%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM125+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 : n013.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 10:12:25 AM UTC 2026
% Result : Theorem 2.29s 0.62s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 21
% Syntax : Number of formulae : 428 ( 205 unt; 0 typ; 0 def)
% Number of atoms : 3575 (2056 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 7942 (1979 ~;1246 |; 105 &;4510 @)
% ( 0 <=>; 102 =>; 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 : 31 ( 28 usr; 12 con; 0-3 aty)
% Number of variables : 2480 ( 0 ^;2480 !; 0 ?;2480 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Vx,type,
sK1_Vx: $i ).
thf(tp_sK2_SY116,type,
sK2_SY116: $i ).
thf(tp_sK3_SY121,type,
sK3_SY121: $i ).
thf(tp_sK4_SY125,type,
sK4_SY125: $i ).
thf(tp_sK5_SY128,type,
sK5_SY128: $i ).
thf(tp_sK6_SY130,type,
sK6_SY130: $i ).
thf(tp_vabs,type,
vabs: $i > $i > $i > $i ).
thf(tp_vapp,type,
vapp: $i > $i > $i ).
thf(tp_varrow,type,
varrow: $i > $i > $i ).
thf(tp_vbind,type,
vbind: $i > $i > $i > $i ).
thf(tp_veabs,type,
veabs: $i ).
thf(tp_vempty,type,
vempty: $i ).
thf(tp_vgensym,type,
vgensym: $i > $i ).
thf(tp_vgetSomeExp,type,
vgetSomeExp: $i > $i ).
thf(tp_vgetSomeType,type,
vgetSomeType: $i > $i ).
thf(tp_visFreeVar,type,
visFreeVar: $i > $i > $o ).
thf(tp_visSomeExp,type,
visSomeExp: $i > $o ).
thf(tp_visSomeType,type,
visSomeType: $i > $o ).
thf(tp_visValue,type,
visValue: $i > $o ).
thf(tp_vlookup,type,
vlookup: $i > $i > $i ).
thf(tp_vnoExp,type,
vnoExp: $i ).
thf(tp_vnoType,type,
vnoType: $i ).
thf(tp_vreduce,type,
vreduce: $i > $i ).
thf(tp_vsomeExp,type,
vsomeExp: $i > $i ).
thf(tp_vsomeType,type,
vsomeType: $i > $i ).
thf(tp_vsubst,type,
vsubst: $i > $i > $i > $i ).
thf(tp_vtcheck,type,
vtcheck: $i > $i > $i > $o ).
thf(tp_vvar,type,
vvar: $i > $i ).
thf(1,axiom,
! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx = Vy )
& ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-2') ).
thf(2,axiom,
! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-1') ).
thf(3,axiom,
! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ veabs )
& ( vtcheck @ VC @ veabs @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ veabs @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-IH') ).
thf(4,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(8,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(26,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(28,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(32,axiom,
! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
thf(33,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(34,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(36,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(43,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
thf(46,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i,VVar1: $i,VTyp1: $i,VCtx1: $i] :
( ( ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) )
=> ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-bind') ).
thf(48,axiom,
! [VVar0: $i,VExp0: $i,Ve1: $i,Vv: $i,Ve2: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar2) ).
thf(49,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(50,axiom,
! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar0) ).
thf(53,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(54,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(56,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(58,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(60,conjecture,
! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar-abs') ).
thf(61,negated_conjecture,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[60]) ).
thf(62,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $false ),
inference(unfold_def,[status(thm)],[61]) ).
thf(63,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx = Vy )
& ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(64,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(65,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ veabs )
& ( vtcheck @ VC @ veabs @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ veabs @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(66,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)],[4]) ).
thf(67,plain,
( ( ! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(68,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)],[26]) ).
thf(69,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)],[28]) ).
thf(70,plain,
( ( ! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(71,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)],[33]) ).
thf(72,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)],[34]) ).
thf(73,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)],[36]) ).
thf(74,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(75,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i,VVar1: $i,VTyp1: $i,VCtx1: $i] :
( ( ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) )
=> ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(76,plain,
( ( ! [VVar0: $i,VExp0: $i,Ve1: $i,Vv: $i,Ve2: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(77,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)],[49]) ).
thf(78,plain,
( ( ! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(79,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(80,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(81,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(82,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)],[58]) ).
thf(83,plain,
( ( ! [SY116: $i,SY117: $i,SY118: $i,SY119: $i,SY120: $i] :
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ SY118 @ SY119 @ veabs ) )
& ( vtcheck @ SY117 @ ( vabs @ SY118 @ SY119 @ veabs ) @ SY120 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ SY116 @ SY117 ) @ ( vabs @ SY118 @ SY119 @ veabs ) @ SY120 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(84,plain,
( ( ! [SY121: $i,SY122: $i,SY123: $i,SY124: $i] :
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ SY122 @ SY123 @ veabs ) )
& ( vtcheck @ SY121 @ ( vabs @ SY122 @ SY123 @ veabs ) @ SY124 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ SY121 ) @ ( vabs @ SY122 @ SY123 @ veabs ) @ SY124 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(85,plain,
( ( ! [SY125: $i,SY126: $i,SY127: $i] :
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ SY125 @ SY126 @ veabs ) )
& ( vtcheck @ sK3_SY121 @ ( vabs @ SY125 @ SY126 @ veabs ) @ SY127 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ SY125 @ SY126 @ veabs ) @ SY127 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(86,plain,
( ( ! [SY128: $i,SY129: $i] :
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ sK4_SY125 @ SY128 @ veabs ) )
& ( vtcheck @ sK3_SY121 @ ( vabs @ sK4_SY125 @ SY128 @ veabs ) @ SY129 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ SY128 @ veabs ) @ SY129 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(87,plain,
( ( ! [SY130: $i] :
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) )
& ( vtcheck @ sK3_SY121 @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ SY130 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ SY130 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) )
& ( vtcheck @ sK3_SY121 @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 ) )
=> ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(90,plain,
( ( vtcheck @ sK3_SY121 @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 )
= $true ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(91,plain,
( ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 )
= $false ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(92,plain,
( ( ~ ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 ) )
= $true ),
inference(polarity_switch,[status(thm)],[91]) ).
thf(93,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)],[82]) ).
thf(94,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(95,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(96,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(97,plain,
( ( ! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(98,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)],[77]) ).
thf(99,plain,
( ( ! [VVar0: $i,VExp0: $i,Ve1: $i,Vv: $i,Ve2: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(100,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i,VVar1: $i,VTyp1: $i,VCtx1: $i] :
( ( ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VCtx0 = VCtx1 ) )
=> ( ( vbind @ VVar0 @ VTyp0 @ VCtx0 )
= ( vbind @ VVar1 @ VTyp1 @ VCtx1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(101,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(102,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)],[73]) ).
thf(103,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)],[72]) ).
thf(104,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(105,plain,
( ( ! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(106,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(107,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)],[68]) ).
thf(108,plain,
( ( ! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(109,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)],[66]) ).
thf(110,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,VT: $i] :
( ( ~ ( visFreeVar @ Vx @ veabs )
& ( vtcheck @ VC @ veabs @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ veabs @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(111,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(112,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Vy: $i,VS1: $i,VT: $i] :
( ( ( Vx = Vy )
& ~ ( visFreeVar @ Vx @ ( vabs @ Vy @ VS1 @ veabs ) )
& ( vtcheck @ VC @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ ( vabs @ Vy @ VS1 @ veabs ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(113,plain,
( ( vtcheck @ sK3_SY121 @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(114,plain,
( ( ~ ( visFreeVar @ sK1_Vx @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(115,plain,
( ( ~ ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(117,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)],[93]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ( SX0 != SX3 )
| ( SX1
!= ( vapp @ SX2 @ SX4 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SX3 @ SX2 )
| ( visFreeVar @ SX3 @ SX4 ) )
| ( visFreeVar @ SX0 @ SX1 ) )
| ~ ( ~ ( visFreeVar @ SX0 @ SX1 )
| ( visFreeVar @ SX3 @ SX2 )
| ( visFreeVar @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ( SX0 != SX3 )
| ( SX1
!= ( vvar @ SX2 ) ) )
| ~ ( ~ ( ( SX2 != SX3 )
| ( visFreeVar @ SX0 @ SX1 ) )
| ~ ( ~ ( visFreeVar @ SX0 @ SX1 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ( SX0 != SX3 )
| ~ ~ ( visFreeVar @ SX0 @ ( vabs @ SX3 @ SX4 @ veabs ) ) )
| ~ ( vtcheck @ SX2 @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SX0 @ veabs )
| ~ ( vtcheck @ SX2 @ veabs @ SX3 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ veabs @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(122,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)],[107]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( vgensym @ SX1 )
!= SX0 )
| ~ ( visFreeVar @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(124,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)],[98]) ).
