,SY330: $i] :
( ~ ~ ( ~ ~ ( ( SY326 != SV9 )
| ( SY327 != SY330 ) )
| ( SY328
!= ( vvar @ SV33 ) ) )
| ( SV9 != SV33 )
| ( SY329
!= ( vsubst @ SY326 @ SY327 @ SY328 ) )
| ( SY329 = SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(185,plain,
! [SV10: $i,SV34: $i] :
( ( ! [SY331: $i,SY332: $i,SY333: $i] :
( ~ ( vtcheck @ ( vbind @ SV34 @ SY332 @ SV10 ) @ SY331 @ SY333 )
| ( vtcheck @ SV10 @ ( vabs @ SV34 @ SY332 @ SY331 ) @ ( varrow @ SY332 @ SY333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(186,plain,
! [SV11: $i,SV35: $i] :
( ( ! [SY334: $i,SY335: $i,SY336: $i,SY337: $i,SY338: $i] :
( ~ ~ ( ( SY334 != SY337 )
| ( SY335
!= ( vbind @ SV35 @ SV11 @ SY338 ) ) )
| ~ ( ( SY337 != SV35 ) )
| ( SY336
!= ( vlookup @ SY334 @ SY335 ) )
| ( SY336
= ( vlookup @ SY337 @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(187,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY339: $i] :
( vempty
!= ( vbind @ SV12 @ SV36 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(188,plain,
! [SV37: $i,SV13: $i] :
( ( ! [SY340: $i,SY341: $i] :
( ( vvar @ SV13 )
!= ( vabs @ SV37 @ SY340 @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(189,plain,
! [SV14: $i,SV38: $i] :
( ( ! [SY342: $i,SY343: $i,SY344: $i] :
( ~ ~ ( ~ ( vtcheck @ SV38 @ SY343 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SY342 @ SV14 @ SV38 ) @ veabs @ SY344 ) )
| ( vtcheck @ SV38 @ ( vsubst @ SY342 @ SY343 @ veabs ) @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(190,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY345: $i,SY346: $i,SY347: $i,SY348: $i,SY349: $i] :
( ~ ~ ( ~ ( ( SY345 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SY345 @ SY346 @ ( vbind @ SV15 @ SV39 @ SY347 ) ) @ SY348 @ SY349 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SY345 @ SY346 @ SY347 ) ) @ SY348 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(191,plain,
! [SV16: $i,SV40: $i] :
( ( ! [SY350: $i,SY351: $i,SY352: $i] :
( ~ ~ ( ~ ( vtcheck @ SV40 @ SY350 @ ( varrow @ SV16 @ SY352 ) )
| ~ ( vtcheck @ SV40 @ SY351 @ SV16 ) )
| ( vtcheck @ SV40 @ ( vapp @ SY350 @ SY351 ) @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(192,plain,
! [SV41: $i,SV17: $i] :
( ( ! [SY353: $i,SY354: $i,SY355: $i] :
( ( vabs @ SV17 @ SV41 @ SY353 )
!= ( vapp @ SY354 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(193,plain,
! [SV42: $i,SV18: $i] :
( ( ! [SY356: $i,SY357: $i,SY358: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV18 @ SY357 )
| ~ ( vtcheck @ SY356 @ SY357 @ SY358 ) )
| ( vtcheck @ ( vbind @ SV18 @ SV42 @ SY356 ) @ SY357 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(194,plain,
! [SV19: $i,SV43: $i] :
( ( ! [SY359: $i,SY360: $i,SY361: $i,SY362: $i,SY363: $i] :
( ~ ~ ( ~ ~ ( ( SY359 != SV43 )
| ( SY360 != SV19 ) )
| ( SY361
!= ( vvar @ SY363 ) ) )
| ~ ( ( SV43 != SY363 ) )
| ( SY362
!= ( vsubst @ SY359 @ SY360 @ SY361 ) )
| ( SY362
= ( vvar @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(195,plain,
! [SV20: $i,SV44: $i] :
( ( ! [SY364: $i,SY365: $i,SY366: $i,SY367: $i,SY368: $i] :
( ~ ~ ( ( SY365 != SV44 )
| ( SY366
!= ( vbind @ SY364 @ SY368 @ SV20 ) ) )
| ( SV44 != SY364 )
| ( SY367
!= ( vlookup @ SY365 @ SY366 ) )
| ( SY367
= ( vsomeType @ SY368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(196,plain,
! [SV45: $i,SV21: $i] :
( ( ! [SY369: $i,SY370: $i] :
( ( SY370
!= ( vabs @ SV21 @ SV45 @ SY369 ) )
| ( visValue @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(197,plain,
! [SV22: $i,SV46: $i] :
( ( ! [SY371: $i,SY372: $i,SY373: $i,SY374: $i] :
( ~ ~ ( ( SV46 != SY373 )
| ( SY371
!= ( vabs @ SY372 @ SV22 @ SY374 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY372 != SY373 ) )
| ~ ( visFreeVar @ SY373 @ SY374 ) )
| ( visFreeVar @ SV46 @ SY371 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SY371 )
| ~ ( ~ ( ( SY372 != SY373 ) )
| ~ ( visFreeVar @ SY373 @ SY374 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(198,plain,
! [SV47: $i,SV23: $i] :
( ( ! [SY375: $i,SY376: $i,SY377: $i,SY378: $i] :
~ ( ~ ( ( ( vbind @ SV23 @ SV47 @ SY375 )
!= ( vbind @ SY376 @ SY377 @ SY378 ) )
| ~ ( ~ ~ ( ( SV23 != SY376 )
| ( SV47 != SY377 ) )
| ( SY375 != SY378 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SY376 )
| ( SV47 != SY377 ) )
| ( SY375 != SY378 ) )
| ( ( vbind @ SV23 @ SV47 @ SY375 )
= ( vbind @ SY376 @ SY377 @ SY378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(199,plain,
! [SV48: $i,SV24: $i] :
( ( ! [SY379: $i,SY380: $i,SY381: $i,SY382: $i,SY383: $i] :
( ~ ~ ( ( SY379 != SV24 )
| ~ ( vtcheck @ ( vbind @ SY379 @ SY380 @ ( vbind @ SV24 @ SV48 @ SY381 ) ) @ SY382 @ SY383 ) )
| ( vtcheck @ ( vbind @ SY379 @ SY380 @ SY381 ) @ SY382 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(200,plain,
! [SV49: $i,SV25: $i,SV1: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ( SY384
!= ( vabs @ SV1 @ SV25 @ SV49 ) )
| ( SY385
!= ( vreduce @ SY384 ) )
| ( SY385 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(201,plain,
! [SV26: $i,SV50: $i,SV2: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ~ ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
| ~ ( vtcheck @ SV50 @ SY386 @ SY387 ) )
| ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SY386 @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(202,plain,
! [SV51: $i,SV27: $i,SV3: $i] :
( ( ! [SY388: $i,SY389: $i,SY390: $i,SY391: $i,SY392: $i,SY393: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SY391 )
| ( SV27 != SY392 ) )
| ( SV51
!= ( vabs @ SY389 @ SY390 @ SY393 ) ) )
| ~ ~ ( ~ ( ( SY391 != SY389 ) )
| ~ ~ ( visFreeVar @ SY389 @ SY392 ) )
| ( SY388
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SY388
= ( vabs @ SY389 @ SY390 @ ( vsubst @ SY391 @ SY392 @ SY393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(203,plain,
! [SV52: $i,SV28: $i,SV4: $i] :
( ( ! [SY394: $i,SY395: $i,SY396: $i] :
~ ( ~ ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SY394 @ SY395 @ SY396 ) )
| ~ ( ~ ~ ( ( SV4 != SY394 )
| ( SV28 != SY395 ) )
| ( SV52 != SY396 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SY394 )
| ( SV28 != SY395 ) )
| ( SV52 != SY396 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SY394 @ SY395 @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(204,plain,
! [SV53: $i,SV29: $i,SV5: $i] :
( ( ! [SY397: $i,SY398: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV5 @ SY397 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SY397 @ SY398 ) )
| ( vtcheck @ SV53 @ SY397 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(205,plain,
! [SV54: $i,SV30: $i,SV6: $i] :
( ( ! [SY399: $i,SY400: $i,SY401: $i,SY402: $i,SY403: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY401 )
| ( SV30 != SY402 ) )
| ( SV54
!= ( vapp @ SY400 @ SY403 ) ) )
| ( SY399
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SY399
= ( vapp @ ( vsubst @ SY401 @ SY402 @ SY400 ) @ ( vsubst @ SY401 @ SY402 @ SY403 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(206,plain,
! [SV7: $i,SV31: $i,SV55: $i] :
( ( ! [SY404: $i,SY405: $i,SY406: $i,SY407: $i,SY408: $i,SY409: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SY404 != SV7 ) )
| ( SY405
!= ( vabs @ SY407 @ SY408 @ SY409 ) ) )
| ( SV31 != SY407 )
| ( SY406
!= ( vsubst @ SV55 @ SY404 @ SY405 ) )
| ( SY406
= ( vabs @ SY407 @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(207,plain,
! [SV56: $i,SV8: $i,SV32: $i] :
( ( ( ( vlookup @ SV32 @ SV8 )
!= ( vsomeType @ SV56 ) )
| ( vtcheck @ SV8 @ ( vvar @ SV32 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(208,plain,
! [SV33: $i,SV9: $i,SV57: $i] :
( ( ! [SY410: $i,SY411: $i,SY412: $i,SY413: $i] :
( ~ ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SY410 != SY413 ) )
| ( SY411
!= ( vvar @ SV33 ) ) )
| ( SV9 != SV33 )
| ( SY412
!= ( vsubst @ SV57 @ SY410 @ SY411 ) )
| ( SY412 = SY413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(209,plain,
! [SV58: $i,SV10: $i,SV34: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( vtcheck @ ( vbind @ SV34 @ SY414 @ SV10 ) @ SV58 @ SY415 )
| ( vtcheck @ SV10 @ ( vabs @ SV34 @ SY414 @ SV58 ) @ ( varrow @ SY414 @ SY415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(210,plain,
! [SV11: $i,SV35: $i,SV59: $i] :
( ( ! [SY416: $i,SY417: $i,SY418: $i,SY419: $i] :
( ~ ~ ( ( SV59 != SY418 )
| ( SY416
!= ( vbind @ SV35 @ SV11 @ SY419 ) ) )
| ~ ( ( SY418 != SV35 ) )
| ( SY417
!= ( vlookup @ SV59 @ SY416 ) )
| ( SY417
= ( vlookup @ SY418 @ SY419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(211,plain,
! [SV60: $i,SV36: $i,SV12: $i] :
( ( vempty
!= ( vbind @ SV12 @ SV36 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(212,plain,
! [SV61: $i,SV37: $i,SV13: $i] :
( ( ! [SY420: $i] :
( ( vvar @ SV13 )
!= ( vabs @ SV37 @ SV61 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(213,plain,
! [SV62: $i,SV14: $i,SV38: $i] :
( ( ! [SY421: $i,SY422: $i] :
( ~ ~ ( ~ ( vtcheck @ SV38 @ SY421 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SY422 ) )
| ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SY421 @ veabs ) @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(214,plain,
! [SV39: $i,SV15: $i,SV63: $i] :
( ( ! [SY423: $i,SY424: $i,SY425: $i,SY426: $i] :
( ~ ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SY423 @ ( vbind @ SV15 @ SV39 @ SY424 ) ) @ SY425 @ SY426 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SY423 @ SY424 ) ) @ SY425 @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(215,plain,
! [SV16: $i,SV64: $i,SV40: $i] :
( ( ! [SY427: $i,SY428: $i] :
( ~ ~ ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SY428 ) )
| ~ ( vtcheck @ SV40 @ SY427 @ SV16 ) )
| ( vtcheck @ SV40 @ ( vapp @ SV64 @ SY427 ) @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(216,plain,
! [SV65: $i,SV41: $i,SV17: $i] :
( ( ! [SY429: $i,SY430: $i] :
( ( vabs @ SV17 @ SV41 @ SV65 )
!= ( vapp @ SY429 @ SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(217,plain,
! [SV42: $i,SV66: $i,SV18: $i] :
( ( ! [SY431: $i,SY432: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV18 @ SY431 )
