%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM133+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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:12:27 AM UTC 2026
% Result : Theorem 3.39s 0.82s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 23
% Syntax : Number of formulae : 492 ( 238 unt; 0 typ; 0 def)
% Number of atoms : 4241 (2532 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 9874 (2447 ~;1486 |; 127 &;5702 @)
% ( 0 <=>; 112 =>; 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 : 32 ( 29 usr; 13 con; 0-3 aty)
% Number of variables : 3177 ( 0 ^;3177 !; 0 ?;3177 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_VT,type,
sK1_VT: $i ).
thf(tp_sK2_SY144,type,
sK2_SY144: $i ).
thf(tp_sK3_SY150,type,
sK3_SY150: $i ).
thf(tp_sK4_SY155,type,
sK4_SY155: $i ).
thf(tp_sK5_SY159,type,
sK5_SY159: $i ).
thf(tp_sK6_SY162,type,
sK6_SY162: $i ).
thf(tp_sK7_SY164,type,
sK7_SY164: $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,Vy: $i,VS: $i,VT2: $i] :
( ( ( Vx != Vy )
& ( visFreeVar @ Vy @ Ve )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-3') ).
thf(2,axiom,
! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-2') ).
thf(3,axiom,
! [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(4,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(5,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(6,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(10,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(28,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(30,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(31,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(32,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(33,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(35,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(36,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(38,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(45,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
thf(48,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(51,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(55,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(56,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(58,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(60,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(62,conjecture,
! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs') ).
thf(63,negated_conjecture,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[62]) ).
thf(64,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[63]) ).
thf(65,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( Vx != Vy )
& ( visFreeVar @ Vy @ Ve )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(66,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(67,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(68,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)],[4]) ).
thf(69,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)],[5]) ).
thf(70,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)],[6]) ).
thf(71,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)],[10]) ).
thf(72,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)],[28]) ).
thf(73,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)],[30]) ).
thf(74,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)],[31]) ).
thf(75,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)],[32]) ).
thf(76,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)],[33]) ).
thf(77,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)],[35]) ).
thf(78,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)],[36]) ).
thf(79,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)],[38]) ).
thf(80,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(81,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)],[48]) ).
thf(82,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)],[51]) ).
thf(83,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(84,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(85,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(86,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)],[60]) ).
thf(87,plain,
( ( ! [SY144: $i,SY145: $i,SY146: $i,SY147: $i,SY148: $i,SY149: $i] :
( ( ( vtcheck @ SY144 @ SY146 @ sK1_VT )
& ( vtcheck @ ( vbind @ SY145 @ sK1_VT @ SY144 ) @ ( vabs @ SY147 @ SY148 @ veabs ) @ SY149 ) )
=> ( vtcheck @ SY144 @ ( vsubst @ SY145 @ SY146 @ ( vabs @ SY147 @ SY148 @ veabs ) ) @ SY149 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(88,plain,
( ( ! [SY150: $i,SY151: $i,SY152: $i,SY153: $i,SY154: $i] :
( ( ( vtcheck @ sK2_SY144 @ SY151 @ sK1_VT )
& ( vtcheck @ ( vbind @ SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ SY152 @ SY153 @ veabs ) @ SY154 ) )
=> ( vtcheck @ sK2_SY144 @ ( vsubst @ SY150 @ SY151 @ ( vabs @ SY152 @ SY153 @ veabs ) ) @ SY154 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ! [SY155: $i,SY156: $i,SY157: $i,SY158: $i] :
( ( ( vtcheck @ sK2_SY144 @ SY155 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ SY156 @ SY157 @ veabs ) @ SY158 ) )
=> ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ SY155 @ ( vabs @ SY156 @ SY157 @ veabs ) ) @ SY158 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ( ( vtcheck @ sK2_SY144 @ sK4_SY155 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ SY159 @ SY160 @ veabs ) @ SY161 ) )
=> ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ SY159 @ SY160 @ veabs ) ) @ SY161 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(91,plain,
( ( ! [SY162: $i,SY163: $i] :
( ( ( vtcheck @ sK2_SY144 @ sK4_SY155 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ sK5_SY159 @ SY162 @ veabs ) @ SY163 ) )
=> ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ SY162 @ veabs ) ) @ SY163 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(92,plain,
( ( ! [SY164: $i] :
( ( ( vtcheck @ sK2_SY144 @ sK4_SY155 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) @ SY164 ) )
=> ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) ) @ SY164 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(93,plain,
( ( ( ( vtcheck @ sK2_SY144 @ sK4_SY155 @ sK1_VT )
& ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) @ sK7_SY164 ) )
=> ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) ) @ sK7_SY164 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(94,plain,
( ( vtcheck @ sK2_SY144 @ sK4_SY155 @ sK1_VT )
= $true ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(95,plain,
( ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) @ sK7_SY164 )
= $true ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(96,plain,
( ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) ) @ sK7_SY164 )
= $false ),
inference(standard_cnf,[status(thm)],[93]) ).
thf(97,plain,
( ( ~ ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) ) @ sK7_SY164 ) )
= $true ),
inference(polarity_switch,[status(thm)],[96]) ).
thf(98,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)],[86]) ).
thf(99,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(100,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(101,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(102,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)],[82]) ).
thf(103,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)],[81]) ).
thf(104,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(105,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)],[79]) ).
thf(106,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)],[78]) ).
thf(107,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)],[77]) ).
thf(108,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)],[76]) ).
thf(109,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)],[75]) ).
thf(110,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)],[74]) ).
thf(111,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)],[73]) ).
thf(112,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)],[72]) ).
thf(113,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)],[71]) ).
thf(114,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)],[70]) ).
thf(115,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)],[69]) ).
thf(116,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)],[68]) ).
thf(117,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 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(118,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(119,plain,
( ( ! [VT: $i,VC: $i,Vx: $i,Ve: $i,Vy: $i,VS: $i,VT2: $i] :
( ( ( Vx != Vy )
& ( visFreeVar @ Vy @ Ve )
& ( vtcheck @ VC @ Ve @ VT )
& ( vtcheck @ ( vbind @ Vx @ VT @ VC ) @ ( vabs @ Vy @ VS @ veabs ) @ VT2 ) )
=> ( vtcheck @ VC @ ( vsubst @ Vx @ Ve @ ( vabs @ Vy @ VS @ veabs ) ) @ VT2 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(120,plain,
( ( vtcheck @ ( vbind @ sK3_SY150 @ sK1_VT @ sK2_SY144 ) @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) @ sK7_SY164 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(121,plain,
( ( vtcheck @ sK2_SY144 @ sK4_SY155 @ sK1_VT )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(122,plain,
( ( ~ ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) ) @ sK7_SY164 ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(123,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)],[115]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX2 != SX4 ) )
| ~ ( visFreeVar @ SX4 @ SX3 ) )
| ~ ( vtcheck @ SX1 @ SX3 @ SX0 ) )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX0 @ SX1 ) @ ( vabs @ SX4 @ SX5 @ veabs ) @ SX6 ) )
| ( vtcheck @ SX1 @ ( vsubst @ SX2 @ SX3 @ ( vabs @ SX4 @ SX5 @ veabs ) ) @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(125,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)],[114]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(127,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)],[112]) ).
thf(128,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)],[113]) ).
thf(129,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)],[116]) ).
thf(130,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)],[110]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX4 )
| ~ ( vtcheck @ SX1 @ SX3 @ SX0 ) )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX0 @ SX1 ) @ ( vabs @ SX4 @ SX5 @ SX6 ) @ SX7 ) )
| ( vtcheck @ SX1 @ ( vsubst @ SX2 @ SX3 @ ( vabs @ SX4 @ SX5 @ SX6 ) ) @ SX7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( ( SX2 != SX0 ) )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX3 @ ( vbind @ SX0 @ SX1 @ SX4 ) ) @ SX5 @ SX6 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ ( vbind @ SX2 @ SX3 @ SX4 ) ) @ SX5 @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(133,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)],[105]) ).
thf(134,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)],[98]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(136,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)],[109]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX2 != SX4 ) )
| ~ ~ ( visFreeVar @ SX4 @ SX3 ) )
| ~ ( vtcheck @ SX1 @ SX3 @ SX0 ) )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX0 @ SX1 ) @ ( vabs @ SX4 @ SX5 @ veabs ) @ SX6 ) )
| ( vtcheck @ SX1 @ ( vsubst @ SX2 @ SX3 @ ( vabs @ SX4 @ SX5 @ veabs ) ) @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( visValue @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(139,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)],[111]) ).
thf(140,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)],[106]) ).
thf(141,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)],[102]) ).
thf(142,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)],[103]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( vempty
!= ( vbind @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(144,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)],[108]) ).