thf(125,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)],[100]) ).
thf(126,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)],[109]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( visValue @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( vempty
!= ( vbind @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SX0 != SX3 ) )
| ~ ~ ( visFreeVar @ SX0 @ ( vabs @ SX3 @ SX4 @ veabs ) ) )
| ~ ( vtcheck @ SX2 @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ ( vabs @ SX3 @ SX4 @ veabs ) @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX1 )
| ( SX3 != SX0 ) )
| ( SX4
!= ( vabs @ SX6 @ SX7 @ SX8 ) ) )
| ( SX1 != SX6 )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5
= ( vabs @ SX6 @ SX7 @ SX8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(132,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)],[102]) ).
thf(133,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)],[103]) ).
thf(134,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)],[104]) ).
thf(135,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)],[108]) ).
thf(136,plain,
( ( visFreeVar @ sK1_Vx @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(137,plain,
( ( vtcheck @ ( vbind @ sK1_Vx @ sK2_SY116 @ sK3_SY121 ) @ ( vabs @ sK4_SY125 @ sK5_SY128 @ veabs ) @ sK6_SY130 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(138,plain,
! [SV1: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i,SY134: $i] :
( ( vabs @ SV1 @ SY131 @ SY132 )
!= ( vapp @ SY133 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV2: $i] :
( ( ! [SY135: $i,SY136: $i,SY137: $i,SY138: $i,SY139: $i] :
~ ( ~ ( ( ( vabs @ SV2 @ SY135 @ SY136 )
!= ( vabs @ SY137 @ SY138 @ SY139 ) )
| ~ ( ~ ~ ( ( SV2 != SY137 )
| ( SY135 != SY138 ) )
| ( SY136 != SY139 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SY137 )
| ( SY135 != SY138 ) )
| ( SY136 != SY139 ) )
| ( ( vabs @ SV2 @ SY135 @ SY136 )
= ( vabs @ SY137 @ SY138 @ SY139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(140,plain,
! [SV3: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i,SY143: $i] :
( ~ ~ ( ( SV3 != SY142 )
| ( SY140
!= ( vapp @ SY141 @ SY143 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY142 @ SY141 )
| ( visFreeVar @ SY142 @ SY143 ) )
| ( visFreeVar @ SV3 @ SY140 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SY140 )
| ( visFreeVar @ SY142 @ SY141 )
| ( visFreeVar @ SY142 @ SY143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV4: $i] :
( ( ! [SY144: $i,SY145: $i,SY146: $i] :
( ~ ~ ( ( SV4 != SY146 )
| ( SY144
!= ( vvar @ SY145 ) ) )
| ~ ( ~ ( ( SY145 != SY146 )
| ( visFreeVar @ SV4 @ SY144 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SY144 )
| ( SY145 = SY146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV5: $i] :
( ( ! [SY147: $i,SY148: $i,SY149: $i,SY150: $i,SY151: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY149 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SY149 @ SY150 @ veabs ) ) )
| ~ ( vtcheck @ SY148 @ ( vabs @ SY149 @ SY150 @ veabs ) @ SY151 ) )
| ( vtcheck @ ( vbind @ SV5 @ SY147 @ SY148 ) @ ( vabs @ SY149 @ SY150 @ veabs ) @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV6: $i] :
( ( ! [SY152: $i,SY153: $i,SY154: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SY153 @ veabs @ SY154 ) )
| ( vtcheck @ ( vbind @ SV6 @ SY152 @ SY153 ) @ veabs @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(144,plain,
! [SV7: $i] :
( ( ! [SY155: $i,SY156: $i,SY157: $i,SY158: $i,SY159: $i,SY160: $i,SY161: $i,SY162: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY160 )
| ( SY155 != SY161 ) )
| ( SY156
!= ( vabs @ SY158 @ SY159 @ SY162 ) ) )
| ~ ~ ( ~ ( ( SY160 != SY158 ) )
| ~ ~ ( visFreeVar @ SY158 @ SY161 ) )
| ( SY157
!= ( vsubst @ SV7 @ SY155 @ SY156 ) )
| ( SY157
= ( vabs @ SY158 @ SY159 @ ( vsubst @ SY160 @ SY161 @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV8: $i] :
( ( ! [SY163: $i] :
( ( ( vgensym @ SY163 )
!= SV8 )
| ~ ( visFreeVar @ SV8 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV9: $i] :
( ( ! [SY164: $i,SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ( SY164 != SY167 )
| ( SY165
!= ( vabs @ SY166 @ SV9 @ SY168 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY166 != SY167 ) )
| ~ ( visFreeVar @ SY167 @ SY168 ) )
| ( visFreeVar @ SY164 @ SY165 ) )
| ~ ( ~ ( visFreeVar @ SY164 @ SY165 )
| ~ ( ~ ( ( SY166 != SY167 ) )
| ~ ( visFreeVar @ SY167 @ SY168 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV10: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i,SY173: $i] :
~ ( ~ ( ( ( vbind @ SV10 @ SY169 @ SY170 )
!= ( vbind @ SY171 @ SY172 @ SY173 ) )
| ~ ( ~ ~ ( ( SV10 != SY171 )
| ( SY169 != SY172 ) )
| ( SY170 != SY173 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SY171 )
| ( SY169 != SY172 ) )
| ( SY170 != SY173 ) )
| ( ( vbind @ SV10 @ SY169 @ SY170 )
= ( vbind @ SY171 @ SY172 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(148,plain,
! [SV11: $i] :
( ( ! [SY174: $i,SY175: $i,SY176: $i,SY177: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SY176 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SY174 @ SY175 ) @ SY176 @ SY177 ) )
| ( vtcheck @ SY175 @ SY176 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(149,plain,
! [SV12: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i] :
( ( vvar @ SV12 )
!= ( vabs @ SY178 @ SY179 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(150,plain,
! [SV13: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i] :
( ( SY183
!= ( vabs @ SV13 @ SY181 @ SY182 ) )
| ( visValue @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(151,plain,
! [SV14: $i] :
( ( ! [SY184: $i,SY185: $i] :
( vempty
!= ( vbind @ SV14 @ SY184 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(152,plain,
! [SV15: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i,SY189: $i,SY190: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SY188 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SY188 @ SY189 @ veabs ) ) )
| ~ ( vtcheck @ SY187 @ ( vabs @ SY188 @ SY189 @ veabs ) @ SY190 ) )
| ( vtcheck @ ( vbind @ SV15 @ SY186 @ SY187 ) @ ( vabs @ SY188 @ SY189 @ veabs ) @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(153,plain,
! [SV16: $i] :
( ( ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i,SY195: $i,SY196: $i,SY197: $i,SY198: $i] :
( ~ ~ ( ~ ~ ( ( SY192 != SY191 )
| ( SY193 != SV16 ) )
| ( SY194
!= ( vabs @ SY196 @ SY197 @ SY198 ) ) )
| ( SY191 != SY196 )
| ( SY195
!= ( vsubst @ SY192 @ SY193 @ SY194 ) )
| ( SY195
= ( vabs @ SY196 @ SY197 @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(154,plain,
! [SV17: $i] :
( ( ! [SY199: $i,SY200: $i,SY201: $i,SY202: $i,SY203: $i,SY204: $i] :
( ~ ~ ( ( SY200 != SY203 )
| ( SY201
!= ( vbind @ SY199 @ SV17 @ SY204 ) ) )
| ~ ( ( SY203 != SY199 ) )
| ( SY202
!= ( vlookup @ SY200 @ SY201 ) )
| ( SY202
= ( vlookup @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(155,plain,
! [SV18: $i] :
( ( ! [SY205: $i,SY206: $i,SY207: $i,SY208: $i,SY209: $i,SY210: $i] :
( ~ ~ ( ( SY206 != SV18 )
| ~ ( vtcheck @ ( vbind @ SY206 @ SY207 @ ( vbind @ SV18 @ SY205 @ SY208 ) ) @ SY209 @ SY210 ) )
| ( vtcheck @ ( vbind @ SY206 @ SY207 @ SY208 ) @ SY209 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(156,plain,
! [SV19: $i] :
( ( ! [SY211: $i,SY212: $i,SY213: $i,SY214: $i,SY215: $i,SY216: $i] :
( ~ ~ ( ~ ( ( SY212 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SY212 @ SY213 @ ( vbind @ SV19 @ SY211 @ SY214 ) ) @ SY215 @ SY216 ) )
| ( vtcheck @ ( vbind @ SV19 @ SY211 @ ( vbind @ SY212 @ SY213 @ SY214 ) ) @ SY215 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(157,plain,
! [SV20: $i] :
( ( ! [SY217: $i,SY218: $i,SY219: $i,SY220: $i] :
( ~ ( vtcheck @ ( vbind @ SY217 @ SY219 @ SV20 ) @ SY218 @ SY220 )
| ( vtcheck @ SV20 @ ( vabs @ SY217 @ SY219 @ SY218 ) @ ( varrow @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(158,plain,
! [SV21: $i,SV1: $i] :
( ( ! [SY221: $i,SY222: $i,SY223: $i] :
( ( vabs @ SV1 @ SV21 @ SY221 )
!= ( vapp @ SY222 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(159,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i,SY227: $i] :
~ ( ~ ( ( ( vabs @ SV2 @ SV22 @ SY224 )
!= ( vabs @ SY225 @ SY226 @ SY227 ) )
| ~ ( ~ ~ ( ( SV2 != SY225 )
| ( SV22 != SY226 ) )
| ( SY224 != SY227 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SY225 )
| ( SV22 != SY226 ) )
| ( SY224 != SY227 ) )
| ( ( vabs @ SV2 @ SV22 @ SY224 )
= ( vabs @ SY225 @ SY226 @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(160,plain,
! [SV23: $i,SV3: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ( SV3 != SY229 )
| ( SV23
!= ( vapp @ SY228 @ SY230 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY229 @ SY228 )
| ( visFreeVar @ SY229 @ SY230 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SY229 @ SY228 )
| ( visFreeVar @ SY229 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(161,plain,
! [SV24: $i,SV4: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ~ ~ ( ( SV4 != SY232 )
| ( SV24
!= ( vvar @ SY231 ) ) )
| ~ ( ~ ( ( SY231 != SY232 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SY231 = SY232 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(162,plain,
! [SV25: $i,SV5: $i] :
( ( ! [SY233: $i,SY234: $i,SY235: $i,SY236: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY234 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SY234 @ SY235 @ veabs ) ) )