| ~ ( vtcheck @ SV66 @ SY431 @ SY432 ) )
| ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SY431 @ SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(218,plain,
! [SV19: $i,SV43: $i,SV67: $i] :
( ( ! [SY433: $i,SY434: $i,SY435: $i,SY436: $i] :
( ~ ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SY433 != SV19 ) )
| ( SY434
!= ( vvar @ SY436 ) ) )
| ~ ( ( SV43 != SY436 ) )
| ( SY435
!= ( vsubst @ SV67 @ SY433 @ SY434 ) )
| ( SY435
= ( vvar @ SY436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(219,plain,
! [SV20: $i,SV68: $i,SV44: $i] :
( ( ! [SY437: $i,SY438: $i,SY439: $i,SY440: $i] :
( ~ ~ ( ( SY437 != SV44 )
| ( SY438
!= ( vbind @ SV68 @ SY440 @ SV20 ) ) )
| ( SV44 != SV68 )
| ( SY439
!= ( vlookup @ SY437 @ SY438 ) )
| ( SY439
= ( vsomeType @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(220,plain,
! [SV69: $i,SV45: $i,SV21: $i] :
( ( ! [SY441: $i] :
( ( SY441
!= ( vabs @ SV21 @ SV45 @ SV69 ) )
| ( visValue @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(221,plain,
! [SV22: $i,SV70: $i,SV46: $i] :
( ( ! [SY442: $i,SY443: $i,SY444: $i] :
( ~ ~ ( ( SV46 != SY443 )
| ( SV70
!= ( vabs @ SY442 @ SV22 @ SY444 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY442 != SY443 ) )
| ~ ( visFreeVar @ SY443 @ SY444 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SY442 != SY443 ) )
| ~ ( visFreeVar @ SY443 @ SY444 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(222,plain,
! [SV71: $i,SV47: $i,SV23: $i] :
( ( ! [SY445: $i,SY446: $i,SY447: $i] :
~ ( ~ ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SY445 @ SY446 @ SY447 ) )
| ~ ( ~ ~ ( ( SV23 != SY445 )
| ( SV47 != SY446 ) )
| ( SV71 != SY447 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SY445 )
| ( SV47 != SY446 ) )
| ( SV71 != SY447 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SY445 @ SY446 @ SY447 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(223,plain,
! [SV48: $i,SV24: $i,SV72: $i] :
( ( ! [SY448: $i,SY449: $i,SY450: $i,SY451: $i] :
( ~ ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SY448 @ ( vbind @ SV24 @ SV48 @ SY449 ) ) @ SY450 @ SY451 ) )
| ( vtcheck @ ( vbind @ SV72 @ SY448 @ SY449 ) @ SY450 @ SY451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(224,plain,
! [SV49: $i,SV25: $i,SV1: $i,SV73: $i] :
( ( ! [SY452: $i] :
( ( SV73
!= ( vabs @ SV1 @ SV25 @ SV49 ) )
| ( SY452
!= ( vreduce @ SV73 ) )
| ( SY452 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(225,plain,
! [SV26: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ! [SY453: $i] :
( ~ ~ ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
| ~ ( vtcheck @ SV50 @ SV74 @ SY453 ) )
| ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SY453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(226,plain,
! [SV75: $i,SV51: $i,SV27: $i,SV3: $i] :
( ( ! [SY454: $i,SY455: $i,SY456: $i,SY457: $i,SY458: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SY456 )
| ( SV27 != SY457 ) )
| ( SV51
!= ( vabs @ SY454 @ SY455 @ SY458 ) ) )
| ~ ~ ( ~ ( ( SY456 != SY454 ) )
| ~ ~ ( visFreeVar @ SY454 @ SY457 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SY454 @ SY455 @ ( vsubst @ SY456 @ SY457 @ SY458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(227,plain,
! [SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ! [SY459: $i,SY460: $i] :
~ ( ~ ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SY459 @ SY460 ) )
| ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SY459 ) )
| ( SV52 != SY460 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SY459 ) )
| ( SV52 != SY460 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SY459 @ SY460 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(228,plain,
! [SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ! [SY461: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV5 @ SV77 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SY461 ) )
| ( vtcheck @ SV53 @ SV77 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(229,plain,
! [SV78: $i,SV54: $i,SV30: $i,SV6: $i] :
( ( ! [SY462: $i,SY463: $i,SY464: $i,SY465: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY463 )
| ( SV30 != SY464 ) )
| ( SV54
!= ( vapp @ SY462 @ SY465 ) ) )
| ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SY463 @ SY464 @ SY462 ) @ ( vsubst @ SY463 @ SY464 @ SY465 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(230,plain,
! [SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ! [SY466: $i,SY467: $i,SY468: $i,SY469: $i,SY470: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SY466
!= ( vabs @ SY468 @ SY469 @ SY470 ) ) )
| ( SV31 != SY468 )
| ( SY467
!= ( vsubst @ SV55 @ SV79 @ SY466 ) )
| ( SY467
= ( vabs @ SY468 @ SY469 @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(231,plain,
! [SV56: $i,SV8: $i,SV32: $i] :
( ( ( ( vlookup @ SV32 @ SV8 )
!= ( vsomeType @ SV56 ) )
= $true )
| ( ( vtcheck @ SV8 @ ( vvar @ SV32 ) @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(232,plain,
! [SV33: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ~ ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SY473 ) )
| ( SY471
!= ( vvar @ SV33 ) ) )
| ( SV9 != SV33 )
| ( SY472
!= ( vsubst @ SV57 @ SV80 @ SY471 ) )
| ( SY472 = SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(233,plain,
! [SV58: $i,SV10: $i,SV81: $i,SV34: $i] :
( ( ! [SY474: $i] :
( ~ ( vtcheck @ ( vbind @ SV34 @ SV81 @ SV10 ) @ SV58 @ SY474 )
| ( vtcheck @ SV10 @ ( vabs @ SV34 @ SV81 @ SV58 ) @ ( varrow @ SV81 @ SY474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(234,plain,
! [SV11: $i,SV35: $i,SV82: $i,SV59: $i] :
( ( ! [SY475: $i,SY476: $i,SY477: $i] :
( ~ ~ ( ( SV59 != SY476 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SY477 ) ) )
| ~ ( ( SY476 != SV35 ) )
| ( SY475
!= ( vlookup @ SV59 @ SV82 ) )
| ( SY475
= ( vlookup @ SY476 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(235,plain,
! [SV60: $i,SV36: $i,SV12: $i] :
( ( vempty
= ( vbind @ SV12 @ SV36 @ SV60 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(236,plain,
! [SV83: $i,SV61: $i,SV37: $i,SV13: $i] :
( ( ( vvar @ SV13 )
!= ( vabs @ SV37 @ SV61 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(237,plain,
! [SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ! [SY478: $i] :
( ~ ~ ( ~ ( vtcheck @ SV38 @ SV84 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SY478 ) )
| ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(238,plain,
! [SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ! [SY479: $i,SY480: $i,SY481: $i] :
( ~ ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SY479 ) ) @ SY480 @ SY481 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SY479 ) ) @ SY480 @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(239,plain,
! [SV86: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ! [SY482: $i] :
( ~ ~ ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SY482 ) )
| ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) )
| ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SY482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(240,plain,
! [SV87: $i,SV65: $i,SV41: $i,SV17: $i] :
( ( ! [SY483: $i] :
( ( vabs @ SV17 @ SV41 @ SV65 )
!= ( vapp @ SV87 @ SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(241,plain,
! [SV42: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ! [SY484: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV18 @ SV88 )
| ~ ( vtcheck @ SV66 @ SV88 @ SY484 ) )
| ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SY484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(242,plain,
! [SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SY485
!= ( vvar @ SY487 ) ) )
| ~ ( ( SV43 != SY487 ) )
| ( SY486
!= ( vsubst @ SV67 @ SV89 @ SY485 ) )
| ( SY486
= ( vvar @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(243,plain,
! [SV20: $i,SV68: $i,SV44: $i,SV90: $i] :
( ( ! [SY488: $i,SY489: $i,SY490: $i] :
( ~ ~ ( ( SV90 != SV44 )
| ( SY488
!= ( vbind @ SV68 @ SY490 @ SV20 ) ) )
| ( SV44 != SV68 )
| ( SY489
!= ( vlookup @ SV90 @ SY488 ) )
| ( SY489
= ( vsomeType @ SY490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(244,plain,
! [SV69: $i,SV45: $i,SV21: $i,SV91: $i] :
( ( ( SV91
!= ( vabs @ SV21 @ SV45 @ SV69 ) )
| ( visValue @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(245,plain,
! [SV22: $i,SV92: $i,SV70: $i,SV46: $i] :
( ( ! [SY491: $i,SY492: $i] :
( ~ ~ ( ( SV46 != SY491 )
| ( SV70
!= ( vabs @ SV92 @ SV22 @ SY492 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SY491 ) )
| ~ ( visFreeVar @ SY491 @ SY492 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SY491 ) )
| ~ ( visFreeVar @ SY491 @ SY492 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(246,plain,
! [SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ! [SY493: $i,SY494: $i] :
~ ( ~ ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SY493 @ SY494 ) )
| ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SY493 ) )
| ( SV71 != SY494 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SY493 ) )
| ( SV71 != SY494 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SY493 @ SY494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(247,plain,
! [SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ! [SY495: $i,SY496: $i,SY497: $i] :
( ~ ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SY495 ) ) @ SY496 @ SY497 ) )
| ( vtcheck @ ( vbind @ SV72 @ SV94 @ SY495 ) @ SY496 @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(248,plain,
! [SV95: $i,SV49: $i,SV25: $i,SV1: $i,SV73: $i] :
( ( ( SV73
!= ( vabs @ SV1 @ SV25 @ SV49 ) )
| ( SV95
!= ( vreduce @ SV73 ) )
| ( SV95 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(249,plain,
! [SV26: $i,SV96: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ~ ~ ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
| ~ ( vtcheck @ SV50 @ SV74 @ SV96 ) )
| ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(250,plain,
! [SV75: $i,SV97: $i,SV51: $i,SV27: $i,SV3: $i] :
( ( ! [SY498: $i,SY499: $i,SY500: $i,SY501: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SY499 )