thf(145,plain,
( ( vtcheck @ sK2_SY144 @ ( vsubst @ sK3_SY150 @ sK4_SY155 @ ( vabs @ sK5_SY159 @ sK6_SY162 @ veabs ) ) @ sK7_SY164 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(146,plain,
! [SV1: $i] :
( ( ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV1 @ SY167 )
| ~ ( vtcheck @ SY166 @ SY167 @ SY168 ) )
| ( vtcheck @ ( vbind @ SV1 @ SY165 @ SY166 ) @ SY167 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV2: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i,SY173: $i,SY174: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY170 != SY172 ) )
| ~ ( visFreeVar @ SY172 @ SY171 ) )
| ~ ( vtcheck @ SY169 @ SY171 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SY170 @ SV2 @ SY169 ) @ ( vabs @ SY172 @ SY173 @ veabs ) @ SY174 ) )
| ( vtcheck @ SY169 @ ( vsubst @ SY170 @ SY171 @ ( vabs @ SY172 @ SY173 @ veabs ) ) @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV3: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV3 @ SY177 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SY175 @ SY176 ) @ SY177 @ SY178 ) )
| ( vtcheck @ SY176 @ SY177 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(149,plain,
! [SV4: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ( vvar @ SV4 )
!= ( vabs @ SY179 @ SY180 @ SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(150,plain,
! [SV5: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i,SY185: $i,SY186: $i,SY187: $i,SY188: $i,SY189: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY187 )
| ( SY182 != SY188 ) )
| ( SY183
!= ( vabs @ SY185 @ SY186 @ SY189 ) ) )
| ~ ~ ( ~ ( ( SY187 != SY185 ) )
| ~ ~ ( visFreeVar @ SY185 @ SY188 ) )
| ( SY184
!= ( vsubst @ SV5 @ SY182 @ SY183 ) )
| ( SY184
= ( vabs @ SY185 @ SY186 @ ( vsubst @ SY187 @ SY188 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(151,plain,
! [SV6: $i] :
( ( ! [SY190: $i,SY191: $i,SY192: $i,SY193: $i] :
( ~ ( vtcheck @ ( vbind @ SY190 @ SY192 @ SV6 ) @ SY191 @ SY193 )
| ( vtcheck @ SV6 @ ( vabs @ SY190 @ SY192 @ SY191 ) @ ( varrow @ SY192 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(152,plain,
! [SV7: $i] :
( ( ! [SY194: $i,SY195: $i,SY196: $i,SY197: $i] :
( ~ ~ ( ~ ( vtcheck @ SY194 @ SY196 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SY195 @ SV7 @ SY194 ) @ veabs @ SY197 ) )
| ( vtcheck @ SY194 @ ( vsubst @ SY195 @ SY196 @ veabs ) @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(153,plain,
! [SV8: $i] :
( ( ! [SY198: $i,SY199: $i,SY200: $i,SY201: $i,SY202: $i,SY203: $i,SY204: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SY202 )
| ( SY198 != SY203 ) )
| ( SY199
!= ( vapp @ SY201 @ SY204 ) ) )
| ( SY200
!= ( vsubst @ SV8 @ SY198 @ SY199 ) )
| ( SY200
= ( vapp @ ( vsubst @ SY202 @ SY203 @ SY201 ) @ ( vsubst @ SY202 @ SY203 @ SY204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV9: $i] :
( ( ! [SY205: $i,SY206: $i,SY207: $i,SY208: $i,SY209: $i,SY210: $i,SY211: $i] :
( ~ ~ ( ~ ~ ( ( SY206 != SY208 )
| ~ ( vtcheck @ SY205 @ SY207 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SY206 @ SV9 @ SY205 ) @ ( vabs @ SY208 @ SY209 @ SY210 ) @ SY211 ) )
| ( vtcheck @ SY205 @ ( vsubst @ SY206 @ SY207 @ ( vabs @ SY208 @ SY209 @ SY210 ) ) @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(155,plain,
! [SV10: $i] :
( ( ! [SY212: $i,SY213: $i,SY214: $i,SY215: $i,SY216: $i,SY217: $i] :
( ~ ~ ( ~ ( ( SY213 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SY213 @ SY214 @ ( vbind @ SV10 @ SY212 @ SY215 ) ) @ SY216 @ SY217 ) )
| ( vtcheck @ ( vbind @ SV10 @ SY212 @ ( vbind @ SY213 @ SY214 @ SY215 ) ) @ SY216 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(156,plain,
! [SV11: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i,SY221: $i,SY222: $i,SY223: $i] :
( ~ ~ ( ( SY219 != SY222 )
| ( SY220
!= ( vbind @ SY218 @ SV11 @ SY223 ) ) )
| ~ ( ( SY222 != SY218 ) )
| ( SY221
!= ( vlookup @ SY219 @ SY220 ) )
| ( SY221
= ( vlookup @ SY222 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(157,plain,
! [SV12: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i,SY227: $i,SY228: $i] :
~ ( ~ ( ( ( vabs @ SV12 @ SY224 @ SY225 )
!= ( vabs @ SY226 @ SY227 @ SY228 ) )
| ~ ( ~ ~ ( ( SV12 != SY226 )
| ( SY224 != SY227 ) )
| ( SY225 != SY228 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SY226 )
| ( SY224 != SY227 ) )
| ( SY225 != SY228 ) )
| ( ( vabs @ SV12 @ SY224 @ SY225 )
= ( vabs @ SY226 @ SY227 @ SY228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV13: $i] :
( ( ! [SY229: $i,SY230: $i,SY231: $i,SY232: $i] :
( ( vabs @ SV13 @ SY229 @ SY230 )
!= ( vapp @ SY231 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV14: $i] :
( ( ! [SY233: $i,SY234: $i,SY235: $i,SY236: $i,SY237: $i,SY238: $i] :
( ~ ~ ( ~ ~ ( ( SY234 != SY233 )
| ( SY235 != SV14 ) )
| ( SY236
!= ( vvar @ SY238 ) ) )
| ~ ( ( SY233 != SY238 ) )
| ( SY237
!= ( vsubst @ SY234 @ SY235 @ SY236 ) )
| ( SY237
= ( vvar @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV15: $i] :
( ( ! [SY239: $i,SY240: $i,SY241: $i,SY242: $i,SY243: $i,SY244: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY240 != SY242 ) )
| ~ ~ ( visFreeVar @ SY242 @ SY241 ) )
| ~ ( vtcheck @ SY239 @ SY241 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SY240 @ SV15 @ SY239 ) @ ( vabs @ SY242 @ SY243 @ veabs ) @ SY244 ) )
| ( vtcheck @ SY239 @ ( vsubst @ SY240 @ SY241 @ ( vabs @ SY242 @ SY243 @ veabs ) ) @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(161,plain,
! [SV16: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i] :
( ( SY247
!= ( vabs @ SV16 @ SY245 @ SY246 ) )
| ( visValue @ SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV17: $i] :
( ( ! [SY248: $i,SY249: $i,SY250: $i,SY251: $i,SY252: $i,SY253: $i,SY254: $i,SY255: $i] :
( ~ ~ ( ~ ~ ( ( SY249 != SY248 )
| ( SY250 != SV17 ) )
| ( SY251
!= ( vabs @ SY253 @ SY254 @ SY255 ) ) )
| ( SY248 != SY253 )
| ( SY252
!= ( vsubst @ SY249 @ SY250 @ SY251 ) )
| ( SY252
= ( vabs @ SY253 @ SY254 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV18: $i] :
( ( ! [SY256: $i,SY257: $i,SY258: $i,SY259: $i,SY260: $i,SY261: $i] :
( ~ ~ ( ( SY257 != SV18 )
| ~ ( vtcheck @ ( vbind @ SY257 @ SY258 @ ( vbind @ SV18 @ SY256 @ SY259 ) ) @ SY260 @ SY261 ) )
| ( vtcheck @ ( vbind @ SY257 @ SY258 @ SY259 ) @ SY260 @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV19: $i] :
( ( ! [SY262: $i,SY263: $i,SY264: $i,SY265: $i,SY266: $i] :
( ~ ~ ( ( SY262 != SY265 )
| ( SY263
!= ( vabs @ SY264 @ SV19 @ SY266 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY264 != SY265 ) )
| ~ ( visFreeVar @ SY265 @ SY266 ) )
| ( visFreeVar @ SY262 @ SY263 ) )
| ~ ( ~ ( visFreeVar @ SY262 @ SY263 )
| ~ ( ~ ( ( SY264 != SY265 ) )
| ~ ( visFreeVar @ SY265 @ SY266 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV20: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i,SY270: $i,SY271: $i] :
~ ( ~ ( ( ( vbind @ SV20 @ SY267 @ SY268 )
!= ( vbind @ SY269 @ SY270 @ SY271 ) )
| ~ ( ~ ~ ( ( SV20 != SY269 )
| ( SY267 != SY270 ) )
| ( SY268 != SY271 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SY269 )
| ( SY267 != SY270 ) )
| ( SY268 != SY271 ) )
| ( ( vbind @ SV20 @ SY267 @ SY268 )
= ( vbind @ SY269 @ SY270 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV21: $i] :
( ( ! [SY272: $i,SY273: $i] :
( vempty
!= ( vbind @ SV21 @ SY272 @ SY273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(167,plain,
! [SV22: $i] :
( ( ! [SY274: $i,SY275: $i,SY276: $i,SY277: $i,SY278: $i,SY279: $i] :
( ~ ~ ( ~ ~ ( ( SY275 != SV22 )
| ( SY276 != SY279 ) )
| ( SY277
!= ( vvar @ SY274 ) ) )
| ( SV22 != SY274 )
| ( SY278
!= ( vsubst @ SY275 @ SY276 @ SY277 ) )
| ( SY278 = SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(168,plain,
! [SV23: $i,SV1: $i] :
( ( ! [SY280: $i,SY281: $i,SY282: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV1 @ SY281 )
| ~ ( vtcheck @ SY280 @ SY281 @ SY282 ) )
| ( vtcheck @ ( vbind @ SV1 @ SV23 @ SY280 ) @ SY281 @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(169,plain,
! [SV2: $i,SV24: $i] :
( ( ! [SY283: $i,SY284: $i,SY285: $i,SY286: $i,SY287: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY283 != SY285 ) )
| ~ ( visFreeVar @ SY285 @ SY284 ) )
| ~ ( vtcheck @ SV24 @ SY284 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SY283 @ SV2 @ SV24 ) @ ( vabs @ SY285 @ SY286 @ veabs ) @ SY287 ) )
| ( vtcheck @ SV24 @ ( vsubst @ SY283 @ SY284 @ ( vabs @ SY285 @ SY286 @ veabs ) ) @ SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(170,plain,
! [SV25: $i,SV3: $i] :
( ( ! [SY288: $i,SY289: $i,SY290: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV3 @ SY289 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SY288 ) @ SY289 @ SY290 ) )
| ( vtcheck @ SY288 @ SY289 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(171,plain,
! [SV26: $i,SV4: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ( vvar @ SV4 )
!= ( vabs @ SV26 @ SY291 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(172,plain,
! [SV27: $i,SV5: $i] :
( ( ! [SY293: $i,SY294: $i,SY295: $i,SY296: $i,SY297: $i,SY298: $i,SY299: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY297 )
| ( SV27 != SY298 ) )
| ( SY293
!= ( vabs @ SY295 @ SY296 @ SY299 ) ) )
| ~ ~ ( ~ ( ( SY297 != SY295 ) )
| ~ ~ ( visFreeVar @ SY295 @ SY298 ) )
| ( SY294
!= ( vsubst @ SV5 @ SV27 @ SY293 ) )
| ( SY294
= ( vabs @ SY295 @ SY296 @ ( vsubst @ SY297 @ SY298 @ SY299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV6: $i,SV28: $i] :
( ( ! [SY300: $i,SY301: $i,SY302: $i] :
( ~ ( vtcheck @ ( vbind @ SV28 @ SY301 @ SV6 ) @ SY300 @ SY302 )
| ( vtcheck @ SV6 @ ( vabs @ SV28 @ SY301 @ SY300 ) @ ( varrow @ SY301 @ SY302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV7: $i,SV29: $i] :
( ( ! [SY303: $i,SY304: $i,SY305: $i] :
( ~ ~ ( ~ ( vtcheck @ SV29 @ SY304 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SY303 @ SV7 @ SV29 ) @ veabs @ SY305 ) )
| ( vtcheck @ SV29 @ ( vsubst @ SY303 @ SY304 @ veabs ) @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(175,plain,
! [SV30: $i,SV8: $i] :
( ( ! [SY306: $i,SY307: $i,SY308: $i,SY309: $i,SY310: $i,SY311: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SY309 )
| ( SV30 != SY310 ) )
| ( SY306
!= ( vapp @ SY308 @ SY311 ) ) )
| ( SY307
!= ( vsubst @ SV8 @ SV30 @ SY306 ) )
| ( SY307
= ( vapp @ ( vsubst @ SY309 @ SY310 @ SY308 ) @ ( vsubst @ SY309 @ SY310 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(176,plain,
! [SV9: $i,SV31: $i] :
( ( ! [SY312: $i,SY313: $i,SY314: $i,SY315: $i,SY316: $i,SY317: $i] :
( ~ ~ ( ~ ~ ( ( SY312 != SY314 )
| ~ ( vtcheck @ SV31 @ SY313 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SY312 @ SV9 @ SV31 ) @ ( vabs @ SY314 @ SY315 @ SY316 ) @ SY317 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SY312 @ SY313 @ ( vabs @ SY314 @ SY315 @ SY316 ) ) @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(177,plain,
! [SV32: $i,SV10: $i] :
( ( ! [SY318: $i,SY319: $i,SY320: $i,SY321: $i,SY322: $i] :
( ~ ~ ( ~ ( ( SY318 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SY318 @ SY319 @ ( vbind @ SV10 @ SV32 @ SY320 ) ) @ SY321 @ SY322 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SY318 @ SY319 @ SY320 ) ) @ SY321 @ SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(178,plain,
! [SV11: $i,SV33: $i] :
( ( ! [SY323: $i,SY324: $i,SY325: $i,SY326: $i,SY327: $i] :
( ~ ~ ( ( SY323 != SY326 )
| ( SY324
!= ( vbind @ SV33 @ SV11 @ SY327 ) ) )
| ~ ( ( SY326 != SV33 ) )
| ( SY325
!= ( vlookup @ SY323 @ SY324 ) )
| ( SY325
= ( vlookup @ SY326 @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(179,plain,
! [SV34: $i,SV12: $i] :
( ( ! [SY328: $i,SY329: $i,SY330: $i,SY331: $i] :
~ ( ~ ( ( ( vabs @ SV12 @ SV34 @ SY328 )
!= ( vabs @ SY329 @ SY330 @ SY331 ) )
| ~ ( ~ ~ ( ( SV12 != SY329 )
| ( SV34 != SY330 ) )
| ( SY328 != SY331 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SY329 )
| ( SV34 != SY330 ) )
| ( SY328 != SY331 ) )
| ( ( vabs @ SV12 @ SV34 @ SY328 )
= ( vabs @ SY329 @ SY330 @ SY331 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(180,plain,
! [SV35: $i,SV13: $i] :
( ( ! [SY332: $i,SY333: $i,SY334: $i] :
( ( vabs @ SV13 @ SV35 @ SY332 )
!= ( vapp @ SY333 @ SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(181,plain,
! [SV14: $i,SV36: $i] :
( ( ! [SY335: $i,SY336: $i,SY337: $i,SY338: $i,SY339: $i] :
( ~ ~ ( ~ ~ ( ( SY335 != SV36 )
| ( SY336 != SV14 ) )
| ( SY337
!= ( vvar @ SY339 ) ) )
| ~ ( ( SV36 != SY339 ) )
| ( SY338
!= ( vsubst @ SY335 @ SY336 @ SY337 ) )
| ( SY338
= ( vvar @ SY339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(182,plain,
! [SV15: $i,SV37: $i] :
( ( ! [SY340: $i,SY341: $i,SY342: $i,SY343: $i,SY344: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SY340 != SY342 ) )
| ~ ~ ( visFreeVar @ SY342 @ SY341 ) )
| ~ ( vtcheck @ SV37 @ SY341 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SY340 @ SV15 @ SV37 ) @ ( vabs @ SY342 @ SY343 @ veabs ) @ SY344 ) )
| ( vtcheck @ SV37 @ ( vsubst @ SY340 @ SY341 @ ( vabs @ SY342 @ SY343 @ veabs ) ) @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(183,plain,
! [SV38: $i,SV16: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ( SY346
!= ( vabs @ SV16 @ SV38 @ SY345 ) )
| ( visValue @ SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(184,plain,
! [SV17: $i,SV39: $i] :
( ( ! [SY347: $i,SY348: $i,SY349: $i,SY350: $i,SY351: $i,SY352: $i,SY353: $i] :