| ~ ( vtcheck @ SY233 @ ( vabs @ SY234 @ SY235 @ veabs ) @ SY236 ) )
| ( vtcheck @ ( vbind @ SV5 @ SV25 @ SY233 ) @ ( vabs @ SY234 @ SY235 @ veabs ) @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV26: $i,SV6: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SY237 @ veabs @ SY238 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV26 @ SY237 ) @ veabs @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
! [SV27: $i,SV7: $i] :
( ( ! [SY239: $i,SY240: $i,SY241: $i,SY242: $i,SY243: $i,SY244: $i,SY245: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY243 )
| ( SV27 != SY244 ) )
| ( SY239
!= ( vabs @ SY241 @ SY242 @ SY245 ) ) )
| ~ ~ ( ~ ( ( SY243 != SY241 ) )
| ~ ~ ( visFreeVar @ SY241 @ SY244 ) )
| ( SY240
!= ( vsubst @ SV7 @ SV27 @ SY239 ) )
| ( SY240
= ( vabs @ SY241 @ SY242 @ ( vsubst @ SY243 @ SY244 @ SY245 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(165,plain,
! [SV8: $i,SV28: $i] :
( ( ( ( vgensym @ SV28 )
!= SV8 )
| ~ ( visFreeVar @ SV8 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(166,plain,
! [SV9: $i,SV29: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i,SY249: $i] :
( ~ ~ ( ( SV29 != SY248 )
| ( SY246
!= ( vabs @ SY247 @ SV9 @ SY249 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY247 != SY248 ) )
| ~ ( visFreeVar @ SY248 @ SY249 ) )
| ( visFreeVar @ SV29 @ SY246 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SY246 )
| ~ ( ~ ( ( SY247 != SY248 ) )
| ~ ( visFreeVar @ SY248 @ SY249 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(167,plain,
! [SV30: $i,SV10: $i] :
( ( ! [SY250: $i,SY251: $i,SY252: $i,SY253: $i] :
~ ( ~ ( ( ( vbind @ SV10 @ SV30 @ SY250 )
!= ( vbind @ SY251 @ SY252 @ SY253 ) )
| ~ ( ~ ~ ( ( SV10 != SY251 )
| ( SV30 != SY252 ) )
| ( SY250 != SY253 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SY251 )
| ( SV30 != SY252 ) )
| ( SY250 != SY253 ) )
| ( ( vbind @ SV10 @ SV30 @ SY250 )
= ( vbind @ SY251 @ SY252 @ SY253 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(168,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY254: $i,SY255: $i,SY256: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SY255 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SY254 ) @ SY255 @ SY256 ) )
| ( vtcheck @ SY254 @ SY255 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(169,plain,
! [SV32: $i,SV12: $i] :
( ( ! [SY257: $i,SY258: $i] :
( ( vvar @ SV12 )
!= ( vabs @ SV32 @ SY257 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(170,plain,
! [SV33: $i,SV13: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ( SY260
!= ( vabs @ SV13 @ SV33 @ SY259 ) )
| ( visValue @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(171,plain,
! [SV34: $i,SV14: $i] :
( ( ! [SY261: $i] :
( vempty
!= ( vbind @ SV14 @ SV34 @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(172,plain,
! [SV35: $i,SV15: $i] :
( ( ! [SY262: $i,SY263: $i,SY264: $i,SY265: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SY263 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SY263 @ SY264 @ veabs ) ) )
| ~ ( vtcheck @ SY262 @ ( vabs @ SY263 @ SY264 @ veabs ) @ SY265 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV35 @ SY262 ) @ ( vabs @ SY263 @ SY264 @ veabs ) @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(173,plain,
! [SV16: $i,SV36: $i] :
( ( ! [SY266: $i,SY267: $i,SY268: $i,SY269: $i,SY270: $i,SY271: $i,SY272: $i] :
( ~ ~ ( ~ ~ ( ( SY266 != SV36 )
| ( SY267 != SV16 ) )
| ( SY268
!= ( vabs @ SY270 @ SY271 @ SY272 ) ) )
| ( SV36 != SY270 )
| ( SY269
!= ( vsubst @ SY266 @ SY267 @ SY268 ) )
| ( SY269
= ( vabs @ SY270 @ SY271 @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(174,plain,
! [SV17: $i,SV37: $i] :
( ( ! [SY273: $i,SY274: $i,SY275: $i,SY276: $i,SY277: $i] :
( ~ ~ ( ( SY273 != SY276 )
| ( SY274
!= ( vbind @ SV37 @ SV17 @ SY277 ) ) )
| ~ ( ( SY276 != SV37 ) )
| ( SY275
!= ( vlookup @ SY273 @ SY274 ) )
| ( SY275
= ( vlookup @ SY276 @ SY277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(175,plain,
! [SV38: $i,SV18: $i] :
( ( ! [SY278: $i,SY279: $i,SY280: $i,SY281: $i,SY282: $i] :
( ~ ~ ( ( SY278 != SV18 )
| ~ ( vtcheck @ ( vbind @ SY278 @ SY279 @ ( vbind @ SV18 @ SV38 @ SY280 ) ) @ SY281 @ SY282 ) )
| ( vtcheck @ ( vbind @ SY278 @ SY279 @ SY280 ) @ SY281 @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(176,plain,
! [SV39: $i,SV19: $i] :
( ( ! [SY283: $i,SY284: $i,SY285: $i,SY286: $i,SY287: $i] :
( ~ ~ ( ~ ( ( SY283 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SY283 @ SY284 @ ( vbind @ SV19 @ SV39 @ SY285 ) ) @ SY286 @ SY287 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SY283 @ SY284 @ SY285 ) ) @ SY286 @ SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(177,plain,
! [SV20: $i,SV40: $i] :
( ( ! [SY288: $i,SY289: $i,SY290: $i] :
( ~ ( vtcheck @ ( vbind @ SV40 @ SY289 @ SV20 ) @ SY288 @ SY290 )
| ( vtcheck @ SV20 @ ( vabs @ SV40 @ SY289 @ SY288 ) @ ( varrow @ SY289 @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(178,plain,
! [SV41: $i,SV21: $i,SV1: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ( vabs @ SV1 @ SV21 @ SV41 )
!= ( vapp @ SY291 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(179,plain,
! [SV42: $i,SV22: $i,SV2: $i] :
( ( ! [SY293: $i,SY294: $i,SY295: $i] :
~ ( ~ ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SY293 @ SY294 @ SY295 ) )
| ~ ( ~ ~ ( ( SV2 != SY293 )
| ( SV22 != SY294 ) )
| ( SV42 != SY295 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SY293 )
| ( SV22 != SY294 ) )
| ( SV42 != SY295 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SY293 @ SY294 @ SY295 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(180,plain,
! [SV43: $i,SV23: $i,SV3: $i] :
( ( ! [SY296: $i,SY297: $i] :
( ~ ~ ( ( SV3 != SY296 )
| ( SV23
!= ( vapp @ SV43 @ SY297 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY296 @ SV43 )
| ( visFreeVar @ SY296 @ SY297 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SY296 @ SV43 )
| ( visFreeVar @ SY296 @ SY297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(181,plain,
! [SV44: $i,SV24: $i,SV4: $i] :
( ( ! [SY298: $i] :
( ~ ~ ( ( SV4 != SY298 )
| ( SV24
!= ( vvar @ SV44 ) ) )
| ~ ( ~ ( ( SV44 != SY298 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SY298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(182,plain,
! [SV25: $i,SV45: $i,SV5: $i] :
( ( ! [SY299: $i,SY300: $i,SY301: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY299 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SY299 @ SY300 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SY299 @ SY300 @ veabs ) @ SY301 ) )
| ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SY299 @ SY300 @ veabs ) @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV26: $i,SV46: $i,SV6: $i] :
( ( ! [SY302: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SV46 @ veabs @ SY302 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(184,plain,
! [SV47: $i,SV27: $i,SV7: $i] :
( ( ! [SY303: $i,SY304: $i,SY305: $i,SY306: $i,SY307: $i,SY308: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY306 )
| ( SV27 != SY307 ) )
| ( SV47
!= ( vabs @ SY304 @ SY305 @ SY308 ) ) )
| ~ ~ ( ~ ( ( SY306 != SY304 ) )
| ~ ~ ( visFreeVar @ SY304 @ SY307 ) )
| ( SY303
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SY303
= ( vabs @ SY304 @ SY305 @ ( vsubst @ SY306 @ SY307 @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(185,plain,
! [SV8: $i,SV28: $i] :
( ( ( ( vgensym @ SV28 )
!= SV8 )
= $true )
| ( ( ~ ( visFreeVar @ SV8 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(186,plain,
! [SV9: $i,SV48: $i,SV29: $i] :
( ( ! [SY309: $i,SY310: $i,SY311: $i] :
( ~ ~ ( ( SV29 != SY310 )
| ( SV48
!= ( vabs @ SY309 @ SV9 @ SY311 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY309 != SY310 ) )
| ~ ( visFreeVar @ SY310 @ SY311 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SY309 != SY310 ) )
| ~ ( visFreeVar @ SY310 @ SY311 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(187,plain,
! [SV49: $i,SV30: $i,SV10: $i] :
( ( ! [SY312: $i,SY313: $i,SY314: $i] :
~ ( ~ ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SY312 @ SY313 @ SY314 ) )
| ~ ( ~ ~ ( ( SV10 != SY312 )
| ( SV30 != SY313 ) )
| ( SV49 != SY314 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SY312 )
| ( SV30 != SY313 ) )
| ( SV49 != SY314 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SY312 @ SY313 @ SY314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(188,plain,
! [SV50: $i,SV31: $i,SV11: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SY315 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SY315 @ SY316 ) )
| ( vtcheck @ SV50 @ SY315 @ SY316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(189,plain,
! [SV51: $i,SV32: $i,SV12: $i] :
( ( ! [SY317: $i] :
( ( vvar @ SV12 )
!= ( vabs @ SV32 @ SV51 @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(190,plain,
! [SV52: $i,SV33: $i,SV13: $i] :
( ( ! [SY318: $i] :
( ( SY318
!= ( vabs @ SV13 @ SV33 @ SV52 ) )
| ( visValue @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(191,plain,
! [SV53: $i,SV34: $i,SV14: $i] :
( ( vempty
!= ( vbind @ SV14 @ SV34 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(192,plain,
! [SV35: $i,SV54: $i,SV15: $i] :