| ( SV27 != SY500 ) )
| ( SV51
!= ( vabs @ SV97 @ SY498 @ SY501 ) ) )
| ~ ~ ( ~ ( ( SY499 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SY500 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SY498 @ ( vsubst @ SY499 @ SY500 @ SY501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(251,plain,
! [SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ! [SY502: $i] :
~ ( ~ ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SV98 @ SY502 ) )
| ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SY502 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SY502 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SY502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(252,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV5 @ SV77 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) )
| ( vtcheck @ SV53 @ SV77 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(253,plain,
! [SV78: $i,SV100: $i,SV54: $i,SV30: $i,SV6: $i] :
( ( ! [SY503: $i,SY504: $i,SY505: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SY503 )
| ( SV30 != SY504 ) )
| ( SV54
!= ( vapp @ SV100 @ SY505 ) ) )
| ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SY503 @ SY504 @ SV100 ) @ ( vsubst @ SY503 @ SY504 @ SY505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(254,plain,
! [SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ! [SY506: $i,SY507: $i,SY508: $i,SY509: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SY507 @ SY508 @ SY509 ) ) )
| ( SV31 != SY507 )
| ( SY506
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SY506
= ( vabs @ SY507 @ SY508 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(255,plain,
! [SV56: $i,SV8: $i,SV32: $i] :
( ( ( ( vlookup @ SV32 @ SV8 )
= ( vsomeType @ SV56 ) )
= $false )
| ( ( vtcheck @ SV8 @ ( vvar @ SV32 ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(256,plain,
! [SV33: $i,SV102: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ! [SY510: $i,SY511: $i] :
( ~ ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SY511 ) )
| ( SV102
!= ( vvar @ SV33 ) ) )
| ( SV9 != SV33 )
| ( SY510
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SY510 = SY511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(257,plain,
! [SV103: $i,SV58: $i,SV10: $i,SV81: $i,SV34: $i] :
( ( ~ ( vtcheck @ ( vbind @ SV34 @ SV81 @ SV10 ) @ SV58 @ SV103 )
| ( vtcheck @ SV10 @ ( vabs @ SV34 @ SV81 @ SV58 ) @ ( varrow @ SV81 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(258,plain,
! [SV104: $i,SV11: $i,SV35: $i,SV82: $i,SV59: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ~ ( ( SV59 != SY512 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SY513 ) ) )
| ~ ( ( SY512 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SY512 @ SY513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(259,plain,
! [SV83: $i,SV61: $i,SV37: $i,SV13: $i] :
( ( ( vvar @ SV13 )
= ( vabs @ SV37 @ SV61 @ SV83 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(260,plain,
! [SV105: $i,SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ~ ~ ( ~ ( vtcheck @ SV38 @ SV84 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 ) )
| ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(261,plain,
! [SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ! [SY514: $i,SY515: $i] :
( ~ ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SY514 @ SY515 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SY514 @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(262,plain,
! [SV86: $i,SV107: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ~ ~ ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) )
| ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) )
| ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(263,plain,
! [SV108: $i,SV87: $i,SV65: $i,SV41: $i,SV17: $i] :
( ( ( vabs @ SV17 @ SV41 @ SV65 )
!= ( vapp @ SV87 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(264,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV18 @ SV88 )
| ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) )
| ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(265,plain,
! [SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SV110
!= ( vvar @ SY517 ) ) )
| ~ ( ( SV43 != SY517 ) )
| ( SY516
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SY516
= ( vvar @ SY517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(266,plain,
! [SV20: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ! [SY518: $i,SY519: $i] :
( ~ ~ ( ( SV90 != SV44 )
| ( SV111
!= ( vbind @ SV68 @ SY519 @ SV20 ) ) )
| ( SV44 != SV68 )
| ( SY518
!= ( vlookup @ SV90 @ SV111 ) )
| ( SY518
= ( vsomeType @ SY519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(267,plain,
! [SV69: $i,SV45: $i,SV21: $i,SV91: $i] :
( ( ( SV91
!= ( vabs @ SV21 @ SV45 @ SV69 ) )
= $true )
| ( ( visValue @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(268,plain,
! [SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ! [SY520: $i] :
( ~ ~ ( ( SV46 != SV112 )
| ( SV70
!= ( vabs @ SV92 @ SV22 @ SY520 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SY520 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SY520 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(269,plain,
! [SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ! [SY521: $i] :
~ ( ~ ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SV113 @ SY521 ) )
| ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SY521 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SY521 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SY521 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(270,plain,
! [SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ! [SY522: $i,SY523: $i] :
( ~ ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SY522 @ SY523 ) )
| ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SY522 @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(271,plain,
! [SV95: $i,SV49: $i,SV25: $i,SV1: $i,SV73: $i] :
( ( ( SV73
!= ( vabs @ SV1 @ SV25 @ SV49 ) )
= $true )
| ( ( ( SV95
!= ( vreduce @ SV73 ) )
| ( SV95 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(272,plain,
! [SV26: $i,SV96: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ( ~ ~ ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
| ~ ( vtcheck @ SV50 @ SV74 @ SV96 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(273,plain,
! [SV75: $i,SV115: $i,SV97: $i,SV51: $i,SV27: $i,SV3: $i] :
( ( ! [SY524: $i,SY525: $i,SY526: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SY524 )
| ( SV27 != SY525 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SY526 ) ) )
| ~ ~ ( ~ ( ( SY524 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SY525 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SY524 @ SY525 @ SY526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(274,plain,
! [SV116: $i,SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ~ ( ~ ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SV98 @ SV116 ) )
| ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(275,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV5 @ SV77 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) ) )
= $true )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(276,plain,
! [SV78: $i,SV100: $i,SV54: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SY527 ) )
| ( SV54
!= ( vapp @ SV100 @ SY528 ) ) )
| ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SY527 @ SV100 ) @ ( vsubst @ SV117 @ SY527 @ SY528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(277,plain,
! [SV118: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ! [SY529: $i,SY530: $i,SY531: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SY529 @ SY530 @ SY531 ) ) )
| ( SV31 != SY529 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SY529 @ SY530 @ SY531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(278,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ! [SY532: $i] :
( ~ ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SY532 ) )
| ( SV102
!= ( vvar @ SV33 ) ) )
| ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(279,plain,
! [SV103: $i,SV58: $i,SV10: $i,SV81: $i,SV34: $i] :
( ( ( ~ ( vtcheck @ ( vbind @ SV34 @ SV81 @ SV10 ) @ SV58 @ SV103 ) )
= $true )
| ( ( vtcheck @ SV10 @ ( vabs @ SV34 @ SV81 @ SV58 ) @ ( varrow @ SV81 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(280,plain,
! [SV104: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ! [SY533: $i] :
( ~ ~ ( ( SV59 != SV120 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SY533 ) ) )
| ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SY533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(281,plain,
! [SV105: $i,SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( vtcheck @ SV38 @ SV84 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 ) ) )
= $true )
| ( ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(282,plain,
! [SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ! [SY534: $i] :
( ~ ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SY534 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(283,plain,
! [SV86: $i,SV107: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) )
| ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) ) )
= $true )
| ( ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(284,plain,
! [SV108: $i,SV87: $i,SV65: $i,SV41: $i,SV17: $i] :
( ( ( vabs @ SV17 @ SV41 @ SV65 )
= ( vapp @ SV87 @ SV108 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(285,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV18 @ SV88 )
| ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(286,plain,
! [SV122: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ! [SY535: $i] :
( ~ ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SV110
!= ( vvar @ SY535 ) ) )
| ~ ( ( SV43 != SY535 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SY535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(287,plain,
! [SV123: $i,SV20: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ! [SY536: $i] :
( ~ ~ ( ( SV90 != SV44 )
| ( SV111
!= ( vbind @ SV68 @ SY536 @ SV20 ) ) )
| ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SY536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(288,plain,
! [SV69: $i,SV45: $i,SV21: $i,SV91: $i] :
( ( ( SV91
= ( vabs @ SV21 @ SV45 @ SV69 ) )
= $false )
| ( ( visValue @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(289,plain,
! [SV124: $i,SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ~ ~ ( ( SV46 != SV112 )
| ( SV70
!= ( vabs @ SV92 @ SV22 @ SV124 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(290,plain,
! [SV125: $i,SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ~ ( ~ ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SV113 @ SV125 ) )
| ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(291,plain,
! [SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ! [SY537: $i] :
( ~ ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SY537 ) )
| ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SY537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(292,plain,
! [SV95: $i,SV49: $i,SV25: $i,SV1: $i,SV73: $i] :
( ( ( SV73
= ( vabs @ SV1 @ SV25 @ SV49 ) )
= $false )
| ( ( ( SV95
!= ( vreduce @ SV73 ) )
| ( SV95 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(293,plain,
! [SV26: $i,SV96: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ( ~ ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
| ~ ( vtcheck @ SV50 @ SV74 @ SV96 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(294,plain,
! [SV75: $i,SV115: $i,SV97: $i,SV51: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ! [SY538: $i,SY539: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SY538 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SY539 ) ) )
| ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SY538 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SY538 @ SY539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(295,plain,
! [SV116: $i,SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ~ ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SV98 @ SV116 ) )
| ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(296,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV5 @ SV77 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) ) )
= $false )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(297,plain,
! [SV78: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ! [SY540: $i] :
( ~ ~ ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) )
| ( SV54
!= ( vapp @ SV100 @ SY540 ) ) )
| ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SY540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(298,plain,
! [SV118: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ! [SY541: $i,SY542: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SV129 @ SY541 @ SY542 ) ) )
| ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SY541 @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(299,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ~ ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SV130 ) )
| ( SV102
!= ( vvar @ SV33 ) ) )
| ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(300,plain,
! [SV103: $i,SV58: $i,SV10: $i,SV81: $i,SV34: $i] :
( ( ( vtcheck @ ( vbind @ SV34 @ SV81 @ SV10 ) @ SV58 @ SV103 )
= $false )
| ( ( vtcheck @ SV10 @ ( vabs @ SV34 @ SV81 @ SV58 ) @ ( varrow @ SV81 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(301,plain,
! [SV104: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ~ ~ ( ( SV59 != SV120 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SV131 ) ) )
| ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(302,plain,
! [SV105: $i,SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ( ~ ( ~ ( vtcheck @ SV38 @ SV84 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 ) ) )
= $false )
| ( ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(303,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ~ ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(304,plain,
! [SV86: $i,SV107: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ( ~ ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) )
| ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) ) )
= $false )
| ( ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(305,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV18 @ SV88 )
| ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(306,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ~ ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SV110
!= ( vvar @ SV133 ) ) )
| ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(307,plain,
! [SV123: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ~ ~ ( ( SV90 != SV44 )
| ( SV111
!= ( vbind @ SV68 @ SV134 @ SV20 ) ) )
| ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(308,plain,
! [SV124: $i,SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ( ~ ~ ( ( SV46 != SV112 )
| ( SV70
!= ( vabs @ SV92 @ SV22 @ SV124 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(309,plain,
! [SV125: $i,SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ~ ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SV113 @ SV125 ) )
| ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(310,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ~ ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 ) )
| ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(311,plain,
! [SV49: $i,SV25: $i,SV1: $i,SV73: $i,SV95: $i] :
( ( ( SV95
!= ( vreduce @ SV73 ) )
= $true )
| ( ( SV95 = vnoExp )
= $true )
| ( ( SV73
= ( vabs @ SV1 @ SV25 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(312,plain,
! [SV26: $i,SV96: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
| ~ ( vtcheck @ SV50 @ SV74 @ SV96 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(313,plain,
! [SV75: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ! [SY543: $i] :
( ~ ~ ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SY543 ) ) )
| ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SY543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(314,plain,
! [SV116: $i,SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ~ ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SV98 @ SV116 ) )
| ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(315,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(316,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ( ~ ~ ( visFreeVar @ SV5 @ SV77 )
| ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) )
= $true )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(317,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) )
| ( SV54
!= ( vapp @ SV100 @ SV137 ) ) )
| ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(318,plain,
! [SV118: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ! [SY544: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SV129 @ SV138 @ SY544 ) ) )
| ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SY544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(319,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SV130 ) )
| ( SV102
!= ( vvar @ SV33 ) ) ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(320,plain,
! [SV104: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ( ~ ~ ( ( SV59 != SV120 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SV131 ) ) ) )
= $true )
| ( ( ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(321,plain,
! [SV105: $i,SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ( ~ ( vtcheck @ SV38 @ SV84 @ SV14 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 ) )
= $true )
| ( ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(322,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(323,plain,
! [SV86: $i,SV107: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) )
| ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) )
= $true )
| ( ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(324,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ( ~ ~ ( visFreeVar @ SV18 @ SV88 )
| ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(325,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SV110
!= ( vvar @ SV133 ) ) ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(326,plain,
! [SV123: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ( ~ ~ ( ( SV90 != SV44 )
| ( SV111
!= ( vbind @ SV68 @ SV134 @ SV20 ) ) ) )
= $true )
| ( ( ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(327,plain,
! [SV124: $i,SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ( ~ ( ( SV46 != SV112 )
| ( SV70
!= ( vabs @ SV92 @ SV22 @ SV124 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(328,plain,
! [SV125: $i,SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ~ ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SV113 @ SV125 ) )
| ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(329,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(330,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ( ~ ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(331,plain,
! [SV49: $i,SV25: $i,SV1: $i,SV73: $i,SV95: $i] :
( ( ( SV95
= ( vreduce @ SV73 ) )
= $false )
| ( ( SV95 = vnoExp )
= $true )
| ( ( SV73
= ( vabs @ SV1 @ SV25 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(332,plain,
! [SV26: $i,SV96: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ( ( vlookup @ SV2 @ SV50 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV50 @ SV74 @ SV96 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(333,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) ) )
| ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(334,plain,
! [SV116: $i,SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SV98 @ SV116 ) )
| ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(335,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) )
| ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(336,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ( ~ ~ ( visFreeVar @ SV5 @ SV77 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) )
= $true )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(337,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) )
| ( SV54