( ~ ~ ( ~ ~ ( ( SY347 != SV39 )
| ( SY348 != SV17 ) )
| ( SY349
!= ( vabs @ SY351 @ SY352 @ SY353 ) ) )
| ( SV39 != SY351 )
| ( SY350
!= ( vsubst @ SY347 @ SY348 @ SY349 ) )
| ( SY350
= ( vabs @ SY351 @ SY352 @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(185,plain,
! [SV40: $i,SV18: $i] :
( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i,SY358: $i] :
( ~ ~ ( ( SY354 != SV18 )
| ~ ( vtcheck @ ( vbind @ SY354 @ SY355 @ ( vbind @ SV18 @ SV40 @ SY356 ) ) @ SY357 @ SY358 ) )
| ( vtcheck @ ( vbind @ SY354 @ SY355 @ SY356 ) @ SY357 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(186,plain,
! [SV19: $i,SV41: $i] :
( ( ! [SY359: $i,SY360: $i,SY361: $i,SY362: $i] :
( ~ ~ ( ( SV41 != SY361 )
| ( SY359
!= ( vabs @ SY360 @ SV19 @ SY362 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY360 != SY361 ) )
| ~ ( visFreeVar @ SY361 @ SY362 ) )
| ( visFreeVar @ SV41 @ SY359 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SY359 )
| ~ ( ~ ( ( SY360 != SY361 ) )
| ~ ( visFreeVar @ SY361 @ SY362 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(187,plain,
! [SV42: $i,SV20: $i] :
( ( ! [SY363: $i,SY364: $i,SY365: $i,SY366: $i] :
~ ( ~ ( ( ( vbind @ SV20 @ SV42 @ SY363 )
!= ( vbind @ SY364 @ SY365 @ SY366 ) )
| ~ ( ~ ~ ( ( SV20 != SY364 )
| ( SV42 != SY365 ) )
| ( SY363 != SY366 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SY364 )
| ( SV42 != SY365 ) )
| ( SY363 != SY366 ) )
| ( ( vbind @ SV20 @ SV42 @ SY363 )
= ( vbind @ SY364 @ SY365 @ SY366 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(188,plain,
! [SV43: $i,SV21: $i] :
( ( ! [SY367: $i] :
( vempty
!= ( vbind @ SV21 @ SV43 @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(189,plain,
! [SV44: $i,SV22: $i] :
( ( ! [SY368: $i,SY369: $i,SY370: $i,SY371: $i,SY372: $i] :
( ~ ~ ( ~ ~ ( ( SY368 != SV22 )
| ( SY369 != SY372 ) )
| ( SY370
!= ( vvar @ SV44 ) ) )
| ( SV22 != SV44 )
| ( SY371
!= ( vsubst @ SY368 @ SY369 @ SY370 ) )
| ( SY371 = SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(190,plain,
! [SV23: $i,SV45: $i,SV1: $i] :
( ( ! [SY373: $i,SY374: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV1 @ SY373 )
| ~ ( vtcheck @ SV45 @ SY373 @ SY374 ) )
| ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SY373 @ SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(191,plain,
! [SV2: $i,SV24: $i,SV46: $i] :
( ( ! [SY375: $i,SY376: $i,SY377: $i,SY378: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SY376 ) )
| ~ ( visFreeVar @ SY376 @ SY375 ) )
| ~ ( vtcheck @ SV24 @ SY375 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SY376 @ SY377 @ veabs ) @ SY378 ) )
| ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SY375 @ ( vabs @ SY376 @ SY377 @ veabs ) ) @ SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(192,plain,
! [SV47: $i,SV25: $i,SV3: $i] :
( ( ! [SY379: $i,SY380: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV3 @ SY379 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SY379 @ SY380 ) )
| ( vtcheck @ SV47 @ SY379 @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(193,plain,
! [SV48: $i,SV26: $i,SV4: $i] :
( ( ! [SY381: $i] :
( ( vvar @ SV4 )
!= ( vabs @ SV26 @ SV48 @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(194,plain,
! [SV49: $i,SV27: $i,SV5: $i] :
( ( ! [SY382: $i,SY383: $i,SY384: $i,SY385: $i,SY386: $i,SY387: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY385 )
| ( SV27 != SY386 ) )
| ( SV49
!= ( vabs @ SY383 @ SY384 @ SY387 ) ) )
| ~ ~ ( ~ ( ( SY385 != SY383 ) )
| ~ ~ ( visFreeVar @ SY383 @ SY386 ) )
| ( SY382
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SY382
= ( vabs @ SY383 @ SY384 @ ( vsubst @ SY385 @ SY386 @ SY387 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(195,plain,
! [SV50: $i,SV6: $i,SV28: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( vtcheck @ ( vbind @ SV28 @ SY388 @ SV6 ) @ SV50 @ SY389 )
| ( vtcheck @ SV6 @ ( vabs @ SV28 @ SY388 @ SV50 ) @ ( varrow @ SY388 @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(196,plain,
! [SV51: $i,SV7: $i,SV29: $i] :
( ( ! [SY390: $i,SY391: $i] :
( ~ ~ ( ~ ( vtcheck @ SV29 @ SY390 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SY391 ) )
| ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SY390 @ veabs ) @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(197,plain,
! [SV52: $i,SV30: $i,SV8: $i] :
( ( ! [SY392: $i,SY393: $i,SY394: $i,SY395: $i,SY396: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SY394 )
| ( SV30 != SY395 ) )
| ( SV52
!= ( vapp @ SY393 @ SY396 ) ) )
| ( SY392
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SY392
= ( vapp @ ( vsubst @ SY394 @ SY395 @ SY393 ) @ ( vsubst @ SY394 @ SY395 @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(198,plain,
! [SV9: $i,SV31: $i,SV53: $i] :
( ( ! [SY397: $i,SY398: $i,SY399: $i,SY400: $i,SY401: $i] :
( ~ ~ ( ~ ~ ( ( SV53 != SY398 )
| ~ ( vtcheck @ SV31 @ SY397 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SY398 @ SY399 @ SY400 ) @ SY401 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SY397 @ ( vabs @ SY398 @ SY399 @ SY400 ) ) @ SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(199,plain,
! [SV32: $i,SV10: $i,SV54: $i] :
( ( ! [SY402: $i,SY403: $i,SY404: $i,SY405: $i] :
( ~ ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SY402 @ ( vbind @ SV10 @ SV32 @ SY403 ) ) @ SY404 @ SY405 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SY402 @ SY403 ) ) @ SY404 @ SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(200,plain,
! [SV11: $i,SV33: $i,SV55: $i] :
( ( ! [SY406: $i,SY407: $i,SY408: $i,SY409: $i] :
( ~ ~ ( ( SV55 != SY408 )
| ( SY406
!= ( vbind @ SV33 @ SV11 @ SY409 ) ) )
| ~ ( ( SY408 != SV33 ) )
| ( SY407
!= ( vlookup @ SV55 @ SY406 ) )
| ( SY407
= ( vlookup @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(201,plain,
! [SV56: $i,SV34: $i,SV12: $i] :
( ( ! [SY410: $i,SY411: $i,SY412: $i] :
~ ( ~ ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SY410 @ SY411 @ SY412 ) )
| ~ ( ~ ~ ( ( SV12 != SY410 )
| ( SV34 != SY411 ) )
| ( SV56 != SY412 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SY410 )
| ( SV34 != SY411 ) )
| ( SV56 != SY412 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SY410 @ SY411 @ SY412 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(202,plain,
! [SV57: $i,SV35: $i,SV13: $i] :
( ( ! [SY413: $i,SY414: $i] :
( ( vabs @ SV13 @ SV35 @ SV57 )
!= ( vapp @ SY413 @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(203,plain,
! [SV14: $i,SV36: $i,SV58: $i] :
( ( ! [SY415: $i,SY416: $i,SY417: $i,SY418: $i] :
( ~ ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SY415 != SV14 ) )
| ( SY416
!= ( vvar @ SY418 ) ) )
| ~ ( ( SV36 != SY418 ) )
| ( SY417
!= ( vsubst @ SV58 @ SY415 @ SY416 ) )
| ( SY417
= ( vvar @ SY418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(204,plain,
! [SV15: $i,SV37: $i,SV59: $i] :
( ( ! [SY419: $i,SY420: $i,SY421: $i,SY422: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SY420 ) )
| ~ ~ ( visFreeVar @ SY420 @ SY419 ) )
| ~ ( vtcheck @ SV37 @ SY419 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SY420 @ SY421 @ veabs ) @ SY422 ) )
| ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SY419 @ ( vabs @ SY420 @ SY421 @ veabs ) ) @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(205,plain,
! [SV60: $i,SV38: $i,SV16: $i] :
( ( ! [SY423: $i] :
( ( SY423
!= ( vabs @ SV16 @ SV38 @ SV60 ) )
| ( visValue @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(206,plain,
! [SV17: $i,SV39: $i,SV61: $i] :
( ( ! [SY424: $i,SY425: $i,SY426: $i,SY427: $i,SY428: $i,SY429: $i] :
( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SY424 != SV17 ) )
| ( SY425
!= ( vabs @ SY427 @ SY428 @ SY429 ) ) )
| ( SV39 != SY427 )
| ( SY426
!= ( vsubst @ SV61 @ SY424 @ SY425 ) )
| ( SY426
= ( vabs @ SY427 @ SY428 @ SY429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(207,plain,
! [SV40: $i,SV18: $i,SV62: $i] :
( ( ! [SY430: $i,SY431: $i,SY432: $i,SY433: $i] :
( ~ ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SY430 @ ( vbind @ SV18 @ SV40 @ SY431 ) ) @ SY432 @ SY433 ) )
| ( vtcheck @ ( vbind @ SV62 @ SY430 @ SY431 ) @ SY432 @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(208,plain,
! [SV19: $i,SV63: $i,SV41: $i] :
( ( ! [SY434: $i,SY435: $i,SY436: $i] :
( ~ ~ ( ( SV41 != SY435 )
| ( SV63
!= ( vabs @ SY434 @ SV19 @ SY436 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY434 != SY435 ) )
| ~ ( visFreeVar @ SY435 @ SY436 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SY434 != SY435 ) )
| ~ ( visFreeVar @ SY435 @ SY436 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(209,plain,
! [SV64: $i,SV42: $i,SV20: $i] :
( ( ! [SY437: $i,SY438: $i,SY439: $i] :
~ ( ~ ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SY437 @ SY438 @ SY439 ) )
| ~ ( ~ ~ ( ( SV20 != SY437 )
| ( SV42 != SY438 ) )
| ( SV64 != SY439 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SY437 )
| ( SV42 != SY438 ) )
| ( SV64 != SY439 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SY437 @ SY438 @ SY439 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(210,plain,
! [SV65: $i,SV43: $i,SV21: $i] :
( ( vempty
!= ( vbind @ SV21 @ SV43 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(211,plain,
! [SV44: $i,SV22: $i,SV66: $i] :
( ( ! [SY440: $i,SY441: $i,SY442: $i,SY443: $i] :
( ~ ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SY440 != SY443 ) )
| ( SY441
!= ( vvar @ SV44 ) ) )
| ( SV22 != SV44 )
| ( SY442
!= ( vsubst @ SV66 @ SY440 @ SY441 ) )
| ( SY442 = SY443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(212,plain,
! [SV23: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ! [SY444: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV1 @ SV67 )
| ~ ( vtcheck @ SV45 @ SV67 @ SY444 ) )
| ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(213,plain,
! [SV2: $i,SV24: $i,SV68: $i,SV46: $i] :
( ( ! [SY445: $i,SY446: $i,SY447: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SY445 ) )
| ~ ( visFreeVar @ SY445 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SY445 @ SY446 @ veabs ) @ SY447 ) )
| ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SY445 @ SY446 @ veabs ) ) @ SY447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(214,plain,
! [SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ! [SY448: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV3 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SY448 ) )
| ( vtcheck @ SV47 @ SV69 @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(215,plain,
! [SV70: $i,SV48: $i,SV26: $i,SV4: $i] :
( ( ( vvar @ SV4 )
!= ( vabs @ SV26 @ SV48 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(216,plain,
! [SV71: $i,SV49: $i,SV27: $i,SV5: $i] :
( ( ! [SY449: $i,SY450: $i,SY451: $i,SY452: $i,SY453: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY451 )
| ( SV27 != SY452 ) )
| ( SV49
!= ( vabs @ SY449 @ SY450 @ SY453 ) ) )
| ~ ~ ( ~ ( ( SY451 != SY449 ) )
| ~ ~ ( visFreeVar @ SY449 @ SY452 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SY449 @ SY450 @ ( vsubst @ SY451 @ SY452 @ SY453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(217,plain,
! [SV50: $i,SV6: $i,SV72: $i,SV28: $i] :
( ( ! [SY454: $i] :
( ~ ( vtcheck @ ( vbind @ SV28 @ SV72 @ SV6 ) @ SV50 @ SY454 )
| ( vtcheck @ SV6 @ ( vabs @ SV28 @ SV72 @ SV50 ) @ ( varrow @ SV72 @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(218,plain,
! [SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ! [SY455: $i] :
( ~ ~ ( ~ ( vtcheck @ SV29 @ SV73 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SY455 ) )
| ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(219,plain,
! [SV74: $i,SV52: $i,SV30: $i,SV8: $i] :
( ( ! [SY456: $i,SY457: $i,SY458: $i,SY459: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SY457 )
| ( SV30 != SY458 ) )
| ( SV52
!= ( vapp @ SY456 @ SY459 ) ) )
| ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SY457 @ SY458 @ SY456 ) @ ( vsubst @ SY457 @ SY458 @ SY459 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(220,plain,
! [SV9: $i,SV75: $i,SV31: $i,SV53: $i] :
( ( ! [SY460: $i,SY461: $i,SY462: $i,SY463: $i] :
( ~ ~ ( ~ ~ ( ( SV53 != SY460 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SY460 @ SY461 @ SY462 ) @ SY463 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SY460 @ SY461 @ SY462 ) ) @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(221,plain,
! [SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ! [SY464: $i,SY465: $i,SY466: $i] :
( ~ ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SY464 ) ) @ SY465 @ SY466 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SY464 ) ) @ SY465 @ SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(222,plain,
! [SV11: $i,SV33: $i,SV77: $i,SV55: $i] :
( ( ! [SY467: $i,SY468: $i,SY469: $i] :
( ~ ~ ( ( SV55 != SY468 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SY469 ) ) )
| ~ ( ( SY468 != SV33 ) )
| ( SY467
!= ( vlookup @ SV55 @ SV77 ) )
| ( SY467
= ( vlookup @ SY468 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(223,plain,
! [SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ! [SY470: $i,SY471: $i] :
~ ( ~ ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SY470 @ SY471 ) )
| ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SY470 ) )
| ( SV56 != SY471 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SY470 ) )