( ( ! [SY319: $i,SY320: $i,SY321: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SY319 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SY319 @ SY320 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SY319 @ SY320 @ veabs ) @ SY321 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SY319 @ SY320 @ veabs ) @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(193,plain,
! [SV16: $i,SV36: $i,SV55: $i] :
( ( ! [SY322: $i,SY323: $i,SY324: $i,SY325: $i,SY326: $i,SY327: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SY322 != SV16 ) )
| ( SY323
!= ( vabs @ SY325 @ SY326 @ SY327 ) ) )
| ( SV36 != SY325 )
| ( SY324
!= ( vsubst @ SV55 @ SY322 @ SY323 ) )
| ( SY324
= ( vabs @ SY325 @ SY326 @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(194,plain,
! [SV17: $i,SV37: $i,SV56: $i] :
( ( ! [SY328: $i,SY329: $i,SY330: $i,SY331: $i] :
( ~ ~ ( ( SV56 != SY330 )
| ( SY328
!= ( vbind @ SV37 @ SV17 @ SY331 ) ) )
| ~ ( ( SY330 != SV37 ) )
| ( SY329
!= ( vlookup @ SV56 @ SY328 ) )
| ( SY329
= ( vlookup @ SY330 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(195,plain,
! [SV38: $i,SV18: $i,SV57: $i] :
( ( ! [SY332: $i,SY333: $i,SY334: $i,SY335: $i] :
( ~ ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SY332 @ ( vbind @ SV18 @ SV38 @ SY333 ) ) @ SY334 @ SY335 ) )
| ( vtcheck @ ( vbind @ SV57 @ SY332 @ SY333 ) @ SY334 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(196,plain,
! [SV39: $i,SV19: $i,SV58: $i] :
( ( ! [SY336: $i,SY337: $i,SY338: $i,SY339: $i] :
( ~ ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SY336 @ ( vbind @ SV19 @ SV39 @ SY337 ) ) @ SY338 @ SY339 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SY336 @ SY337 ) ) @ SY338 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(197,plain,
! [SV59: $i,SV20: $i,SV40: $i] :
( ( ! [SY340: $i,SY341: $i] :
( ~ ( vtcheck @ ( vbind @ SV40 @ SY340 @ SV20 ) @ SV59 @ SY341 )
| ( vtcheck @ SV20 @ ( vabs @ SV40 @ SY340 @ SV59 ) @ ( varrow @ SY340 @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(198,plain,
! [SV60: $i,SV41: $i,SV21: $i,SV1: $i] :
( ( ! [SY342: $i] :
( ( vabs @ SV1 @ SV21 @ SV41 )
!= ( vapp @ SV60 @ SY342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(199,plain,
! [SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ! [SY343: $i,SY344: $i] :
~ ( ~ ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SY343 @ SY344 ) )
| ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SY343 ) )
| ( SV42 != SY344 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SY343 ) )
| ( SV42 != SY344 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SY343 @ SY344 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(200,plain,
! [SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ! [SY345: $i] :
( ~ ~ ( ( SV3 != SV62 )
| ( SV23
!= ( vapp @ SV43 @ SY345 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SY345 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SY345 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(201,plain,
! [SV44: $i,SV24: $i,SV63: $i,SV4: $i] :
( ( ~ ~ ( ( SV4 != SV63 )
| ( SV24
!= ( vvar @ SV44 ) ) )
| ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(202,plain,
! [SV25: $i,SV45: $i,SV64: $i,SV5: $i] :
( ( ! [SY346: $i,SY347: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SY346 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SY346 @ veabs ) @ SY347 ) )
| ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SY346 @ veabs ) @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(203,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SV46 @ veabs @ SV65 ) )
| ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(204,plain,
! [SV66: $i,SV47: $i,SV27: $i,SV7: $i] :
( ( ! [SY348: $i,SY349: $i,SY350: $i,SY351: $i,SY352: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY350 )
| ( SV27 != SY351 ) )
| ( SV47
!= ( vabs @ SY348 @ SY349 @ SY352 ) ) )
| ~ ~ ( ~ ( ( SY350 != SY348 ) )
| ~ ~ ( visFreeVar @ SY348 @ SY351 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SY348 @ SY349 @ ( vsubst @ SY350 @ SY351 @ SY352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(205,plain,
! [SV8: $i,SV28: $i] :
( ( ( ( vgensym @ SV28 )
= SV8 )
= $false )
| ( ( ~ ( visFreeVar @ SV8 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(206,plain,
! [SV9: $i,SV67: $i,SV48: $i,SV29: $i] :
( ( ! [SY353: $i,SY354: $i] :
( ~ ~ ( ( SV29 != SY353 )
| ( SV48
!= ( vabs @ SV67 @ SV9 @ SY354 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SY353 ) )
| ~ ( visFreeVar @ SY353 @ SY354 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SY353 ) )
| ~ ( visFreeVar @ SY353 @ SY354 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(207,plain,
! [SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ! [SY355: $i,SY356: $i] :
~ ( ~ ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SY355 @ SY356 ) )
| ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SY355 ) )
| ( SV49 != SY356 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SY355 ) )
| ( SV49 != SY356 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SY355 @ SY356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(208,plain,
! [SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ! [SY357: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SY357 ) )
| ( vtcheck @ SV50 @ SV69 @ SY357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(209,plain,
! [SV70: $i,SV51: $i,SV32: $i,SV12: $i] :
( ( ( vvar @ SV12 )
!= ( vabs @ SV32 @ SV51 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV52: $i,SV33: $i,SV13: $i,SV71: $i] :
( ( ( SV71
!= ( vabs @ SV13 @ SV33 @ SV52 ) )
| ( visValue @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV53: $i,SV34: $i,SV14: $i] :
( ( vempty
= ( vbind @ SV14 @ SV34 @ SV53 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(212,plain,
! [SV35: $i,SV54: $i,SV72: $i,SV15: $i] :
( ( ! [SY358: $i,SY359: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SY358 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SY358 @ veabs ) @ SY359 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SY358 @ veabs ) @ SY359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(213,plain,
! [SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ! [SY360: $i,SY361: $i,SY362: $i,SY363: $i,SY364: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SY360
!= ( vabs @ SY362 @ SY363 @ SY364 ) ) )
| ( SV36 != SY362 )
| ( SY361
!= ( vsubst @ SV55 @ SV73 @ SY360 ) )
| ( SY361
= ( vabs @ SY362 @ SY363 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(214,plain,
! [SV17: $i,SV37: $i,SV74: $i,SV56: $i] :
( ( ! [SY365: $i,SY366: $i,SY367: $i] :
( ~ ~ ( ( SV56 != SY366 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SY367 ) ) )
| ~ ( ( SY366 != SV37 ) )
| ( SY365
!= ( vlookup @ SV56 @ SV74 ) )
| ( SY365
= ( vlookup @ SY366 @ SY367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(215,plain,
! [SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ! [SY368: $i,SY369: $i,SY370: $i] :
( ~ ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SY368 ) ) @ SY369 @ SY370 ) )
| ( vtcheck @ ( vbind @ SV57 @ SV75 @ SY368 ) @ SY369 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(216,plain,
! [SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ! [SY371: $i,SY372: $i,SY373: $i] :
( ~ ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SY371 ) ) @ SY372 @ SY373 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SY371 ) ) @ SY372 @ SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(217,plain,
! [SV59: $i,SV20: $i,SV77: $i,SV40: $i] :
( ( ! [SY374: $i] :
( ~ ( vtcheck @ ( vbind @ SV40 @ SV77 @ SV20 ) @ SV59 @ SY374 )
| ( vtcheck @ SV20 @ ( vabs @ SV40 @ SV77 @ SV59 ) @ ( varrow @ SV77 @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(218,plain,
! [SV78: $i,SV60: $i,SV41: $i,SV21: $i,SV1: $i] :
( ( ( vabs @ SV1 @ SV21 @ SV41 )
!= ( vapp @ SV60 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(219,plain,
! [SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ! [SY375: $i] :
~ ( ~ ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SV79 @ SY375 ) )
| ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SY375 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SY375 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SY375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(220,plain,
! [SV80: $i,SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ~ ~ ( ( SV3 != SV62 )
| ( SV23
!= ( vapp @ SV43 @ SV80 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV44: $i,SV24: $i,SV63: $i,SV4: $i] :
( ( ( ~ ~ ( ( SV4 != SV63 )
| ( SV24
!= ( vvar @ SV44 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV25: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ! [SY376: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SY376 ) )
| ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(223,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SV46 @ veabs @ SV65 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(224,plain,
! [SV66: $i,SV82: $i,SV47: $i,SV27: $i,SV7: $i] :
( ( ! [SY377: $i,SY378: $i,SY379: $i,SY380: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY378 )
| ( SV27 != SY379 ) )
| ( SV47
!= ( vabs @ SV82 @ SY377 @ SY380 ) ) )
| ~ ~ ( ~ ( ( SY378 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SY379 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SY377 @ ( vsubst @ SY378 @ SY379 @ SY380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(225,plain,
! [SV28: $i,SV8: $i] :
( ( ( visFreeVar @ SV8 @ SV28 )
= $false )
| ( ( ( vgensym @ SV28 )
= SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(226,plain,
! [SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ! [SY381: $i] :
( ~ ~ ( ( SV29 != SV83 )
| ( SV48
!= ( vabs @ SV67 @ SV9 @ SY381 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SY381 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SY381 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(227,plain,
! [SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ! [SY382: $i] :
~ ( ~ ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SV84 @ SY382 ) )
| ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SY382 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SY382 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SY382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(228,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) )
| ( vtcheck @ SV50 @ SV69 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(229,plain,
! [SV70: $i,SV51: $i,SV32: $i,SV12: $i] :
( ( ( vvar @ SV12 )
= ( vabs @ SV32 @ SV51 @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(230,plain,
! [SV52: $i,SV33: $i,SV13: $i,SV71: $i] :
( ( ( SV71
!= ( vabs @ SV13 @ SV33 @ SV52 ) )
= $true )
| ( ( visValue @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(231,plain,
! [SV35: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ! [SY383: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SY383 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(232,plain,
! [SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ! [SY384: $i,SY385: $i,SY386: $i,SY387: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SY385 @ SY386 @ SY387 ) ) )
| ( SV36 != SY385 )
| ( SY384
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SY384
= ( vabs @ SY385 @ SY386 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(233,plain,
! [SV88: $i,SV17: $i,SV37: $i,SV74: $i,SV56: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ~ ( ( SV56 != SY388 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SY389 ) ) )
| ~ ( ( SY388 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SY388 @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(234,plain,
! [SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ! [SY390: $i,SY391: $i] :
( ~ ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SY390 @ SY391 ) )
| ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SY390 @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(235,plain,
! [SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ! [SY392: $i,SY393: $i] :
( ~ ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SY392 @ SY393 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SY392 @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(236,plain,
! [SV91: $i,SV59: $i,SV20: $i,SV77: $i,SV40: $i] :
( ( ~ ( vtcheck @ ( vbind @ SV40 @ SV77 @ SV20 ) @ SV59 @ SV91 )
| ( vtcheck @ SV20 @ ( vabs @ SV40 @ SV77 @ SV59 ) @ ( varrow @ SV77 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(237,plain,
! [SV78: $i,SV60: $i,SV41: $i,SV21: $i,SV1: $i] :
( ( ( vabs @ SV1 @ SV21 @ SV41 )
= ( vapp @ SV60 @ SV78 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(238,plain,
! [SV92: $i,SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ~ ( ~ ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SV79 @ SV92 ) )
| ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(239,plain,
! [SV80: $i,SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV62 )
| ( SV23
!= ( vapp @ SV43 @ SV80 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(240,plain,
! [SV44: $i,SV24: $i,SV63: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != SV63 )
| ( SV24
!= ( vvar @ SV44 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(241,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
| ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(242,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SV46 @ veabs @ SV65 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(243,plain,
! [SV66: $i,SV94: $i,SV82: $i,SV47: $i,SV27: $i,SV7: $i] :
( ( ! [SY394: $i,SY395: $i,SY396: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY394 )
| ( SV27 != SY395 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SY396 ) ) )
| ~ ~ ( ~ ( ( SY394 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SY395 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SY394 @ SY395 @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(244,plain,
! [SV95: $i,SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ~ ~ ( ( SV29 != SV83 )
| ( SV48
!= ( vabs @ SV67 @ SV9 @ SV95 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(245,plain,
! [SV96: $i,SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ~ ( ~ ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SV84 @ SV96 ) )
| ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(246,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) ) )
= $true )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(247,plain,
! [SV52: $i,SV33: $i,SV13: $i,SV71: $i] :
( ( ( SV71
= ( vabs @ SV13 @ SV33 @ SV52 ) )
= $false )
| ( ( visValue @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(248,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
| ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(249,plain,
! [SV98: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ! [SY397: $i,SY398: $i,SY399: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SY397 @ SY398 @ SY399 ) ) )
| ( SV36 != SY397 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SY397 @ SY398 @ SY399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(250,plain,
! [SV88: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ! [SY400: $i] :
( ~ ~ ( ( SV56 != SV99 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SY400 ) ) )
| ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SY400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(251,plain,
! [SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ! [SY401: $i] :
( ~ ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SY401 ) )
| ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(252,plain,
! [SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ! [SY402: $i] :
( ~ ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SY402 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SY402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(253,plain,
! [SV91: $i,SV59: $i,SV20: $i,SV77: $i,SV40: $i] :
( ( ( ~ ( vtcheck @ ( vbind @ SV40 @ SV77 @ SV20 ) @ SV59 @ SV91 ) )
= $true )
| ( ( vtcheck @ SV20 @ ( vabs @ SV40 @ SV77 @ SV59 ) @ ( varrow @ SV77 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(254,plain,
! [SV92: $i,SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ~ ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SV79 @ SV92 ) )
| ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(255,plain,
! [SV80: $i,SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV62 )
| ( SV23
!= ( vapp @ SV43 @ SV80 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(256,plain,
! [SV44: $i,SV24: $i,SV63: $i,SV4: $i] :
( ( ( ( SV4 != SV63 )
| ( SV24
!= ( vvar @ SV44 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(257,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(258,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ( ~ ~ ( visFreeVar @ SV6 @ veabs )
| ~ ( vtcheck @ SV46 @ veabs @ SV65 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(259,plain,
! [SV66: $i,SV94: $i,SV82: $i,SV47: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ! [SY403: $i,SY404: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SY403 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SY404 ) ) )
| ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SY403 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SY403 @ SY404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(260,plain,
! [SV95: $i,SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ( ~ ~ ( ( SV29 != SV83 )
| ( SV48
!= ( vabs @ SV67 @ SV9 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(261,plain,
! [SV96: $i,SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ~ ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SV84 @ SV96 ) )
| ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(262,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV11 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) ) )
= $false )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(263,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV98: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ! [SY405: $i,SY406: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SV103 @ SY405 @ SY406 ) ) )
| ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SY405 @ SY406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV88: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ~ ~ ( ( SV56 != SV99 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SV104 ) ) )
| ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(266,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ~ ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 ) )
| ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(267,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ~ ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) )
| ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(268,plain,
! [SV91: $i,SV59: $i,SV20: $i,SV77: $i,SV40: $i] :
( ( ( vtcheck @ ( vbind @ SV40 @ SV77 @ SV20 ) @ SV59 @ SV91 )