!= ( vapp @ SV100 @ SV137 ) ) ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(338,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
| ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(339,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( ~ ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SV130 ) )
| ( SV102
!= ( vvar @ SV33 ) ) ) )
= $false )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(340,plain,
! [SV104: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != SV120 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SV131 ) ) ) )
= $false )
| ( ( ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(341,plain,
! [SV105: $i,SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ( ~ ( vtcheck @ SV38 @ SV84 @ SV14 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 ) )
= $true )
| ( ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(342,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ( ~ ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(343,plain,
! [SV86: $i,SV107: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ( ~ ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) )
= $true )
| ( ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(344,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ( ~ ~ ( visFreeVar @ SV18 @ SV88 ) )
= $true )
| ( ( ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(345,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( ~ ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SV110
!= ( vvar @ SV133 ) ) ) )
= $false )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(346,plain,
! [SV123: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ( ~ ( ( SV90 != SV44 )
| ( SV111
!= ( vbind @ SV68 @ SV134 @ SV20 ) ) ) )
= $false )
| ( ( ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(347,plain,
! [SV124: $i,SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ( ( SV46 != SV112 )
| ( SV70
!= ( vabs @ SV92 @ SV22 @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(348,plain,
! [SV125: $i,SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SV113 @ SV125 ) )
| ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(349,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) )
| ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(350,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ( ~ ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(351,plain,
! [SV26: $i,SV96: $i,SV74: $i,SV50: $i,SV2: $i] :
( ( ( ( vlookup @ SV2 @ SV50 )
= vnoType )
= $false )
| ( ( ~ ( vtcheck @ SV50 @ SV74 @ SV96 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(352,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(353,plain,
! [SV116: $i,SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ( ( vabs @ SV4 @ SV28 @ SV52 )
!= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(354,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(355,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ( ~ ( visFreeVar @ SV5 @ SV77 ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) )
= $true )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(356,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) )
| ( SV54
!= ( vapp @ SV100 @ SV137 ) ) ) )
= $false )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(357,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(358,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SV130 ) )
| ( SV102
!= ( vvar @ SV33 ) ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(359,plain,
! [SV104: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ( ( SV59 != SV120 )
| ( SV82
!= ( vbind @ SV35 @ SV11 @ SV131 ) ) )
= $true )
| ( ( ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(360,plain,
! [SV105: $i,SV62: $i,SV14: $i,SV84: $i,SV38: $i] :
( ( ( vtcheck @ SV38 @ SV84 @ SV14 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 ) )
= $true )
| ( ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(361,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ( ~ ( ( SV63 != SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(362,plain,
! [SV86: $i,SV107: $i,SV16: $i,SV64: $i,SV40: $i] :
( ( ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) )
= $false )
| ( ( ~ ( vtcheck @ SV40 @ SV86 @ SV16 ) )
= $true )
| ( ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(363,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ( ~ ( visFreeVar @ SV18 @ SV88 ) )
= $false )
| ( ( ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(364,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
| ( SV110
!= ( vvar @ SV133 ) ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(365,plain,
! [SV123: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ( ( SV90 != SV44 )
| ( SV111
!= ( vbind @ SV68 @ SV134 @ SV20 ) ) )
= $true )
| ( ( ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(366,plain,
! [SV124: $i,SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ( SV46 != SV112 )
= $true )
| ( ( SV70
!= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(367,plain,
! [SV125: $i,SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ( ( vbind @ SV23 @ SV47 @ SV71 )
!= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(368,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(369,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ( ( SV72 != SV24 )
| ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(370,plain,
! [SV26: $i,SV2: $i,SV96: $i,SV74: $i,SV50: $i] :
( ( ( vtcheck @ SV50 @ SV74 @ SV96 )
= $false )
| ( ( ( vlookup @ SV2 @ SV50 )
= vnoType )
= $false )
| ( ( vtcheck @ ( vbind @ SV2 @ SV26 @ SV50 ) @ SV74 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(371,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(372,plain,
! [SV116: $i,SV98: $i,SV76: $i,SV52: $i,SV28: $i,SV4: $i] :
( ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(373,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) ) )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(374,plain,
! [SV99: $i,SV53: $i,SV29: $i,SV77: $i,SV5: $i] :
( ( ( visFreeVar @ SV5 @ SV77 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 ) )
= $true )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(375,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) )
| ( SV54
!= ( vapp @ SV100 @ SV137 ) ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(376,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( ~ ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) ) ) )
= $false )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(377,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( ~ ~ ( ( SV57 != SV9 )
| ( SV80 != SV130 ) ) )
= $true )
| ( ( SV102
!= ( vvar @ SV33 ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(378,plain,
! [SV104: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ( SV59 != SV120 )
= $true )
| ( ( SV82
!= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $true )
| ( ( ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(379,plain,
! [SV84: $i,SV105: $i,SV38: $i,SV14: $i,SV62: $i] :
( ( ( vtcheck @ ( vbind @ SV62 @ SV14 @ SV38 ) @ veabs @ SV105 )
= $false )
| ( ( vtcheck @ SV38 @ SV84 @ SV14 )
= $false )
| ( ( vtcheck @ SV38 @ ( vsubst @ SV62 @ SV84 @ veabs ) @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(380,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ( ~ ( ( SV63 != SV15 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(381,plain,
! [SV107: $i,SV64: $i,SV16: $i,SV86: $i,SV40: $i] :
( ( ( vtcheck @ SV40 @ SV86 @ SV16 )
= $false )
| ( ( vtcheck @ SV40 @ SV64 @ ( varrow @ SV16 @ SV107 ) )
= $false )
| ( ( vtcheck @ SV40 @ ( vapp @ SV64 @ SV86 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(382,plain,
! [SV42: $i,SV109: $i,SV66: $i,SV88: $i,SV18: $i] :
( ( ( visFreeVar @ SV18 @ SV88 )
= $true )
| ( ( ~ ( vtcheck @ SV66 @ SV88 @ SV109 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(383,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( ~ ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) ) )
= $true )
| ( ( SV110
!= ( vvar @ SV133 ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(384,plain,
! [SV123: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ( SV90 != SV44 )
= $true )
| ( ( SV111
!= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $true )
| ( ( ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(385,plain,
! [SV124: $i,SV22: $i,SV92: $i,SV70: $i,SV112: $i,SV46: $i] :
( ( ( SV46 = SV112 )
= $false )
| ( ( SV70
!= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(386,plain,
! [SV125: $i,SV113: $i,SV93: $i,SV71: $i,SV47: $i,SV23: $i] :
( ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(387,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) ) )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(388,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ( SV72 != SV24 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(389,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) )
| ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(390,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(391,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
| ( SV52 != SV116 ) )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(392,plain,
! [SV99: $i,SV77: $i,SV53: $i,SV29: $i,SV5: $i] :
( ( ( vtcheck @ ( vbind @ SV5 @ SV29 @ SV53 ) @ SV77 @ SV99 )
= $false )
| ( ( visFreeVar @ SV5 @ SV77 )
= $true )
| ( ( vtcheck @ SV53 @ SV77 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(393,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( ~ ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) ) )
= $true )
| ( ( SV54
!= ( vapp @ SV100 @ SV137 ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(394,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
| ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(395,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( ~ ( ( SV57 != SV9 )
| ( SV80 != SV130 ) ) )
= $false )
| ( ( SV102
!= ( vvar @ SV33 ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(396,plain,
! [SV104: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i,SV120: $i,SV59: $i] :