| ( SV56 != SY471 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SY470 @ SY471 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(224,plain,
! [SV79: $i,SV57: $i,SV35: $i,SV13: $i] :
( ( ! [SY472: $i] :
( ( vabs @ SV13 @ SV35 @ SV57 )
!= ( vapp @ SV79 @ SY472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(225,plain,
! [SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ! [SY473: $i,SY474: $i,SY475: $i] :
( ~ ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SY473
!= ( vvar @ SY475 ) ) )
| ~ ( ( SV36 != SY475 ) )
| ( SY474
!= ( vsubst @ SV58 @ SV80 @ SY473 ) )
| ( SY474
= ( vvar @ SY475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(226,plain,
! [SV15: $i,SV37: $i,SV81: $i,SV59: $i] :
( ( ! [SY476: $i,SY477: $i,SY478: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SY476 ) )
| ~ ~ ( visFreeVar @ SY476 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SY476 @ SY477 @ veabs ) @ SY478 ) )
| ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SY476 @ SY477 @ veabs ) ) @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(227,plain,
! [SV60: $i,SV38: $i,SV16: $i,SV82: $i] :
( ( ( SV82
!= ( vabs @ SV16 @ SV38 @ SV60 ) )
| ( visValue @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(228,plain,
! [SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ! [SY479: $i,SY480: $i,SY481: $i,SY482: $i,SY483: $i] :
( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SY479
!= ( vabs @ SY481 @ SY482 @ SY483 ) ) )
| ( SV39 != SY481 )
| ( SY480
!= ( vsubst @ SV61 @ SV83 @ SY479 ) )
| ( SY480
= ( vabs @ SY481 @ SY482 @ SY483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(229,plain,
! [SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ! [SY484: $i,SY485: $i,SY486: $i] :
( ~ ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SY484 ) ) @ SY485 @ SY486 ) )
| ( vtcheck @ ( vbind @ SV62 @ SV84 @ SY484 ) @ SY485 @ SY486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(230,plain,
! [SV19: $i,SV85: $i,SV63: $i,SV41: $i] :
( ( ! [SY487: $i,SY488: $i] :
( ~ ~ ( ( SV41 != SY487 )
| ( SV63
!= ( vabs @ SV85 @ SV19 @ SY488 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SY487 ) )
| ~ ( visFreeVar @ SY487 @ SY488 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SY487 ) )
| ~ ( visFreeVar @ SY487 @ SY488 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(231,plain,
! [SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ! [SY489: $i,SY490: $i] :
~ ( ~ ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SY489 @ SY490 ) )
| ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SY489 ) )
| ( SV64 != SY490 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SY489 ) )
| ( SV64 != SY490 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SY489 @ SY490 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(232,plain,
! [SV65: $i,SV43: $i,SV21: $i] :
( ( vempty
= ( vbind @ SV21 @ SV43 @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(233,plain,
! [SV44: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ! [SY491: $i,SY492: $i,SY493: $i] :
( ~ ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SY493 ) )
| ( SY491
!= ( vvar @ SV44 ) ) )
| ( SV22 != SV44 )
| ( SY492
!= ( vsubst @ SV66 @ SV87 @ SY491 ) )
| ( SY492 = SY493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(234,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV1 @ SV67 )
| ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) )
| ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(235,plain,
! [SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ! [SY494: $i,SY495: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SY494 @ veabs ) @ SY495 ) )
| ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SY494 @ veabs ) ) @ SY495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(236,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV3 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) )
| ( vtcheck @ SV47 @ SV69 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(237,plain,
! [SV70: $i,SV48: $i,SV26: $i,SV4: $i] :
( ( ( vvar @ SV4 )
= ( vabs @ SV26 @ SV48 @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(238,plain,
! [SV71: $i,SV91: $i,SV49: $i,SV27: $i,SV5: $i] :
( ( ! [SY496: $i,SY497: $i,SY498: $i,SY499: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY497 )
| ( SV27 != SY498 ) )
| ( SV49
!= ( vabs @ SV91 @ SY496 @ SY499 ) ) )
| ~ ~ ( ~ ( ( SY497 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SY498 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SY496 @ ( vsubst @ SY497 @ SY498 @ SY499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(239,plain,
! [SV92: $i,SV50: $i,SV6: $i,SV72: $i,SV28: $i] :
( ( ~ ( vtcheck @ ( vbind @ SV28 @ SV72 @ SV6 ) @ SV50 @ SV92 )
| ( vtcheck @ SV6 @ ( vabs @ SV28 @ SV72 @ SV50 ) @ ( varrow @ SV72 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(240,plain,
! [SV93: $i,SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ~ ~ ( ~ ( vtcheck @ SV29 @ SV73 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 ) )
| ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(241,plain,
! [SV74: $i,SV94: $i,SV52: $i,SV30: $i,SV8: $i] :
( ( ! [SY500: $i,SY501: $i,SY502: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SY500 )
| ( SV30 != SY501 ) )
| ( SV52
!= ( vapp @ SV94 @ SY502 ) ) )
| ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SY500 @ SY501 @ SV94 ) @ ( vsubst @ SY500 @ SY501 @ SY502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(242,plain,
! [SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ! [SY503: $i,SY504: $i,SY505: $i] :
( ~ ~ ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SY503 @ SY504 ) @ SY505 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SY503 @ SY504 ) ) @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(243,plain,
! [SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ! [SY506: $i,SY507: $i] :
( ~ ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SY506 @ SY507 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SY506 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(244,plain,
! [SV97: $i,SV11: $i,SV33: $i,SV77: $i,SV55: $i] :
( ( ! [SY508: $i,SY509: $i] :
( ~ ~ ( ( SV55 != SY508 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SY509 ) ) )
| ~ ( ( SY508 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SY508 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(245,plain,
! [SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ! [SY510: $i] :
~ ( ~ ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SV98 @ SY510 ) )
| ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SY510 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SY510 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SY510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(246,plain,
! [SV99: $i,SV79: $i,SV57: $i,SV35: $i,SV13: $i] :
( ( ( vabs @ SV13 @ SV35 @ SV57 )
!= ( vapp @ SV79 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(247,plain,
! [SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ! [SY511: $i,SY512: $i] :
( ~ ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SV100
!= ( vvar @ SY512 ) ) )
| ~ ( ( SV36 != SY512 ) )
| ( SY511
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SY511
= ( vvar @ SY512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(248,plain,
! [SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SY513 @ veabs ) @ SY514 ) )
| ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SY513 @ veabs ) ) @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(249,plain,
! [SV60: $i,SV38: $i,SV16: $i,SV82: $i] :
( ( ( SV82
!= ( vabs @ SV16 @ SV38 @ SV60 ) )
= $true )
| ( ( visValue @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(250,plain,
! [SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ! [SY515: $i,SY516: $i,SY517: $i,SY518: $i] :
( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SY516 @ SY517 @ SY518 ) ) )
| ( SV39 != SY516 )
| ( SY515
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SY515
= ( vabs @ SY516 @ SY517 @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(251,plain,
! [SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ! [SY519: $i,SY520: $i] :
( ~ ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SY519 @ SY520 ) )
| ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SY519 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(252,plain,
! [SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ! [SY521: $i] :
( ~ ~ ( ( SV41 != SV104 )
| ( SV63
!= ( vabs @ SV85 @ SV19 @ SY521 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SY521 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SY521 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(253,plain,
! [SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ! [SY522: $i] :
~ ( ~ ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SV105 @ SY522 ) )
| ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SY522 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SY522 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SY522 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(254,plain,
! [SV44: $i,SV106: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ! [SY523: $i,SY524: $i] :
( ~ ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SY524 ) )
| ( SV106
!= ( vvar @ SV44 ) ) )
| ( SV22 != SV44 )
| ( SY523
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SY523 = SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(255,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV1 @ SV67 )
| ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(256,plain,
! [SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ! [SY525: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SY525 ) )
| ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV3 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) ) )
= $true )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(258,plain,
! [SV71: $i,SV108: $i,SV91: $i,SV49: $i,SV27: $i,SV5: $i] :
( ( ! [SY526: $i,SY527: $i,SY528: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY526 )
| ( SV27 != SY527 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SY528 ) ) )
| ~ ~ ( ~ ( ( SY526 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SY527 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SY526 @ SY527 @ SY528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(259,plain,
! [SV92: $i,SV50: $i,SV6: $i,SV72: $i,SV28: $i] :
( ( ( ~ ( vtcheck @ ( vbind @ SV28 @ SV72 @ SV6 ) @ SV50 @ SV92 ) )
= $true )
| ( ( vtcheck @ SV6 @ ( vabs @ SV28 @ SV72 @ SV50 ) @ ( varrow @ SV72 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(260,plain,
! [SV93: $i,SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( vtcheck @ SV29 @ SV73 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 ) ) )
= $true )
| ( ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(261,plain,
! [SV74: $i,SV94: $i,SV52: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SY529 ) )
| ( SV52
!= ( vapp @ SV94 @ SY530 ) ) )
| ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SY529 @ SV94 ) @ ( vsubst @ SV109 @ SY529 @ SY530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(262,plain,
! [SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ! [SY531: $i,SY532: $i] :
( ~ ~ ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SY531 ) @ SY532 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SY531 ) ) @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(263,plain,
! [SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ! [SY533: $i] :
( ~ ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SY533 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(264,plain,
! [SV97: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ! [SY534: $i] :
( ~ ~ ( ( SV55 != SV112 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SY534 ) ) )
| ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SY534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(265,plain,
! [SV113: $i,SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ~ ( ~ ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SV98 @ SV113 ) )
| ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(266,plain,
! [SV99: $i,SV79: $i,SV57: $i,SV35: $i,SV13: $i] :
( ( ( vabs @ SV13 @ SV35 @ SV57 )
= ( vapp @ SV79 @ SV99 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(267,plain,
! [SV114: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ! [SY535: $i] :
( ~ ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SV100
!= ( vvar @ SY535 ) ) )
| ~ ( ( SV36 != SY535 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SY535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(268,plain,
! [SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ! [SY536: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SY536 ) )
| ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(269,plain,
! [SV60: $i,SV38: $i,SV16: $i,SV82: $i] :
( ( ( SV82
= ( vabs @ SV16 @ SV38 @ SV60 ) )
= $false )
| ( ( visValue @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(270,plain,
! [SV116: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ! [SY537: $i,SY538: $i,SY539: $i] :
( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SY537 @ SY538 @ SY539 ) ) )
| ( SV39 != SY537 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SY537 @ SY538 @ SY539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(271,plain,