= $false )
| ( ( vtcheck @ SV20 @ ( vabs @ SV40 @ SV77 @ SV59 ) @ ( varrow @ SV77 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(269,plain,
! [SV92: $i,SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ~ ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SV79 @ SV92 ) )
| ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(270,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(271,plain,
! [SV80: $i,SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ( ( SV3 != SV62 )
| ( SV23
!= ( vapp @ SV43 @ SV80 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(272,plain,
! [SV44: $i,SV24: $i,SV63: $i,SV4: $i] :
( ( ( SV4 != SV63 )
= $true )
| ( ( SV24
!= ( vvar @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(273,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(274,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ( ~ ~ ( visFreeVar @ SV6 @ veabs ) )
= $true )
| ( ( ~ ( vtcheck @ SV46 @ veabs @ SV65 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(275,plain,
! [SV66: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ! [SY407: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SY407 ) ) )
| ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SY407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(276,plain,
! [SV95: $i,SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ( ~ ( ( SV29 != SV83 )
| ( SV48
!= ( vabs @ SV67 @ SV9 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(277,plain,
! [SV96: $i,SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ~ ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SV84 @ SV96 ) )
| ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(278,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(279,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ( visFreeVar @ SV11 @ SV69 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) )
= $true )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(280,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(281,plain,
! [SV98: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ! [SY408: $i] :
( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SV103 @ SV108 @ SY408 ) ) )
| ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SY408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(282,plain,
! [SV88: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ( ~ ~ ( ( SV56 != SV99 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SV104 ) ) ) )
= $true )
| ( ( ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(283,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ( ~ ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(284,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(285,plain,
! [SV92: $i,SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SV79 @ SV92 ) )
| ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(286,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) )
| ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(287,plain,
! [SV80: $i,SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ( SV3 != SV62 )
= $true )
| ( ( SV23
!= ( vapp @ SV43 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(288,plain,
! [SV44: $i,SV24: $i,SV63: $i,SV4: $i] :
( ( ( SV4 = SV63 )
= $false )
| ( ( SV24
!= ( vvar @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(289,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
| ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(290,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ( ~ ( visFreeVar @ SV6 @ veabs ) )
= $false )
| ( ( ~ ( vtcheck @ SV46 @ veabs @ SV65 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(291,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) ) )
| ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(292,plain,
! [SV95: $i,SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ( ( SV29 != SV83 )
| ( SV48
!= ( vabs @ SV67 @ SV9 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(293,plain,
! [SV96: $i,SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SV84 @ SV96 ) )
| ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(294,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) )
| ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(295,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ( ~ ~ ( visFreeVar @ SV11 @ SV69 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) )
= $true )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(296,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
| ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(297,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
| ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(298,plain,
! [SV88: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ( ~ ( ( SV56 != SV99 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SV104 ) ) ) )
= $false )
| ( ( ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(299,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ( ~ ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(300,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ( ~ ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(301,plain,
! [SV92: $i,SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ( ( vabs @ SV2 @ SV22 @ SV42 )
!= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(302,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(303,plain,
! [SV80: $i,SV43: $i,SV23: $i,SV62: $i,SV3: $i] :
( ( ( SV3 = SV62 )
= $false )
| ( ( SV23
!= ( vapp @ SV43 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(304,plain,
! [SV63: $i,SV4: $i,SV44: $i,SV24: $i] :
( ( ( SV24
= ( vvar @ SV44 ) )
= $false )
| ( ( SV4 = SV63 )
= $false )
| ( ( ~ ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(305,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(306,plain,
! [SV26: $i,SV65: $i,SV46: $i,SV6: $i] :
( ( ( visFreeVar @ SV6 @ veabs )
= $true )
| ( ( ~ ( vtcheck @ SV46 @ veabs @ SV65 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(307,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(308,plain,
! [SV95: $i,SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ( SV29 != SV83 )
= $true )
| ( ( SV48
!= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(309,plain,
! [SV96: $i,SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ( ( vbind @ SV10 @ SV30 @ SV49 )
!= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(310,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(311,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( visFreeVar @ SV11 @ SV69 ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) )
= $true )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(312,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(313,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) ) ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(314,plain,
! [SV88: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ( ( SV56 != SV99 )
| ( SV74
!= ( vbind @ SV37 @ SV17 @ SV104 ) ) )
= $true )
| ( ( ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(315,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ( ( SV57 != SV18 )
| ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(316,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != SV19 ) )
| ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(317,plain,
! [SV92: $i,SV79: $i,SV61: $i,SV42: $i,SV22: $i,SV2: $i] :
( ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(318,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) ) )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(319,plain,
! [SV62: $i,SV3: $i,SV80: $i,SV43: $i,SV23: $i] :
( ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false )
| ( ( SV3 = SV62 )
= $false )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(320,plain,
! [SV24: $i,SV4: $i,SV63: $i,SV44: $i] :
( ( ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) )
= $false )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(321,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) ) )
= $false )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(322,plain,
! [SV26: $i,SV6: $i,SV65: $i,SV46: $i] :
( ( ( vtcheck @ SV46 @ veabs @ SV65 )
= $false )
| ( ( visFreeVar @ SV6 @ veabs )
= $true )
| ( ( vtcheck @ ( vbind @ SV6 @ SV26 @ SV46 ) @ veabs @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(323,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(324,plain,
! [SV95: $i,SV9: $i,SV67: $i,SV48: $i,SV83: $i,SV29: $i] :
( ( ( SV29 = SV83 )
= $false )
| ( ( SV48
!= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(325,plain,
! [SV96: $i,SV84: $i,SV68: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(326,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) ) )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(327,plain,
! [SV85: $i,SV50: $i,SV31: $i,SV69: $i,SV11: $i] :
( ( ( visFreeVar @ SV11 @ SV69 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 ) )
= $true )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(328,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) ) )
= $false )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(329,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( ~ ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) ) ) )
= $false )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(330,plain,
! [SV88: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ( SV56 != SV99 )
= $true )
| ( ( SV74
!= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $true )
| ( ( ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(331,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ( SV57 != SV18 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(332,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != SV19 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(333,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(334,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
| ( SV42 != SV92 ) )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(335,plain,
! [SV23: $i,SV3: $i,SV80: $i,SV43: $i,SV62: $i] :
( ( ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) )
= $false )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(336,plain,
! [SV24: $i,SV4: $i,SV63: $i,SV44: $i] :
( ( ( ~ ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) ) )
= $false )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(337,plain,
! [SV63: $i,SV44: $i,SV24: $i,SV4: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) ) )
= $false )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(338,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ( SV5 != SV64 )
| ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(339,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) )
| ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(340,plain,
! [SV83: $i,SV29: $i,SV95: $i,SV9: $i,SV67: $i,SV48: $i] :
( ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(341,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(342,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
| ( SV49 != SV96 ) )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(343,plain,
! [SV85: $i,SV69: $i,SV50: $i,SV31: $i,SV11: $i] :
( ( ( vtcheck @ ( vbind @ SV11 @ SV31 @ SV50 ) @ SV69 @ SV85 )
= $false )
| ( ( visFreeVar @ SV11 @ SV69 )
= $true )
| ( ( vtcheck @ SV50 @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(344,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( ( SV15 != SV72 ) )
| ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(345,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
| ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(346,plain,
! [SV88: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i,SV99: $i,SV56: $i] :
( ( ( SV56 = SV99 )
= $false )
| ( ( SV74
!= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $true )
| ( ( ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(347,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV75: $i,SV18: $i,SV57: $i] :
( ( ( SV57 = SV18 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ( SV58 != SV19 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(349,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) ) )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(350,plain,
! [SV79: $i,SV61: $i,SV22: $i,SV2: $i,SV92: $i,SV42: $i] :
( ( ( SV42 != SV92 )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(351,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) ) )
= $true )
| ( ( SV42 != SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(352,plain,
! [SV23: $i,SV3: $i,SV80: $i,SV43: $i,SV62: $i] :
( ( ( ~ ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) ) )
= $false )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(353,plain,
! [SV80: $i,SV43: $i,SV62: $i,SV23: $i,SV3: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) )
= $false )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(354,plain,
! [SV24: $i,SV4: $i,SV63: $i,SV44: $i] :
( ( ( ( SV44 != SV63 )
| ( visFreeVar @ SV4 @ SV24 ) )
= $true )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(355,plain,
! [SV63: $i,SV44: $i,SV24: $i,SV4: $i] :
( ( ( ~ ( visFreeVar @ SV4 @ SV24 )
| ( SV44 = SV63 ) )
= $true )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(356,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( SV5 != SV64 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(357,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( ~ ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) ) )
= $true )
| ( ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(358,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
| ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(359,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) ) )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(360,plain,
! [SV84: $i,SV68: $i,SV30: $i,SV10: $i,SV96: $i,SV49: $i] :
( ( ( SV49 != SV96 )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(361,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) ) )
= $true )
| ( ( SV49 != SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(362,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( ( SV15 != SV72 ) ) )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(363,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( ~ ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) ) )
= $true )
| ( ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(364,plain,
! [SV88: $i,SV99: $i,SV56: $i,SV104: $i,SV17: $i,SV37: $i,SV74: $i] :
( ( ( SV74
= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $false )
| ( ( SV56 = SV99 )
= $false )
| ( ( ~ ( ( SV99 != SV37 ) )
| ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(365,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV38: $i,SV18: $i,SV75: $i,SV57: $i] :
( ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ ( vbind @ SV18 @ SV38 @ SV89 ) ) @ SV100 @ SV105 )
= $false )
| ( ( SV57 = SV18 )
= $false )
| ( ( vtcheck @ ( vbind @ SV57 @ SV75 @ SV89 ) @ SV100 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(366,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV76: $i,SV19: $i,SV58: $i] :
( ( ( SV58 = SV19 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(367,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) ) )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(368,plain,
! [SV79: $i,SV61: $i,SV22: $i,SV2: $i,SV92: $i,SV42: $i] :
( ( ( SV42 = SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(369,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ~ ( ( SV2 != SV61 )
| ( SV22 != SV79 ) ) )
= $false )
| ( ( SV42 != SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(370,plain,
! [SV23: $i,SV3: $i,SV80: $i,SV43: $i,SV62: $i] :
( ( ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
| ( visFreeVar @ SV3 @ SV23 ) )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(371,plain,
! [SV80: $i,SV43: $i,SV62: $i,SV23: $i,SV3: $i] :
( ( ( ~ ( visFreeVar @ SV3 @ SV23 )
| ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(372,plain,
! [SV24: $i,SV4: $i,SV63: $i,SV44: $i] :
( ( ( SV44 != SV63 )
= $true )
| ( ( visFreeVar @ SV4 @ SV24 )
= $true )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(373,plain,
! [SV63: $i,SV44: $i,SV24: $i,SV4: $i] :
( ( ( ~ ( visFreeVar @ SV4 @ SV24 ) )
= $true )
| ( ( SV44 = SV63 )
= $true )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(374,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( SV5 = SV64 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(375,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( ~ ( ( SV7 != SV102 )
| ( SV27 != SV107 ) ) )
= $false )
| ( ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(376,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) ) )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(377,plain,
! [SV9: $i,SV95: $i,SV83: $i,SV67: $i,SV48: $i,SV29: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) ) )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(378,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) ) )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(379,plain,
! [SV84: $i,SV68: $i,SV30: $i,SV10: $i,SV96: $i,SV49: $i] :
( ( ( SV49 = SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(380,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != SV68 )
| ( SV30 != SV84 ) ) )
= $false )
| ( ( SV49 != SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(381,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( SV15 != SV72 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(382,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( ~ ( ( SV55 != SV36 )
| ( SV73 != SV16 ) ) )
= $false )
| ( ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(383,plain,
! [SV17: $i,SV104: $i,SV74: $i,SV56: $i,SV88: $i,SV37: $i,SV99: $i] :
( ( ( ~ ( ( SV99 != SV37 ) ) )
= $true )
| ( ( ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true )
| ( ( SV56 = SV99 )
= $false )
| ( ( SV74
= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(384,plain,
! [SV106: $i,SV101: $i,SV90: $i,SV39: $i,SV19: $i,SV76: $i,SV58: $i] :
( ( ( vtcheck @ ( vbind @ SV58 @ SV76 @ ( vbind @ SV19 @ SV39 @ SV90 ) ) @ SV101 @ SV106 )
= $false )
| ( ( SV58 = SV19 )
= $true )
| ( ( vtcheck @ ( vbind @ SV19 @ SV39 @ ( vbind @ SV58 @ SV76 @ SV90 ) ) @ SV101 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(385,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(386,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( ( SV2 != SV61 )
| ( SV22 != SV79 ) )
= $true )
| ( ( SV42 != SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(387,plain,
! [SV23: $i,SV3: $i,SV80: $i,SV43: $i,SV62: $i] :
( ( ( ~ ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) ) )
= $true )
| ( ( visFreeVar @ SV3 @ SV23 )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(388,plain,
! [SV80: $i,SV43: $i,SV62: $i,SV23: $i,SV3: $i] :