( ( ( SV59 = SV120 )
= $false )
| ( ( SV82
!= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $true )
| ( ( ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(397,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ( SV63 != SV15 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(398,plain,
! [SV42: $i,SV18: $i,SV109: $i,SV88: $i,SV66: $i] :
( ( ( vtcheck @ SV66 @ SV88 @ SV109 )
= $false )
| ( ( visFreeVar @ SV18 @ SV88 )
= $true )
| ( ( vtcheck @ ( vbind @ SV18 @ SV42 @ SV66 ) @ SV88 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(399,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV43 )
| ( SV89 != SV19 ) ) )
= $false )
| ( ( SV110
!= ( vvar @ SV133 ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(400,plain,
! [SV123: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i,SV44: $i,SV90: $i] :
( ( ( SV90 = SV44 )
= $false )
| ( ( SV111
!= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $true )
| ( ( ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(401,plain,
! [SV112: $i,SV46: $i,SV124: $i,SV22: $i,SV92: $i,SV70: $i] :
( ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(402,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(403,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
| ( SV71 != SV125 ) )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(404,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV94: $i,SV24: $i,SV72: $i] :
( ( ( SV72 = SV24 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(405,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) ) )
= $true )
| ( ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(406,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) ) )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(407,plain,
! [SV98: $i,SV76: $i,SV28: $i,SV4: $i,SV116: $i,SV52: $i] :
( ( ( SV52 != SV116 )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(408,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) ) )
= $true )
| ( ( SV52 != SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(409,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( ~ ( ( SV6 != SV117 )
| ( SV30 != SV128 ) ) )
= $false )
| ( ( SV54
!= ( vapp @ SV100 @ SV137 ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(410,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( ~ ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) ) )
= $true )
| ( ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(411,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( ( SV57 != SV9 )
| ( SV80 != SV130 ) )
= $true )
| ( ( SV102
!= ( vvar @ SV33 ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(412,plain,
! [SV104: $i,SV120: $i,SV59: $i,SV131: $i,SV11: $i,SV35: $i,SV82: $i] :
( ( ( SV82
= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $false )
| ( ( SV59 = SV120 )
= $false )
| ( ( ~ ( ( SV120 != SV35 ) )
| ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(413,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV85: $i,SV15: $i,SV63: $i] :
( ( ( SV63 = SV15 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(414,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( ( SV67 != SV43 )
| ( SV89 != SV19 ) )
= $true )
| ( ( SV110
!= ( vvar @ SV133 ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(415,plain,
! [SV123: $i,SV44: $i,SV90: $i,SV20: $i,SV134: $i,SV68: $i,SV111: $i] :
( ( ( SV111
= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $false )
| ( ( SV90 = SV44 )
= $false )
| ( ( ( SV44 != SV68 )
| ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(416,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
| ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(417,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) ) )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(418,plain,
! [SV113: $i,SV93: $i,SV47: $i,SV23: $i,SV125: $i,SV71: $i] :
( ( ( SV71 != SV125 )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(419,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) ) )
= $true )
| ( ( SV71 != SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(420,plain,
! [SV135: $i,SV126: $i,SV114: $i,SV48: $i,SV24: $i,SV94: $i,SV72: $i] :
( ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ ( vbind @ SV24 @ SV48 @ SV114 ) ) @ SV126 @ SV135 )
= $false )
| ( ( SV72 = SV24 )
= $false )
| ( ( vtcheck @ ( vbind @ SV72 @ SV94 @ SV114 ) @ SV126 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV127 )
| ( SV27 != SV136 ) ) )
= $false )
| ( ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(422,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) ) )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(423,plain,
! [SV98: $i,SV76: $i,SV28: $i,SV4: $i,SV116: $i,SV52: $i] :
( ( ( SV52 = SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(424,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != SV76 )
| ( SV28 != SV98 ) ) )
= $false )
| ( ( SV52 != SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(425,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( ( SV6 != SV117 )
| ( SV30 != SV128 ) )
= $true )
| ( ( SV54
!= ( vapp @ SV100 @ SV137 ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(426,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV31 )
| ( SV79 != SV7 ) ) )
= $false )
| ( ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(427,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( SV57 != SV9 )
= $true )
| ( ( SV80 != SV130 )
= $true )
| ( ( SV102
!= ( vvar @ SV33 ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(428,plain,
! [SV11: $i,SV131: $i,SV82: $i,SV59: $i,SV104: $i,SV35: $i,SV120: $i] :
( ( ( ~ ( ( SV120 != SV35 ) ) )
= $true )
| ( ( ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true )
| ( ( SV59 = SV120 )
= $false )
| ( ( SV82
= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(429,plain,
! [SV132: $i,SV121: $i,SV106: $i,SV39: $i,SV15: $i,SV85: $i,SV63: $i] :
( ( ( vtcheck @ ( vbind @ SV63 @ SV85 @ ( vbind @ SV15 @ SV39 @ SV106 ) ) @ SV121 @ SV132 )
= $false )
| ( ( SV63 = SV15 )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV39 @ ( vbind @ SV63 @ SV85 @ SV106 ) ) @ SV121 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(430,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( SV67 != SV43 )
= $true )
| ( ( SV89 != SV19 )
= $true )
| ( ( SV110
!= ( vvar @ SV133 ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(431,plain,
! [SV20: $i,SV134: $i,SV111: $i,SV90: $i,SV123: $i,SV68: $i,SV44: $i] :
( ( ( SV44 != SV68 )
= $true )
| ( ( ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true )
| ( ( SV90 = SV44 )
= $false )
| ( ( SV111
= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(432,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) ) )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(433,plain,
! [SV22: $i,SV124: $i,SV112: $i,SV92: $i,SV70: $i,SV46: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) ) )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(434,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) ) )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(435,plain,
! [SV113: $i,SV93: $i,SV47: $i,SV23: $i,SV125: $i,SV71: $i] :
( ( ( SV71 = SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(436,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ~ ( ( SV23 != SV93 )
| ( SV47 != SV113 ) ) )
= $false )
| ( ( SV71 != SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(437,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( ( SV3 != SV127 )
| ( SV27 != SV136 ) )
= $true )
| ( ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(438,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(439,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( ( SV4 != SV76 )
| ( SV28 != SV98 ) )
= $true )
| ( ( SV52 != SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(440,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( SV6 != SV117 )
= $true )
| ( ( SV30 != SV128 )
= $true )
| ( ( SV54
!= ( vapp @ SV100 @ SV137 ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(441,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( ( SV55 != SV31 )
| ( SV79 != SV7 ) )
= $true )
| ( ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(442,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i] :
( ( ( SV57 = SV9 )
= $false )
| ( ( SV80 != SV130 )
= $true )
| ( ( SV102
!= ( vvar @ SV33 ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(443,plain,
! [SV11: $i,SV131: $i,SV82: $i,SV59: $i,SV104: $i,SV35: $i,SV120: $i] :
( ( ( SV120 != SV35 )
= $false )
| ( ( ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true )
| ( ( SV59 = SV120 )
= $false )
| ( ( SV82
= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(444,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i] :
( ( ( SV67 = SV43 )
= $false )
| ( ( SV89 != SV19 )
= $true )
| ( ( SV110
!= ( vvar @ SV133 ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(445,plain,
! [SV20: $i,SV134: $i,SV111: $i,SV90: $i,SV123: $i,SV68: $i,SV44: $i] :
( ( ( SV44 = SV68 )
= $false )
| ( ( ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
| ( SV123
= ( vsomeType @ SV134 ) ) )
= $true )
| ( ( SV90 = SV44 )
= $false )
| ( ( SV111
= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(446,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
| ( visFreeVar @ SV46 @ SV70 ) )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(447,plain,
! [SV22: $i,SV124: $i,SV112: $i,SV92: $i,SV70: $i,SV46: $i] :
( ( ( ~ ( visFreeVar @ SV46 @ SV70 )
| ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(448,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(449,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( ( SV23 != SV93 )
| ( SV47 != SV113 ) )
= $true )
| ( ( SV71 != SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(450,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( SV3 != SV127 )
= $true )
| ( ( SV27 != SV136 )
= $true )
| ( ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(451,plain,
! [SV116: $i,SV98: $i,SV52: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( SV4 != SV76 )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(452,plain,