! [SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ! [SY540: $i] :
( ~ ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SY540 ) )
| ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SY540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(272,plain,
! [SV118: $i,SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ~ ~ ( ( SV41 != SV104 )
| ( SV63
!= ( vabs @ SV85 @ SV19 @ SV118 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(273,plain,
! [SV119: $i,SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ~ ( ~ ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SV105 @ SV119 ) )
| ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(274,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ! [SY541: $i] :
( ~ ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SY541 ) )
| ( SV106
!= ( vvar @ SV44 ) ) )
| ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(275,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV1 @ SV67 )
| ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(276,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
| ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(277,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV3 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) ) )
= $false )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(278,plain,
! [SV71: $i,SV108: $i,SV91: $i,SV49: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ! [SY542: $i,SY543: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SY542 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SY543 ) ) )
| ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SY542 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SY542 @ SY543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(279,plain,
! [SV92: $i,SV50: $i,SV6: $i,SV72: $i,SV28: $i] :
( ( ( vtcheck @ ( vbind @ SV28 @ SV72 @ SV6 ) @ SV50 @ SV92 )
= $false )
| ( ( vtcheck @ SV6 @ ( vabs @ SV28 @ SV72 @ SV50 ) @ ( varrow @ SV72 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(280,plain,
! [SV93: $i,SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ( ~ ( ~ ( vtcheck @ SV29 @ SV73 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 ) ) )
= $false )
| ( ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(281,plain,
! [SV74: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ! [SY544: $i] :
( ~ ~ ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) )
| ( SV52
!= ( vapp @ SV94 @ SY544 ) ) )
| ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SY544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(282,plain,
! [SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ! [SY545: $i] :
( ~ ~ ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SY545 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(283,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ~ ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(284,plain,
! [SV97: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ~ ~ ( ( SV55 != SV112 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SV126 ) ) )
| ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(285,plain,
! [SV113: $i,SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ~ ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SV98 @ SV113 ) )
| ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(286,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ~ ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SV100
!= ( vvar @ SV127 ) ) )
| ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(287,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
| ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(288,plain,
! [SV116: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ! [SY546: $i,SY547: $i] :
( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SV129 @ SY546 @ SY547 ) ) )
| ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SY546 @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(289,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ~ ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 ) )
| ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(290,plain,
! [SV118: $i,SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ( ~ ~ ( ( SV41 != SV104 )
| ( SV63
!= ( vabs @ SV85 @ SV19 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(291,plain,
! [SV119: $i,SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ~ ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SV105 @ SV119 ) )
| ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(292,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ~ ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SV131 ) )
| ( SV106
!= ( vvar @ SV44 ) ) )
| ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(293,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ( ~ ~ ( visFreeVar @ SV1 @ SV67 )
| ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(294,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(295,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ( ~ ~ ( visFreeVar @ SV3 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) )
= $true )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(296,plain,
! [SV71: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ! [SY548: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SY548 ) ) )
| ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SY548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(297,plain,
! [SV93: $i,SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ( ~ ( vtcheck @ SV29 @ SV73 @ SV7 )
| ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 ) )
= $true )
| ( ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(298,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) )
| ( SV52
!= ( vapp @ SV94 @ SV133 ) ) )
| ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(299,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ~ ~ ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
| ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(300,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(301,plain,
! [SV97: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ( ~ ~ ( ( SV55 != SV112 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SV126 ) ) ) )
= $true )
| ( ( ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(302,plain,
! [SV113: $i,SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ~ ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SV98 @ SV113 ) )
| ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(303,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(304,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SV100
!= ( vvar @ SV127 ) ) ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(305,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(306,plain,
! [SV116: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ! [SY549: $i] :
( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SV129 @ SV135 @ SY549 ) ) )
| ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SY549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(307,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ( ~ ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(308,plain,
! [SV118: $i,SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ( ~ ( ( SV41 != SV104 )
| ( SV63
!= ( vabs @ SV85 @ SV19 @ SV118 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(309,plain,
! [SV119: $i,SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ~ ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SV105 @ SV119 ) )
| ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(310,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(311,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SV131 ) )
| ( SV106
!= ( vvar @ SV44 ) ) ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(312,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ( ~ ~ ( visFreeVar @ SV1 @ SV67 ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(313,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) ) )
= $false )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(314,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ( ~ ~ ( visFreeVar @ SV3 @ SV69 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) )
= $true )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(315,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) ) )
| ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(316,plain,
! [SV93: $i,SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ( ~ ( vtcheck @ SV29 @ SV73 @ SV7 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 ) )
= $true )
| ( ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(317,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) )
| ( SV52
!= ( vapp @ SV94 @ SV133 ) ) ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(318,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(319,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ( ~ ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(320,plain,
! [SV97: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV112 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SV126 ) ) ) )
= $false )
| ( ( ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(321,plain,
! [SV113: $i,SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SV98 @ SV113 ) )
| ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(322,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) )
| ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(323,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( ~ ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SV100
!= ( vvar @ SV127 ) ) ) )
= $false )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(324,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) ) )
= $false )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(325,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
| ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(326,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ( ~ ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(327,plain,
! [SV118: $i,SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ( ( SV41 != SV104 )
| ( SV63
!= ( vabs @ SV85 @ SV19 @ SV118 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(328,plain,
! [SV119: $i,SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SV105 @ SV119 ) )
| ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(329,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) )
| ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(330,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( ~ ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SV131 ) )
| ( SV106
!= ( vvar @ SV44 ) ) ) )
= $false )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(331,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ( ~ ( visFreeVar @ SV1 @ SV67 ) )
= $false )
| ( ( ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(332,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
| ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(333,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ( ~ ( visFreeVar @ SV3 @ SV69 ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) )
= $true )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(334,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(335,plain,
! [SV93: $i,SV51: $i,SV7: $i,SV73: $i,SV29: $i] :
( ( ( vtcheck @ SV29 @ SV73 @ SV7 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 ) )
= $true )
| ( ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(336,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) )
| ( SV52
!= ( vapp @ SV94 @ SV133 ) ) ) )
= $false )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(337,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( ~ ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) ) )
= $false )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(338,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ( ~ ( ( SV54 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(339,plain,
! [SV97: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ( ( SV55 != SV112 )
| ( SV77
!= ( vbind @ SV33 @ SV11 @ SV126 ) ) )
= $true )
| ( ( ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(340,plain,
! [SV113: $i,SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ( ( vabs @ SV12 @ SV34 @ SV56 )
!= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(341,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(342,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
| ( SV100
!= ( vvar @ SV127 ) ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(343,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
| ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(344,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) ) ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(345,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ( ( SV62 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(346,plain,
! [SV118: $i,SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ( SV41 != SV104 )
= $true )
| ( ( SV63
!= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(347,plain,
! [SV119: $i,SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ( ( vbind @ SV20 @ SV42 @ SV64 )
!= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(348,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(349,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SV131 ) )
| ( SV106
!= ( vvar @ SV44 ) ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(350,plain,
! [SV23: $i,SV88: $i,SV45: $i,SV67: $i,SV1: $i] :
( ( ( visFreeVar @ SV1 @ SV67 )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ SV67 @ SV88 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(351,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(352,plain,
! [SV90: $i,SV47: $i,SV25: $i,SV69: $i,SV3: $i] :
( ( ( visFreeVar @ SV3 @ SV69 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 ) )
= $true )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(353,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(354,plain,
! [SV73: $i,SV93: $i,SV29: $i,SV7: $i,SV51: $i] :
( ( ( vtcheck @ ( vbind @ SV51 @ SV7 @ SV29 ) @ veabs @ SV93 )
= $false )
| ( ( vtcheck @ SV29 @ SV73 @ SV7 )
= $false )
| ( ( vtcheck @ SV29 @ ( vsubst @ SV51 @ SV73 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(355,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) )
| ( SV52
!= ( vapp @ SV94 @ SV133 ) ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(356,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
| ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(357,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ( ~ ( ( SV54 != SV10 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(358,plain,
! [SV97: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ( SV55 != SV112 )
= $true )
| ( ( SV77
!= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $true )
| ( ( ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(359,plain,
! [SV113: $i,SV98: $i,SV78: $i,SV56: $i,SV34: $i,SV12: $i] :
( ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(360,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) ) )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(361,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( ~ ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) ) )
= $true )
| ( ( SV100
!= ( vvar @ SV127 ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(362,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(363,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( ~ ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) ) ) )
= $false )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(364,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ( SV62 != SV18 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(365,plain,
! [SV118: $i,SV19: $i,SV85: $i,SV63: $i,SV104: $i,SV41: $i] :
( ( ( SV41 = SV104 )
= $false )
| ( ( SV63
!= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(366,plain,
! [SV119: $i,SV105: $i,SV86: $i,SV64: $i,SV42: $i,SV20: $i] :
( ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(367,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) ) )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(368,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( ~ ~ ( ( SV66 != SV22 )
| ( SV87 != SV131 ) ) )
= $true )
| ( ( SV106
!= ( vvar @ SV44 ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(369,plain,
! [SV23: $i,SV1: $i,SV88: $i,SV67: $i,SV45: $i] :
( ( ( vtcheck @ SV45 @ SV67 @ SV88 )
= $false )
| ( ( visFreeVar @ SV1 @ SV67 )
= $true )
| ( ( vtcheck @ ( vbind @ SV1 @ SV23 @ SV45 ) @ SV67 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(370,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(371,plain,
! [SV90: $i,SV69: $i,SV47: $i,SV25: $i,SV3: $i] :
( ( ( vtcheck @ ( vbind @ SV3 @ SV25 @ SV47 ) @ SV69 @ SV90 )
= $false )
| ( ( visFreeVar @ SV3 @ SV69 )
= $true )
| ( ( vtcheck @ SV47 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(372,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) )
| ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(373,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( ~ ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) ) )
= $true )
| ( ( SV52
!= ( vapp @ SV94 @ SV133 ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(374,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( ~ ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(375,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ( SV54 != SV10 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(376,plain,
! [SV97: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i,SV112: $i,SV55: $i] :
( ( ( SV55 = SV112 )
= $false )
| ( ( SV77
!= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $true )
| ( ( ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(377,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(378,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
| ( SV56 != SV113 ) )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(379,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != SV36 )
| ( SV80 != SV14 ) ) )
= $false )
| ( ( SV100
!= ( vvar @ SV127 ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(380,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(381,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
| ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(382,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV84: $i,SV18: $i,SV62: $i] :
( ( ( SV62 = SV18 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(383,plain,
! [SV104: $i,SV41: $i,SV118: $i,SV19: $i,SV85: $i,SV63: $i] :
( ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(384,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(385,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
| ( SV64 != SV119 ) )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(386,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( ~ ( ( SV66 != SV22 )
| ( SV87 != SV131 ) ) )
= $false )
| ( ( SV106
!= ( vvar @ SV44 ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(387,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
| ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(388,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) ) )
= $true )
| ( ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(389,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( ~ ( ( SV8 != SV109 )
| ( SV30 != SV123 ) ) )
= $false )
| ( ( SV52
!= ( vapp @ SV94 @ SV133 ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(390,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( ~ ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(391,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV76: $i,SV10: $i,SV54: $i] :
( ( ( SV54 = SV10 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(392,plain,
! [SV97: $i,SV112: $i,SV55: $i,SV126: $i,SV11: $i,SV33: $i,SV77: $i] :
( ( ( SV77
= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $false )
| ( ( SV55 = SV112 )
= $false )
| ( ( ~ ( ( SV112 != SV33 ) )
| ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(393,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) ) )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(394,plain,
! [SV98: $i,SV78: $i,SV34: $i,SV12: $i,SV113: $i,SV56: $i] :
( ( ( SV56 != SV113 )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(395,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) ) )
= $true )
| ( ( SV56 != SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(396,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( ( SV58 != SV36 )
| ( SV80 != SV14 ) )
= $true )
| ( ( SV100
!= ( vvar @ SV127 ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(397,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
| ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(398,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( ~ ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) ) )
= $true )
| ( ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(399,plain,
! [SV130: $i,SV117: $i,SV103: $i,SV40: $i,SV18: $i,SV84: $i,SV62: $i] :
( ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ ( vbind @ SV18 @ SV40 @ SV103 ) ) @ SV117 @ SV130 )
= $false )
| ( ( SV62 = SV18 )
= $false )
| ( ( vtcheck @ ( vbind @ SV62 @ SV84 @ SV103 ) @ SV117 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(400,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
| ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(401,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) ) )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(402,plain,
! [SV105: $i,SV86: $i,SV42: $i,SV20: $i,SV119: $i,SV64: $i] :
( ( ( SV64 != SV119 )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(403,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) ) )
= $true )
| ( ( SV64 != SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(404,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( ( SV66 != SV22 )
| ( SV87 != SV131 ) )
= $true )
| ( ( SV106
!= ( vvar @ SV44 ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(405,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(406,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV122 )
| ( SV27 != SV132 ) ) )
= $false )
| ( ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(407,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( ( SV8 != SV109 )
| ( SV30 != SV123 ) )
= $true )
| ( ( SV52
!= ( vapp @ SV94 @ SV133 ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(408,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( ( SV53 != SV95 )
| ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(409,plain,
! [SV125: $i,SV111: $i,SV96: $i,SV32: $i,SV10: $i,SV76: $i,SV54: $i] :
( ( ( vtcheck @ ( vbind @ SV54 @ SV76 @ ( vbind @ SV10 @ SV32 @ SV96 ) ) @ SV111 @ SV125 )
= $false )
| ( ( SV54 = SV10 )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV32 @ ( vbind @ SV54 @ SV76 @ SV96 ) ) @ SV111 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(410,plain,
! [SV11: $i,SV126: $i,SV77: $i,SV55: $i,SV97: $i,SV33: $i,SV112: $i] :
( ( ( ~ ( ( SV112 != SV33 ) ) )
= $true )
| ( ( ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true )
| ( ( SV55 = SV112 )
= $false )
| ( ( SV77
= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(411,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) ) )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(412,plain,
! [SV98: $i,SV78: $i,SV34: $i,SV12: $i,SV113: $i,SV56: $i] :
( ( ( SV56 = SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(413,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV78 )
| ( SV34 != SV98 ) ) )
= $false )
| ( ( SV56 != SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(414,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( SV58 != SV36 )
= $true )
| ( ( SV80 != SV14 )
= $true )
| ( ( SV100
!= ( vvar @ SV127 ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(415,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(416,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( ~ ( ( SV61 != SV39 )
| ( SV83 != SV17 ) ) )
= $false )
| ( ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(417,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) ) )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(418,plain,
! [SV19: $i,SV118: $i,SV104: $i,SV85: $i,SV63: $i,SV41: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) ) )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(419,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) ) )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(420,plain,
! [SV105: $i,SV86: $i,SV42: $i,SV20: $i,SV119: $i,SV64: $i] :
( ( ( SV64 = SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(421,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ~ ( ( SV20 != SV86 )
| ( SV42 != SV105 ) ) )
= $false )
| ( ( SV64 != SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(422,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( SV66 != SV22 )
= $true )
| ( ( SV87 != SV131 )
= $true )
| ( ( SV106
!= ( vvar @ SV44 ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(423,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) ) )
= $false )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(424,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( ( SV5 != SV122 )
| ( SV27 != SV132 ) )
= $true )
| ( ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(425,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( SV8 != SV109 )
= $true )
| ( ( SV30 != SV123 )
= $true )
| ( ( SV52
!= ( vapp @ SV94 @ SV133 ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(426,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( SV53 != SV95 )
= $true )
| ( ( ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(427,plain,
! [SV11: $i,SV126: $i,SV77: $i,SV55: $i,SV97: $i,SV33: $i,SV112: $i] :
( ( ( SV112 != SV33 )
= $false )
| ( ( ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true )
| ( ( SV55 = SV112 )
= $false )
| ( ( SV77
= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(428,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(429,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( ( SV12 != SV78 )
| ( SV34 != SV98 ) )
= $true )
| ( ( SV56 != SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(430,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i] :
( ( ( SV58 = SV36 )
= $false )
| ( ( SV80 != SV14 )
= $true )
| ( ( SV100
!= ( vvar @ SV127 ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(431,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) ) )
= $false )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(432,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( ( SV61 != SV39 )