! [SV116: $i,SV76: $i,SV52: $i,SV4: $i,SV98: $i,SV28: $i] :
( ( ( SV28 != SV98 )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(453,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( SV4 != SV76 )
= $true )
| ( ( SV28 != SV98 )
= $true )
| ( ( SV52 != SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(454,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i] :
( ( ( SV6 = SV117 )
= $false )
| ( ( SV30 != SV128 )
= $true )
| ( ( SV54
!= ( vapp @ SV100 @ SV137 ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(455,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( SV55 != SV31 )
= $true )
| ( ( SV79 != SV7 )
= $true )
| ( ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(456,plain,
! [SV119: $i,SV33: $i,SV102: $i,SV9: $i,SV57: $i,SV130: $i,SV80: $i] :
( ( ( SV80 = SV130 )
= $false )
| ( ( SV57 = SV9 )
= $false )
| ( ( SV102
!= ( vvar @ SV33 ) )
= $true )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(457,plain,
! [SV11: $i,SV131: $i,SV82: $i,SV59: $i,SV104: $i,SV35: $i,SV120: $i] :
( ( ( SV120 = SV35 )
= $true )
| ( ( ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
| ( SV104
= ( vlookup @ SV120 @ SV131 ) ) )
= $true )
| ( ( SV59 = SV120 )
= $false )
| ( ( SV82
= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(458,plain,
! [SV122: $i,SV133: $i,SV110: $i,SV43: $i,SV67: $i,SV19: $i,SV89: $i] :
( ( ( SV89 = SV19 )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV110
!= ( vvar @ SV133 ) )
= $true )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(459,plain,
! [SV20: $i,SV68: $i,SV44: $i,SV134: $i,SV111: $i,SV90: $i,SV123: $i] :
( ( ( SV123
!= ( vlookup @ SV90 @ SV111 ) )
= $true )
| ( ( SV123
= ( vsomeType @ SV134 ) )
= $true )
| ( ( SV44 = SV68 )
= $false )
| ( ( SV90 = SV44 )
= $false )
| ( ( SV111
= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(460,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(461,plain,
! [SV22: $i,SV124: $i,SV112: $i,SV92: $i,SV70: $i,SV46: $i] :
( ( ( ~ ( visFreeVar @ SV46 @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(462,plain,
! [SV125: $i,SV113: $i,SV71: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( SV23 != SV93 )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(463,plain,
! [SV125: $i,SV93: $i,SV71: $i,SV23: $i,SV113: $i,SV47: $i] :
( ( ( SV47 != SV113 )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(464,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( SV23 != SV93 )
= $true )
| ( ( SV47 != SV113 )
= $true )
| ( ( SV71 != SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(465,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i] :
( ( ( SV3 = SV127 )
= $false )
| ( ( SV27 != SV136 )
= $true )
| ( ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(466,plain,
! [SV116: $i,SV98: $i,SV52: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( SV4 = SV76 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(467,plain,
! [SV116: $i,SV76: $i,SV52: $i,SV4: $i,SV98: $i,SV28: $i] :
( ( ( SV28 = SV98 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(468,plain,
! [SV116: $i,SV52: $i,SV98: $i,SV28: $i,SV76: $i,SV4: $i] :
( ( ( SV4 = SV76 )
= $false )
| ( ( SV28 != SV98 )
= $true )
| ( ( SV52 != SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(469,plain,
! [SV78: $i,SV137: $i,SV100: $i,SV54: $i,SV117: $i,SV6: $i,SV128: $i,SV30: $i] :
( ( ( SV30 = SV128 )
= $false )
| ( ( SV6 = SV117 )
= $false )
| ( ( SV54
!= ( vapp @ SV100 @ SV137 ) )
= $true )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(470,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i] :
( ( ( SV55 = SV31 )
= $false )
| ( ( SV79 != SV7 )
= $true )
| ( ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(471,plain,
! [SV119: $i,SV130: $i,SV80: $i,SV9: $i,SV57: $i,SV33: $i,SV102: $i] :
( ( ( SV102
= ( vvar @ SV33 ) )
= $false )
| ( ( SV57 = SV9 )
= $false )
| ( ( SV80 = SV130 )
= $false )
| ( ( ( SV9 != SV33 )
| ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(472,plain,
! [SV11: $i,SV35: $i,SV131: $i,SV120: $i,SV82: $i,SV59: $i,SV104: $i] :
( ( ( SV104
!= ( vlookup @ SV59 @ SV82 ) )
= $true )
| ( ( SV104
= ( vlookup @ SV120 @ SV131 ) )
= $true )
| ( ( SV120 = SV35 )
= $true )
| ( ( SV59 = SV120 )
= $false )
| ( ( SV82
= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(473,plain,
! [SV122: $i,SV19: $i,SV89: $i,SV43: $i,SV67: $i,SV133: $i,SV110: $i] :
( ( ( SV110
= ( vvar @ SV133 ) )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV89 = SV19 )
= $false )
| ( ( ~ ( ( SV43 != SV133 ) )
| ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(474,plain,
! [SV20: $i,SV68: $i,SV44: $i,SV134: $i,SV111: $i,SV90: $i,SV123: $i] :
( ( ( SV123
= ( vlookup @ SV90 @ SV111 ) )
= $false )
| ( ( SV123
= ( vsomeType @ SV134 ) )
= $true )
| ( ( SV44 = SV68 )
= $false )
| ( ( SV90 = SV44 )
= $false )
| ( ( SV111
= ( vbind @ SV68 @ SV134 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(475,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) )
= $false )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(476,plain,
! [SV22: $i,SV124: $i,SV112: $i,SV92: $i,SV70: $i,SV46: $i] :
( ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( ~ ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) ) )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(477,plain,
! [SV125: $i,SV113: $i,SV71: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( SV23 = SV93 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(478,plain,
! [SV125: $i,SV93: $i,SV71: $i,SV23: $i,SV113: $i,SV47: $i] :
( ( ( SV47 = SV113 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(479,plain,
! [SV125: $i,SV71: $i,SV113: $i,SV47: $i,SV93: $i,SV23: $i] :
( ( ( SV23 = SV93 )
= $false )
| ( ( SV47 != SV113 )
= $true )
| ( ( SV71 != SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(480,plain,
! [SV75: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i,SV127: $i,SV3: $i,SV136: $i,SV27: $i] :
( ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
!= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(481,plain,
! [SV116: $i,SV52: $i,SV76: $i,SV4: $i,SV98: $i,SV28: $i] :
( ( ( SV28 = SV98 )
= $false )
| ( ( SV4 = SV76 )
= $false )
| ( ( SV52 != SV116 )
= $true )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(482,plain,
! [SV78: $i,SV128: $i,SV30: $i,SV117: $i,SV6: $i,SV137: $i,SV100: $i,SV54: $i] :
( ( ( SV54
= ( vapp @ SV100 @ SV137 ) )
= $false )
| ( ( SV6 = SV117 )
= $false )
| ( ( SV30 = SV128 )
= $false )
| ( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
| ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(483,plain,
! [SV118: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV31: $i,SV55: $i,SV7: $i,SV79: $i] :
( ( ( SV79 = SV7 )
= $false )
| ( ( SV55 = SV31 )
= $false )
| ( ( SV101
!= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(484,plain,
! [SV130: $i,SV102: $i,SV80: $i,SV57: $i,SV119: $i,SV33: $i,SV9: $i] :
( ( ( SV9 != SV33 )
= $true )
| ( ( ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true )
| ( ( SV80 = SV130 )
= $false )
| ( ( SV57 = SV9 )
= $false )
| ( ( SV102
= ( vvar @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(485,plain,
! [SV11: $i,SV35: $i,SV131: $i,SV120: $i,SV82: $i,SV59: $i,SV104: $i] :
( ( ( SV104
= ( vlookup @ SV59 @ SV82 ) )
= $false )
| ( ( SV104
= ( vlookup @ SV120 @ SV131 ) )
= $true )
| ( ( SV120 = SV35 )
= $true )
| ( ( SV59 = SV120 )
= $false )
| ( ( SV82
= ( vbind @ SV35 @ SV11 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(486,plain,
! [SV19: $i,SV110: $i,SV89: $i,SV67: $i,SV122: $i,SV133: $i,SV43: $i] :
( ( ( ~ ( ( SV43 != SV133 ) ) )
= $true )
| ( ( ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true )
| ( ( SV89 = SV19 )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV110
= ( vvar @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(487,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(488,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ( SV92 != SV112 ) )
| ~ ( visFreeVar @ SV112 @ SV124 ) )
= $false )
| ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(489,plain,
! [SV125: $i,SV71: $i,SV93: $i,SV23: $i,SV113: $i,SV47: $i] :
( ( ( SV47 = SV113 )
= $false )
| ( ( SV23 = SV93 )
= $false )
| ( ( SV71 != SV125 )
= $true )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(490,plain,
! [SV75: $i,SV136: $i,SV27: $i,SV127: $i,SV3: $i,SV139: $i,SV115: $i,SV97: $i,SV51: $i] :
( ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV27 = SV136 )
= $false )
| ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
| ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(491,plain,
! [SV98: $i,SV28: $i,SV76: $i,SV4: $i,SV116: $i,SV52: $i] :
( ( ( SV52 = SV116 )
= $false )
| ( ( SV4 = SV76 )
= $false )
| ( ( SV28 = SV98 )
= $false )
| ( ( ( vabs @ SV4 @ SV28 @ SV52 )
= ( vabs @ SV76 @ SV98 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(492,plain,
! [SV137: $i,SV100: $i,SV128: $i,SV117: $i,SV54: $i,SV30: $i,SV6: $i,SV78: $i] :
( ( ( SV78
!= ( vsubst @ SV6 @ SV30 @ SV54 ) )
= $true )
| ( ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) )
= $true )
| ( ( SV30 = SV128 )
= $false )
| ( ( SV6 = SV117 )
= $false )
| ( ( SV54
= ( vapp @ SV100 @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(493,plain,
! [SV118: $i,SV7: $i,SV79: $i,SV31: $i,SV55: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i] :
( ( ( SV101
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $false )
| ( ( SV55 = SV31 )
= $false )
| ( ( SV79 = SV7 )
= $false )
| ( ( ( SV31 != SV129 )
| ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(494,plain,
! [SV130: $i,SV102: $i,SV80: $i,SV57: $i,SV119: $i,SV33: $i,SV9: $i] :
( ( ( SV9 = SV33 )
= $false )
| ( ( ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
| ( SV119 = SV130 ) )
= $true )
| ( ( SV80 = SV130 )
= $false )
| ( ( SV57 = SV9 )
= $false )
| ( ( SV102
= ( vvar @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(495,plain,
! [SV19: $i,SV110: $i,SV89: $i,SV67: $i,SV122: $i,SV133: $i,SV43: $i] :
( ( ( SV43 != SV133 )
= $false )
| ( ( ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true )
| ( ( SV89 = SV19 )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV110
= ( vvar @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(496,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ( SV92 != SV112 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV112 @ SV124 ) )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(497,plain,
! [SV124: $i,SV22: $i,SV70: $i,SV46: $i,SV112: $i,SV92: $i] :
( ( ( ~ ( ( SV92 != SV112 ) ) )
= $false )
| ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(498,plain,
! [SV22: $i,SV92: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i] :
( ( ( ~ ( visFreeVar @ SV112 @ SV124 ) )
= $false )
| ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(499,plain,
! [SV113: $i,SV47: $i,SV93: $i,SV23: $i,SV125: $i,SV71: $i] :
( ( ( SV71 = SV125 )
= $false )
| ( ( SV23 = SV93 )
= $false )
| ( ( SV47 = SV113 )
= $false )
| ( ( ( vbind @ SV23 @ SV47 @ SV71 )
= ( vbind @ SV93 @ SV113 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(500,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV136: $i,SV97: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) ) )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(501,plain,
! [SV137: $i,SV100: $i,SV128: $i,SV117: $i,SV54: $i,SV30: $i,SV6: $i,SV78: $i] :
( ( ( SV78
= ( vsubst @ SV6 @ SV30 @ SV54 ) )
= $false )
| ( ( SV78
= ( vapp @ ( vsubst @ SV117 @ SV128 @ SV100 ) @ ( vsubst @ SV117 @ SV128 @ SV137 ) ) )
= $true )
| ( ( SV30 = SV128 )
= $false )
| ( ( SV6 = SV117 )
= $false )
| ( ( SV54
= ( vapp @ SV100 @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(502,plain,
! [SV7: $i,SV140: $i,SV138: $i,SV101: $i,SV79: $i,SV55: $i,SV118: $i,SV129: $i,SV31: $i] :
( ( ( SV31 != SV129 )
= $true )
| ( ( ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true )
| ( ( SV79 = SV7 )
= $false )
| ( ( SV55 = SV31 )
= $false )
| ( ( SV101
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(503,plain,
! [SV33: $i,SV9: $i,SV130: $i,SV102: $i,SV80: $i,SV57: $i,SV119: $i] :
( ( ( SV119
!= ( vsubst @ SV57 @ SV80 @ SV102 ) )
= $true )
| ( ( SV119 = SV130 )
= $true )
| ( ( SV9 = SV33 )
= $false )
| ( ( SV80 = SV130 )
= $false )
| ( ( SV57 = SV9 )
= $false )
| ( ( SV102
= ( vvar @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(504,plain,
! [SV19: $i,SV110: $i,SV89: $i,SV67: $i,SV122: $i,SV133: $i,SV43: $i] :
( ( ( SV43 = SV133 )
= $true )
| ( ( ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
| ( SV122
= ( vvar @ SV133 ) ) )
= $true )
| ( ( SV89 = SV19 )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV110
= ( vvar @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(505,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( SV92 != SV112 )
= $false )
| ( ( ~ ( visFreeVar @ SV112 @ SV124 ) )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(506,plain,
! [SV124: $i,SV22: $i,SV70: $i,SV46: $i,SV112: $i,SV92: $i] :
( ( ( SV92 != SV112 )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(507,plain,
! [SV22: $i,SV92: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i] :
( ( ( visFreeVar @ SV112 @ SV124 )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(508,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV136: $i,SV97: $i,SV127: $i] :
( ( ( ~ ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) ) )
= $false )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(509,plain,
! [SV7: $i,SV140: $i,SV138: $i,SV101: $i,SV79: $i,SV55: $i,SV118: $i,SV129: $i,SV31: $i] :
( ( ( SV31 = SV129 )
= $false )
| ( ( ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
| ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) ) )
= $true )
| ( ( SV79 = SV7 )
= $false )
| ( ( SV55 = SV31 )
= $false )
| ( ( SV101
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(510,plain,
! [SV33: $i,SV9: $i,SV130: $i,SV102: $i,SV80: $i,SV57: $i,SV119: $i] :
( ( ( SV119
= ( vsubst @ SV57 @ SV80 @ SV102 ) )
= $false )
| ( ( SV119 = SV130 )
= $true )
| ( ( SV9 = SV33 )
= $false )
| ( ( SV80 = SV130 )
= $false )
| ( ( SV57 = SV9 )
= $false )
| ( ( SV102
= ( vvar @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(511,plain,
! [SV19: $i,SV43: $i,SV133: $i,SV110: $i,SV89: $i,SV67: $i,SV122: $i] :
( ( ( SV122
!= ( vsubst @ SV67 @ SV89 @ SV110 ) )
= $true )
| ( ( SV122
= ( vvar @ SV133 ) )
= $true )
| ( ( SV43 = SV133 )
= $true )
| ( ( SV89 = SV19 )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV110
= ( vvar @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(512,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV124: $i,SV112: $i,SV92: $i] :
( ( ( SV92 = SV112 )
= $true )
| ( ( ~ ( visFreeVar @ SV112 @ SV124 ) )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(513,plain,
! [SV124: $i,SV22: $i,SV70: $i,SV46: $i,SV112: $i,SV92: $i] :
( ( ( SV92 = SV112 )
= $false )
| ( ( visFreeVar @ SV46 @ SV70 )
= $false )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(514,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV136: $i,SV97: $i,SV127: $i] :
( ( ( ~ ( ( SV127 != SV97 ) )
| ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(515,plain,
! [SV7: $i,SV31: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV79: $i,SV55: $i,SV118: $i] :
( ( ( SV118
!= ( vsubst @ SV55 @ SV79 @ SV101 ) )
= $true )
| ( ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( SV31 = SV129 )
= $false )
| ( ( SV79 = SV7 )
= $false )
| ( ( SV55 = SV31 )
= $false )
| ( ( SV101
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(516,plain,
! [SV19: $i,SV43: $i,SV133: $i,SV110: $i,SV89: $i,SV67: $i,SV122: $i] :
( ( ( SV122
= ( vsubst @ SV67 @ SV89 @ SV110 ) )
= $false )
| ( ( SV122
= ( vvar @ SV133 ) )
= $true )
| ( ( SV43 = SV133 )
= $true )
| ( ( SV89 = SV19 )
= $false )
| ( ( SV67 = SV43 )
= $false )
| ( ( SV110
= ( vvar @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(517,plain,
! [SV22: $i,SV70: $i,SV46: $i,SV92: $i,SV124: $i,SV112: $i] :
( ( ( visFreeVar @ SV112 @ SV124 )
= $false )
| ( ( SV92 = SV112 )
= $true )
| ( ( visFreeVar @ SV46 @ SV70 )
= $true )
| ( ( SV46 = SV112 )
= $false )
| ( ( SV70
= ( vabs @ SV92 @ SV22 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(518,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV136: $i,SV97: $i,SV127: $i] :
( ( ( ~ ( ( SV127 != SV97 ) ) )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(519,plain,
! [SV7: $i,SV31: $i,SV140: $i,SV138: $i,SV129: $i,SV101: $i,SV79: $i,SV55: $i,SV118: $i] :
( ( ( SV118
= ( vsubst @ SV55 @ SV79 @ SV101 ) )
= $false )
| ( ( SV118
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $true )
| ( ( SV31 = SV129 )
= $false )
| ( ( SV79 = SV7 )
= $false )
| ( ( SV55 = SV31 )
= $false )
| ( ( SV101
= ( vabs @ SV129 @ SV138 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(520,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV136: $i,SV97: $i,SV127: $i] :
( ( ( SV127 != SV97 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(521,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV136: $i,SV97: $i,SV127: $i] :
( ( ( SV127 = SV97 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV97 @ SV136 ) )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(522,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV127: $i,SV136: $i,SV97: $i] :
( ( ( ~ ( visFreeVar @ SV97 @ SV136 ) )
= $false )
| ( ( SV127 = SV97 )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(523,plain,
! [SV139: $i,SV115: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i,SV127: $i,SV136: $i,SV97: $i] :
( ( ( visFreeVar @ SV97 @ SV136 )
= $true )
| ( ( SV127 = SV97 )
= $true )
| ( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
| ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) ) )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(524,plain,
! [SV139: $i,SV136: $i,SV127: $i,SV115: $i,SV97: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i] :
( ( ( SV75
!= ( vsubst @ SV3 @ SV27 @ SV51 ) )
= $true )
| ( ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) )
= $true )
| ( ( SV127 = SV97 )
= $true )
| ( ( visFreeVar @ SV97 @ SV136 )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(525,plain,
! [SV139: $i,SV136: $i,SV127: $i,SV115: $i,SV97: $i,SV51: $i,SV27: $i,SV3: $i,SV75: $i] :
( ( ( SV75
= ( vsubst @ SV3 @ SV27 @ SV51 ) )
= $false )
| ( ( SV75
= ( vabs @ SV97 @ SV115 @ ( vsubst @ SV127 @ SV136 @ SV139 ) ) )
= $true )
| ( ( SV127 = SV97 )
= $true )
| ( ( visFreeVar @ SV97 @ SV136 )
= $true )
| ( ( SV27 = SV136 )
= $false )
| ( ( SV3 = SV127 )
= $false )
| ( ( SV51
= ( vabs @ SV97 @ SV115 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(526,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[123,525,519,517,516,513,510,507,501,499,491,485,478,477,474,467,466,435,429,423,420,398,392,381,379,370,331,300,288,284,259,255,235,151,125,124]) ).
thf(527,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM130+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n026.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 18:41:55 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.14/0.71
% 3.14/0.71 No.of.Axioms: 24
% 3.14/0.71
% 3.14/0.71 Length.of.Defs: 0
% 3.14/0.71
% 3.14/0.71 Contains.Choice.Funs: false
% 3.14/0.71 ...........................
% 3.14/0.71
% 3.14/0.71 ********************************
% 3.14/0.71 * All subproblems solved! *
% 3.14/0.71 ********************************
% 3.14/0.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:27,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:526,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.14/0.71
% 3.14/0.71 %**** Beginning of derivation protocol ****
% 3.14/0.71 % SZS output start CNFRefutation
% See solution above
% 3.14/0.71
% 3.14/0.71 %**** End of derivation protocol ****
% 3.14/0.71 %**** no. of clauses in derivation: 493 ****
% 3.14/0.71 %**** clause counter: 526 ****
% 3.14/0.71
% 3.14/0.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:27,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:526,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------