| ( SV83 != SV17 ) )
= $true )
| ( ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(433,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
| ( visFreeVar @ SV41 @ SV63 ) )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(434,plain,
! [SV19: $i,SV118: $i,SV104: $i,SV85: $i,SV63: $i,SV41: $i] :
( ( ( ~ ( visFreeVar @ SV41 @ SV63 )
| ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(435,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(436,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( ( SV20 != SV86 )
| ( SV42 != SV105 ) )
= $true )
| ( ( SV64 != SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(437,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i] :
( ( ( SV66 = SV22 )
= $false )
| ( ( SV87 != SV131 )
= $true )
| ( ( SV106
!= ( vvar @ SV44 ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(438,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ( ( SV46 != SV89 ) )
| ~ ( visFreeVar @ SV89 @ SV68 ) )
= $true )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(439,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( SV5 != SV122 )
= $true )
| ( ( SV27 != SV132 )
= $true )
| ( ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(440,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i] :
( ( ( SV8 = SV109 )
= $false )
| ( ( SV30 != SV123 )
= $true )
| ( ( SV52
!= ( vapp @ SV94 @ SV133 ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(441,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV9: $i,SV75: $i,SV31: $i,SV95: $i,SV53: $i] :
( ( ( SV53 = SV95 )
= $false )
| ( ( ~ ( vtcheck @ SV31 @ SV75 @ SV9 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(442,plain,
! [SV11: $i,SV126: $i,SV77: $i,SV55: $i,SV97: $i,SV33: $i,SV112: $i] :
( ( ( SV112 = SV33 )
= $true )
| ( ( ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
| ( SV97
= ( vlookup @ SV112 @ SV126 ) ) )
= $true )
| ( ( SV55 = SV112 )
= $false )
| ( ( SV77
= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(443,plain,
! [SV113: $i,SV98: $i,SV56: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( SV12 != SV78 )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(444,plain,
! [SV113: $i,SV78: $i,SV56: $i,SV12: $i,SV98: $i,SV34: $i] :
( ( ( SV34 != SV98 )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(445,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( SV12 != SV78 )
= $true )
| ( ( SV34 != SV98 )
= $true )
| ( ( SV56 != SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(446,plain,
! [SV114: $i,SV127: $i,SV100: $i,SV36: $i,SV58: $i,SV14: $i,SV80: $i] :
( ( ( SV80 = SV14 )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV100
!= ( vvar @ SV127 ) )
= $true )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(447,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != SV101 ) )
| ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(448,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( SV61 != SV39 )
= $true )
| ( ( SV83 != SV17 )
= $true )
| ( ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(449,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(450,plain,
! [SV19: $i,SV118: $i,SV104: $i,SV85: $i,SV63: $i,SV41: $i] :
( ( ( ~ ( visFreeVar @ SV41 @ SV63 ) )
= $true )
| ( ( ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(451,plain,
! [SV119: $i,SV105: $i,SV64: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( SV20 != SV86 )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(452,plain,
! [SV119: $i,SV86: $i,SV64: $i,SV20: $i,SV105: $i,SV42: $i] :
( ( ( SV42 != SV105 )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(453,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( SV20 != SV86 )
= $true )
| ( ( SV42 != SV105 )
= $true )
| ( ( SV64 != SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(454,plain,
! [SV120: $i,SV44: $i,SV106: $i,SV22: $i,SV66: $i,SV131: $i,SV87: $i] :
( ( ( SV87 = SV131 )
= $false )
| ( ( SV66 = SV22 )
= $false )
| ( ( SV106
!= ( vvar @ SV44 ) )
= $true )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(455,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( ~ ( ( SV46 != SV89 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV89 @ SV68 ) )
= $true )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i] :
( ( ( SV5 = SV122 )
= $false )
| ( ( SV27 != SV132 )
= $true )
| ( ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(457,plain,
! [SV74: $i,SV133: $i,SV94: $i,SV52: $i,SV109: $i,SV8: $i,SV123: $i,SV30: $i] :
( ( ( SV30 = SV123 )
= $false )
| ( ( SV8 = SV109 )
= $false )
| ( ( SV52
!= ( vapp @ SV94 @ SV133 ) )
= $true )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(458,plain,
! [SV134: $i,SV124: $i,SV110: $i,SV95: $i,SV53: $i,SV9: $i,SV75: $i,SV31: $i] :
( ( ( vtcheck @ SV31 @ SV75 @ SV9 )
= $false )
| ( ( SV53 = SV95 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 ) )
= $true )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(459,plain,
! [SV11: $i,SV33: $i,SV126: $i,SV112: $i,SV77: $i,SV55: $i,SV97: $i] :
( ( ( SV97
!= ( vlookup @ SV55 @ SV77 ) )
= $true )
| ( ( SV97
= ( vlookup @ SV112 @ SV126 ) )
= $true )
| ( ( SV112 = SV33 )
= $true )
| ( ( SV55 = SV112 )
= $false )
| ( ( SV77
= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(460,plain,
! [SV113: $i,SV98: $i,SV56: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( SV12 = SV78 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(461,plain,
! [SV113: $i,SV78: $i,SV56: $i,SV12: $i,SV98: $i,SV34: $i] :
( ( ( SV34 = SV98 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(462,plain,
! [SV113: $i,SV56: $i,SV98: $i,SV34: $i,SV78: $i,SV12: $i] :
( ( ( SV12 = SV78 )
= $false )
| ( ( SV34 != SV98 )
= $true )
| ( ( SV56 != SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(463,plain,
! [SV114: $i,SV14: $i,SV80: $i,SV36: $i,SV58: $i,SV127: $i,SV100: $i] :
( ( ( SV100
= ( vvar @ SV127 ) )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV80 = SV14 )
= $false )
| ( ( ~ ( ( SV36 != SV127 ) )
| ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(464,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != SV101 ) ) )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(465,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i] :
( ( ( SV61 = SV39 )
= $false )
| ( ( SV83 != SV17 )
= $true )
| ( ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(466,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) )
= $false )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(467,plain,
! [SV19: $i,SV118: $i,SV104: $i,SV85: $i,SV63: $i,SV41: $i] :
( ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( ~ ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) ) )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(468,plain,
! [SV119: $i,SV105: $i,SV64: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( SV20 = SV86 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(469,plain,
! [SV119: $i,SV86: $i,SV64: $i,SV20: $i,SV105: $i,SV42: $i] :
( ( ( SV42 = SV105 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(470,plain,
! [SV119: $i,SV64: $i,SV105: $i,SV42: $i,SV86: $i,SV20: $i] :
( ( ( SV20 = SV86 )
= $false )
| ( ( SV42 != SV105 )
= $true )
| ( ( SV64 != SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(471,plain,
! [SV120: $i,SV131: $i,SV87: $i,SV22: $i,SV66: $i,SV44: $i,SV106: $i] :
( ( ( SV106
= ( vvar @ SV44 ) )
= $false )
| ( ( SV66 = SV22 )
= $false )
| ( ( SV87 = SV131 )
= $false )
| ( ( ( SV22 != SV44 )
| ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(472,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( SV46 != SV89 )
= $false )
| ( ( ~ ( visFreeVar @ SV89 @ SV68 ) )
= $true )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(473,plain,
! [SV71: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i,SV122: $i,SV5: $i,SV132: $i,SV27: $i] :
( ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
!= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(474,plain,
! [SV74: $i,SV123: $i,SV30: $i,SV109: $i,SV8: $i,SV133: $i,SV94: $i,SV52: $i] :
( ( ( SV52
= ( vapp @ SV94 @ SV133 ) )
= $false )
| ( ( SV8 = SV109 )
= $false )
| ( ( SV30 = SV123 )
= $false )
| ( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
| ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(475,plain,
! [SV75: $i,SV134: $i,SV124: $i,SV110: $i,SV95: $i,SV31: $i,SV9: $i,SV53: $i] :
( ( ( vtcheck @ ( vbind @ SV53 @ SV9 @ SV31 ) @ ( vabs @ SV95 @ SV110 @ SV124 ) @ SV134 )
= $false )
| ( ( SV53 = SV95 )
= $false )
| ( ( vtcheck @ SV31 @ SV75 @ SV9 )
= $false )
| ( ( vtcheck @ SV31 @ ( vsubst @ SV53 @ SV75 @ ( vabs @ SV95 @ SV110 @ SV124 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(476,plain,
! [SV11: $i,SV33: $i,SV126: $i,SV112: $i,SV77: $i,SV55: $i,SV97: $i] :
( ( ( SV97
= ( vlookup @ SV55 @ SV77 ) )
= $false )
| ( ( SV97
= ( vlookup @ SV112 @ SV126 ) )
= $true )
| ( ( SV112 = SV33 )
= $true )
| ( ( SV55 = SV112 )
= $false )
| ( ( SV77
= ( vbind @ SV33 @ SV11 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(477,plain,
! [SV113: $i,SV56: $i,SV78: $i,SV12: $i,SV98: $i,SV34: $i] :
( ( ( SV34 = SV98 )
= $false )
| ( ( SV12 = SV78 )
= $false )
| ( ( SV56 != SV113 )
= $true )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(478,plain,
! [SV14: $i,SV100: $i,SV80: $i,SV58: $i,SV114: $i,SV127: $i,SV36: $i] :
( ( ( ~ ( ( SV36 != SV127 ) ) )
= $true )
| ( ( ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true )
| ( ( SV80 = SV14 )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV100
= ( vvar @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(479,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( SV59 != SV101 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(480,plain,
! [SV116: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV39: $i,SV61: $i,SV17: $i,SV83: $i] :
( ( ( SV83 = SV17 )
= $false )
| ( ( SV61 = SV39 )
= $false )
| ( ( SV102
!= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(481,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(482,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ( SV85 != SV104 ) )
| ~ ( visFreeVar @ SV104 @ SV118 ) )
= $false )
| ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(483,plain,
! [SV119: $i,SV64: $i,SV86: $i,SV20: $i,SV105: $i,SV42: $i] :
( ( ( SV42 = SV105 )
= $false )
| ( ( SV20 = SV86 )
= $false )
| ( ( SV64 != SV119 )
= $true )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(484,plain,
! [SV131: $i,SV106: $i,SV87: $i,SV66: $i,SV120: $i,SV44: $i,SV22: $i] :
( ( ( SV22 != SV44 )
= $true )
| ( ( ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true )
| ( ( SV87 = SV131 )
= $false )
| ( ( SV66 = SV22 )
= $false )
| ( ( SV106
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(485,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV68: $i,SV89: $i,SV46: $i] :
( ( ( SV46 = SV89 )
= $true )
| ( ( ~ ( visFreeVar @ SV89 @ SV68 ) )
= $true )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(486,plain,
! [SV71: $i,SV132: $i,SV27: $i,SV122: $i,SV5: $i,SV136: $i,SV108: $i,SV91: $i,SV49: $i] :
( ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV27 = SV132 )
= $false )
| ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
| ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(487,plain,
! [SV133: $i,SV94: $i,SV123: $i,SV109: $i,SV52: $i,SV30: $i,SV8: $i,SV74: $i] :
( ( ( SV74
!= ( vsubst @ SV8 @ SV30 @ SV52 ) )
= $true )
| ( ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) )
= $true )
| ( ( SV30 = SV123 )
= $false )
| ( ( SV8 = SV109 )
= $false )
| ( ( SV52
= ( vapp @ SV94 @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(488,plain,
! [SV98: $i,SV34: $i,SV78: $i,SV12: $i,SV113: $i,SV56: $i] :
( ( ( SV56 = SV113 )
= $false )
| ( ( SV12 = SV78 )
= $false )
| ( ( SV34 = SV98 )
= $false )
| ( ( ( vabs @ SV12 @ SV34 @ SV56 )
= ( vabs @ SV78 @ SV98 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(489,plain,
! [SV14: $i,SV100: $i,SV80: $i,SV58: $i,SV114: $i,SV127: $i,SV36: $i] :
( ( ( SV36 != SV127 )
= $false )
| ( ( ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true )
| ( ( SV80 = SV14 )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV100
= ( vvar @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(490,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV81: $i,SV101: $i,SV59: $i] :
( ( ( SV59 = SV101 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV101 @ SV81 ) )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(491,plain,
! [SV116: $i,SV17: $i,SV83: $i,SV39: $i,SV61: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i] :
( ( ( SV102
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $false )
| ( ( SV61 = SV39 )
= $false )
| ( ( SV83 = SV17 )
= $false )
| ( ( ( SV39 != SV129 )
| ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(492,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ( SV85 != SV104 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV104 @ SV118 ) )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(493,plain,
! [SV118: $i,SV19: $i,SV63: $i,SV41: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( ( SV85 != SV104 ) ) )
= $false )
| ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(494,plain,
! [SV19: $i,SV85: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i] :
( ( ( ~ ( visFreeVar @ SV104 @ SV118 ) )
= $false )
| ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[482]) ).
thf(495,plain,
! [SV105: $i,SV42: $i,SV86: $i,SV20: $i,SV119: $i,SV64: $i] :
( ( ( SV64 = SV119 )
= $false )
| ( ( SV20 = SV86 )
= $false )
| ( ( SV42 = SV105 )
= $false )
| ( ( ( vbind @ SV20 @ SV42 @ SV64 )
= ( vbind @ SV86 @ SV105 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(496,plain,
! [SV131: $i,SV106: $i,SV87: $i,SV66: $i,SV120: $i,SV44: $i,SV22: $i] :
( ( ( SV22 = SV44 )
= $false )
| ( ( ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
| ( SV120 = SV131 ) )
= $true )
| ( ( SV87 = SV131 )
= $false )
| ( ( SV66 = SV22 )
= $false )
| ( ( SV106
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(497,plain,
! [SV121: $i,SV107: $i,SV2: $i,SV24: $i,SV46: $i,SV68: $i,SV89: $i] :
( ( ( visFreeVar @ SV89 @ SV68 )
= $false )
| ( ( SV46 = SV89 )
= $true )
| ( ( ~ ( vtcheck @ SV24 @ SV68 @ SV2 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(498,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV132: $i,SV91: $i,SV122: $i] :
( ( ( ~ ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) ) )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(499,plain,
! [SV133: $i,SV94: $i,SV123: $i,SV109: $i,SV52: $i,SV30: $i,SV8: $i,SV74: $i] :
( ( ( SV74
= ( vsubst @ SV8 @ SV30 @ SV52 ) )
= $false )
| ( ( SV74
= ( vapp @ ( vsubst @ SV109 @ SV123 @ SV94 ) @ ( vsubst @ SV109 @ SV123 @ SV133 ) ) )
= $true )
| ( ( SV30 = SV123 )
= $false )
| ( ( SV8 = SV109 )
= $false )
| ( ( SV52
= ( vapp @ SV94 @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(500,plain,
! [SV14: $i,SV100: $i,SV80: $i,SV58: $i,SV114: $i,SV127: $i,SV36: $i] :
( ( ( SV36 = SV127 )
= $true )
| ( ( ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
| ( SV114
= ( vvar @ SV127 ) ) )
= $true )
| ( ( SV80 = SV14 )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV100
= ( vvar @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(501,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV59: $i,SV81: $i,SV101: $i] :
( ( ( ~ ( visFreeVar @ SV101 @ SV81 ) )
= $false )
| ( ( SV59 = SV101 )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(502,plain,
! [SV17: $i,SV137: $i,SV135: $i,SV102: $i,SV83: $i,SV61: $i,SV116: $i,SV129: $i,SV39: $i] :
( ( ( SV39 != SV129 )
= $true )
| ( ( ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true )
| ( ( SV83 = SV17 )
= $false )
| ( ( SV61 = SV39 )
= $false )
| ( ( SV102
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(503,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( SV85 != SV104 )
= $false )
| ( ( ~ ( visFreeVar @ SV104 @ SV118 ) )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(504,plain,
! [SV118: $i,SV19: $i,SV63: $i,SV41: $i,SV104: $i,SV85: $i] :
( ( ( SV85 != SV104 )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(505,plain,
! [SV19: $i,SV85: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i] :
( ( ( visFreeVar @ SV104 @ SV118 )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(506,plain,
! [SV44: $i,SV22: $i,SV131: $i,SV106: $i,SV87: $i,SV66: $i,SV120: $i] :
( ( ( SV120
!= ( vsubst @ SV66 @ SV87 @ SV106 ) )
= $true )
| ( ( SV120 = SV131 )
= $true )
| ( ( SV22 = SV44 )
= $false )
| ( ( SV87 = SV131 )
= $false )
| ( ( SV66 = SV22 )
= $false )
| ( ( SV106
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(507,plain,
! [SV121: $i,SV107: $i,SV89: $i,SV46: $i,SV2: $i,SV68: $i,SV24: $i] :
( ( ( vtcheck @ SV24 @ SV68 @ SV2 )
= $false )
| ( ( SV46 = SV89 )
= $true )
| ( ( visFreeVar @ SV89 @ SV68 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 ) )
= $true )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(508,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV132: $i,SV91: $i,SV122: $i] :
( ( ( ~ ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) ) )
= $false )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(509,plain,
! [SV14: $i,SV36: $i,SV127: $i,SV100: $i,SV80: $i,SV58: $i,SV114: $i] :
( ( ( SV114
!= ( vsubst @ SV58 @ SV80 @ SV100 ) )
= $true )
| ( ( SV114
= ( vvar @ SV127 ) )
= $true )
| ( ( SV36 = SV127 )
= $true )
| ( ( SV80 = SV14 )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV100
= ( vvar @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(510,plain,
! [SV128: $i,SV115: $i,SV15: $i,SV37: $i,SV59: $i,SV81: $i,SV101: $i] :
( ( ( visFreeVar @ SV101 @ SV81 )
= $true )
| ( ( SV59 = SV101 )
= $true )
| ( ( ~ ( vtcheck @ SV37 @ SV81 @ SV15 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(511,plain,
! [SV17: $i,SV137: $i,SV135: $i,SV102: $i,SV83: $i,SV61: $i,SV116: $i,SV129: $i,SV39: $i] :
( ( ( SV39 = SV129 )
= $false )
| ( ( ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
| ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) ) )
= $true )
| ( ( SV83 = SV17 )
= $false )
| ( ( SV61 = SV39 )
= $false )
| ( ( SV102
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(512,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV118: $i,SV104: $i,SV85: $i] :
( ( ( SV85 = SV104 )
= $true )
| ( ( ~ ( visFreeVar @ SV104 @ SV118 ) )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(513,plain,
! [SV118: $i,SV19: $i,SV63: $i,SV41: $i,SV104: $i,SV85: $i] :
( ( ( SV85 = SV104 )
= $false )
| ( ( visFreeVar @ SV41 @ SV63 )
= $false )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(514,plain,
! [SV44: $i,SV22: $i,SV131: $i,SV106: $i,SV87: $i,SV66: $i,SV120: $i] :
( ( ( SV120
= ( vsubst @ SV66 @ SV87 @ SV106 ) )
= $false )
| ( ( SV120 = SV131 )
= $true )
| ( ( SV22 = SV44 )
= $false )
| ( ( SV87 = SV131 )
= $false )
| ( ( SV66 = SV22 )
= $false )
| ( ( SV106
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(515,plain,
! [SV68: $i,SV121: $i,SV107: $i,SV89: $i,SV24: $i,SV2: $i,SV46: $i] :
( ( ( vtcheck @ ( vbind @ SV46 @ SV2 @ SV24 ) @ ( vabs @ SV89 @ SV107 @ veabs ) @ SV121 )
= $false )
| ( ( visFreeVar @ SV89 @ SV68 )
= $false )
| ( ( SV46 = SV89 )
= $true )
| ( ( vtcheck @ SV24 @ SV68 @ SV2 )
= $false )
| ( ( vtcheck @ SV24 @ ( vsubst @ SV46 @ SV68 @ ( vabs @ SV89 @ SV107 @ veabs ) ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(516,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV132: $i,SV91: $i,SV122: $i] :
( ( ( ~ ( ( SV122 != SV91 ) )
| ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(517,plain,
! [SV14: $i,SV36: $i,SV127: $i,SV100: $i,SV80: $i,SV58: $i,SV114: $i] :
( ( ( SV114
= ( vsubst @ SV58 @ SV80 @ SV100 ) )
= $false )
| ( ( SV114
= ( vvar @ SV127 ) )
= $true )
| ( ( SV36 = SV127 )
= $true )
| ( ( SV80 = SV14 )
= $false )
| ( ( SV58 = SV36 )
= $false )
| ( ( SV100
= ( vvar @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(518,plain,
! [SV128: $i,SV115: $i,SV101: $i,SV59: $i,SV15: $i,SV81: $i,SV37: $i] :
( ( ( vtcheck @ SV37 @ SV81 @ SV15 )
= $false )
| ( ( SV59 = SV101 )
= $true )
| ( ( visFreeVar @ SV101 @ SV81 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 ) )
= $true )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(519,plain,
! [SV17: $i,SV39: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV83: $i,SV61: $i,SV116: $i] :
( ( ( SV116
!= ( vsubst @ SV61 @ SV83 @ SV102 ) )
= $true )
| ( ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( SV39 = SV129 )
= $false )
| ( ( SV83 = SV17 )
= $false )
| ( ( SV61 = SV39 )
= $false )
| ( ( SV102
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(520,plain,
! [SV19: $i,SV63: $i,SV41: $i,SV85: $i,SV118: $i,SV104: $i] :
( ( ( visFreeVar @ SV104 @ SV118 )
= $false )
| ( ( SV85 = SV104 )
= $true )
| ( ( visFreeVar @ SV41 @ SV63 )
= $true )
| ( ( SV41 = SV104 )
= $false )
| ( ( SV63
= ( vabs @ SV85 @ SV19 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(521,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV132: $i,SV91: $i,SV122: $i] :
( ( ( ~ ( ( SV122 != SV91 ) ) )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(522,plain,
! [SV81: $i,SV128: $i,SV115: $i,SV101: $i,SV37: $i,SV15: $i,SV59: $i] :
( ( ( vtcheck @ ( vbind @ SV59 @ SV15 @ SV37 ) @ ( vabs @ SV101 @ SV115 @ veabs ) @ SV128 )
= $false )
| ( ( visFreeVar @ SV101 @ SV81 )
= $true )
| ( ( SV59 = SV101 )
= $true )
| ( ( vtcheck @ SV37 @ SV81 @ SV15 )
= $false )
| ( ( vtcheck @ SV37 @ ( vsubst @ SV59 @ SV81 @ ( vabs @ SV101 @ SV115 @ veabs ) ) @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(523,plain,
! [SV17: $i,SV39: $i,SV137: $i,SV135: $i,SV129: $i,SV102: $i,SV83: $i,SV61: $i,SV116: $i] :
( ( ( SV116
= ( vsubst @ SV61 @ SV83 @ SV102 ) )
= $false )
| ( ( SV116
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $true )
| ( ( SV39 = SV129 )
= $false )
| ( ( SV83 = SV17 )
= $false )
| ( ( SV61 = SV39 )
= $false )
| ( ( SV102
= ( vabs @ SV129 @ SV135 @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(524,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV132: $i,SV91: $i,SV122: $i] :
( ( ( SV122 != SV91 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(525,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV132: $i,SV91: $i,SV122: $i] :
( ( ( SV122 = SV91 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV91 @ SV132 ) )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(526,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV122: $i,SV132: $i,SV91: $i] :
( ( ( ~ ( visFreeVar @ SV91 @ SV132 ) )
= $false )
| ( ( SV122 = SV91 )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(527,plain,
! [SV136: $i,SV108: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i,SV122: $i,SV132: $i,SV91: $i] :
( ( ( visFreeVar @ SV91 @ SV132 )
= $true )
| ( ( SV122 = SV91 )
= $true )
| ( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
| ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) ) )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(528,plain,
! [SV136: $i,SV132: $i,SV122: $i,SV108: $i,SV91: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i] :
( ( ( SV71
!= ( vsubst @ SV5 @ SV27 @ SV49 ) )
= $true )
| ( ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) )
= $true )
| ( ( SV122 = SV91 )
= $true )
| ( ( visFreeVar @ SV91 @ SV132 )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(529,plain,
! [SV136: $i,SV132: $i,SV122: $i,SV108: $i,SV91: $i,SV49: $i,SV27: $i,SV5: $i,SV71: $i] :
( ( ( SV71
= ( vsubst @ SV5 @ SV27 @ SV49 ) )
= $false )
| ( ( SV71
= ( vabs @ SV91 @ SV108 @ ( vsubst @ SV122 @ SV132 @ SV136 ) ) )
= $true )
| ( ( SV122 = SV91 )
= $true )
| ( ( visFreeVar @ SV91 @ SV132 )
= $true )
| ( ( SV27 = SV132 )
= $false )
| ( ( SV5 = SV122 )
= $false )
| ( ( SV49
= ( vabs @ SV91 @ SV108 @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(530,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[120,529,523,522,520,517,515,514,513,505,499,495,488,476,475,469,468,461,460,420,412,409,399,371,369,354,279,269,266,237,232,145,121]) ).
thf(531,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM133+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
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 18:39:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/0.82
% 3.39/0.82 No.of.Axioms: 22
% 3.39/0.82
% 3.39/0.82 Length.of.Defs: 0
% 3.39/0.82
% 3.39/0.82 Contains.Choice.Funs: false
% 3.39/0.82 ............................
% 3.39/0.82
% 3.39/0.82 ********************************
% 3.39/0.82 * All subproblems solved! *
% 3.39/0.82 ********************************
% 3.39/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:24,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:530,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.39/0.82
% 3.39/0.82 %**** Beginning of derivation protocol ****
% 3.39/0.82 % SZS output start CNFRefutation
% See solution above
% 3.39/0.83
% 3.39/0.83 %**** End of derivation protocol ****
% 3.39/0.83 %**** no. of clauses in derivation: 492 ****
% 3.39/0.83 %**** clause counter: 530 ****
% 3.39/0.83
% 3.39/0.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:24,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:530,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------