( ( ( ~ ( visFreeVar @ SV3 @ SV23 ) )
= $true )
| ( ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(389,plain,
! [SV24: $i,SV4: $i,SV63: $i,SV44: $i] :
( ( ( SV44 = SV63 )
= $false )
| ( ( visFreeVar @ SV4 @ SV24 )
= $true )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(390,plain,
! [SV63: $i,SV44: $i,SV24: $i,SV4: $i] :
( ( ( visFreeVar @ SV4 @ SV24 )
= $false )
| ( ( SV44 = SV63 )
= $true )
| ( ( SV4 = SV63 )
= $false )
| ( ( SV24
= ( vvar @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(391,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( ~ ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) ) )
= $false )
| ( ( SV5 = SV64 )
= $false )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(392,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( ( SV7 != SV102 )
| ( SV27 != SV107 ) )
= $true )
| ( ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(393,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
| ( visFreeVar @ SV29 @ SV48 ) )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(394,plain,
! [SV9: $i,SV95: $i,SV83: $i,SV67: $i,SV48: $i,SV29: $i] :
( ( ( ~ ( visFreeVar @ SV29 @ SV48 )
| ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(395,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(396,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( ( SV10 != SV68 )
| ( SV30 != SV84 ) )
= $true )
| ( ( SV49 != SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(397,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( SV15 = SV72 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(398,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( ( SV55 != SV36 )
| ( SV73 != SV16 ) )
= $true )
| ( ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(399,plain,
! [SV17: $i,SV104: $i,SV74: $i,SV56: $i,SV88: $i,SV37: $i,SV99: $i] :
( ( ( SV99 != SV37 )
= $false )
| ( ( ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true )
| ( ( SV56 = SV99 )
= $false )
| ( ( SV74
= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(400,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( SV2 != SV61 )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(401,plain,
! [SV92: $i,SV61: $i,SV42: $i,SV2: $i,SV79: $i,SV22: $i] :
( ( ( SV22 != SV79 )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(402,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( SV2 != SV61 )
= $true )
| ( ( SV22 != SV79 )
= $true )
| ( ( SV42 != SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(403,plain,
! [SV23: $i,SV3: $i,SV80: $i,SV43: $i,SV62: $i] :
( ( ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
= $false )
| ( ( visFreeVar @ SV3 @ SV23 )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(404,plain,
! [SV80: $i,SV43: $i,SV62: $i,SV23: $i,SV3: $i] :
( ( ( visFreeVar @ SV3 @ SV23 )
= $false )
| ( ( ( visFreeVar @ SV62 @ SV43 )
| ( visFreeVar @ SV62 @ SV80 ) )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(405,plain,
! [SV25: $i,SV93: $i,SV45: $i,SV81: $i,SV64: $i,SV5: $i] :
( ( ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) )
= $true )
| ( ( SV5 = SV64 )
= $false )
| ( ( ~ ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(406,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( SV7 != SV102 )
= $true )
| ( ( SV27 != SV107 )
= $true )
| ( ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(407,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(408,plain,
! [SV9: $i,SV95: $i,SV83: $i,SV67: $i,SV48: $i,SV29: $i] :
( ( ( ~ ( visFreeVar @ SV29 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(409,plain,
! [SV96: $i,SV84: $i,SV49: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( SV10 != SV68 )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(410,plain,
! [SV96: $i,SV68: $i,SV49: $i,SV10: $i,SV84: $i,SV30: $i] :
( ( ( SV30 != SV84 )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(411,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( SV10 != SV68 )
= $true )
| ( ( SV30 != SV84 )
= $true )
| ( ( SV49 != SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(412,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) ) )
= $false )
| ( ( SV15 = SV72 )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(413,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( SV55 != SV36 )
= $true )
| ( ( SV73 != SV16 )
= $true )
| ( ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(414,plain,
! [SV17: $i,SV104: $i,SV74: $i,SV56: $i,SV88: $i,SV37: $i,SV99: $i] :
( ( ( SV99 = SV37 )
= $true )
| ( ( ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
| ( SV88
= ( vlookup @ SV99 @ SV104 ) ) )
= $true )
| ( ( SV56 = SV99 )
= $false )
| ( ( SV74
= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(415,plain,
! [SV92: $i,SV79: $i,SV42: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( SV2 = SV61 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(416,plain,
! [SV92: $i,SV61: $i,SV42: $i,SV2: $i,SV79: $i,SV22: $i] :
( ( ( SV22 = SV79 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(417,plain,
! [SV92: $i,SV42: $i,SV79: $i,SV22: $i,SV61: $i,SV2: $i] :
( ( ( SV2 = SV61 )
= $false )
| ( ( SV22 != SV79 )
= $true )
| ( ( SV42 != SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(418,plain,
! [SV80: $i,SV23: $i,SV3: $i,SV43: $i,SV62: $i] :
( ( ( visFreeVar @ SV62 @ SV43 )
= $false )
| ( ( visFreeVar @ SV3 @ SV23 )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(419,plain,
! [SV43: $i,SV23: $i,SV3: $i,SV80: $i,SV62: $i] :
( ( ( visFreeVar @ SV62 @ SV80 )
= $false )
| ( ( visFreeVar @ SV3 @ SV23 )
= $true )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(420,plain,
! [SV23: $i,SV3: $i,SV80: $i,SV43: $i,SV62: $i] :
( ( ( visFreeVar @ SV62 @ SV43 )
= $true )
| ( ( visFreeVar @ SV62 @ SV80 )
= $true )
| ( ( visFreeVar @ SV3 @ SV23 )
= $false )
| ( ( SV3 = SV62 )
= $false )
| ( ( SV23
= ( vapp @ SV43 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV25: $i,SV5: $i,SV93: $i,SV81: $i,SV64: $i,SV45: $i] :
( ( ( vtcheck @ SV45 @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $false )
| ( ( SV5 = SV64 )
= $false )
| ( ( visFreeVar @ SV5 @ ( vabs @ SV64 @ SV81 @ veabs ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV5 @ SV25 @ SV45 ) @ ( vabs @ SV64 @ SV81 @ veabs ) @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(422,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i] :
( ( ( SV7 = SV102 )
= $false )
| ( ( SV27 != SV107 )
= $true )
| ( ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(423,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) )
= $false )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(424,plain,
! [SV9: $i,SV95: $i,SV83: $i,SV67: $i,SV48: $i,SV29: $i] :
( ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( ~ ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) ) )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(425,plain,
! [SV96: $i,SV84: $i,SV49: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( SV10 = SV68 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(426,plain,
! [SV96: $i,SV68: $i,SV49: $i,SV10: $i,SV84: $i,SV30: $i] :
( ( ( SV30 = SV84 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(427,plain,
! [SV96: $i,SV49: $i,SV84: $i,SV30: $i,SV68: $i,SV10: $i] :
( ( ( SV10 = SV68 )
= $false )
| ( ( SV30 != SV84 )
= $true )
| ( ( SV49 != SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(428,plain,
! [SV35: $i,SV97: $i,SV54: $i,SV86: $i,SV72: $i,SV15: $i] :
( ( ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) )
= $true )
| ( ( SV15 = SV72 )
= $true )
| ( ( ~ ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(429,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i] :
( ( ( SV55 = SV36 )
= $false )
| ( ( SV73 != SV16 )
= $true )
| ( ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(430,plain,
! [SV17: $i,SV37: $i,SV104: $i,SV99: $i,SV74: $i,SV56: $i,SV88: $i] :
( ( ( SV88
!= ( vlookup @ SV56 @ SV74 ) )
= $true )
| ( ( SV88
= ( vlookup @ SV99 @ SV104 ) )
= $true )
| ( ( SV99 = SV37 )
= $true )
| ( ( SV56 = SV99 )
= $false )
| ( ( SV74
= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(431,plain,
! [SV92: $i,SV42: $i,SV61: $i,SV2: $i,SV79: $i,SV22: $i] :
( ( ( SV22 = SV79 )
= $false )
| ( ( SV2 = SV61 )
= $false )
| ( ( SV42 != SV92 )
= $true )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV66: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i,SV102: $i,SV7: $i,SV107: $i,SV27: $i] :
( ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
!= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(433,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(434,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV83 ) )
| ~ ( visFreeVar @ SV83 @ SV95 ) )
= $false )
| ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(435,plain,
! [SV96: $i,SV49: $i,SV68: $i,SV10: $i,SV84: $i,SV30: $i] :
( ( ( SV30 = SV84 )
= $false )
| ( ( SV10 = SV68 )
= $false )
| ( ( SV49 != SV96 )
= $true )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(436,plain,
! [SV35: $i,SV15: $i,SV97: $i,SV86: $i,SV72: $i,SV54: $i] :
( ( ( vtcheck @ SV54 @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $false )
| ( ( SV15 = SV72 )
= $true )
| ( ( visFreeVar @ SV15 @ ( vabs @ SV72 @ SV86 @ veabs ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV15 @ SV35 @ SV54 ) @ ( vabs @ SV72 @ SV86 @ veabs ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(437,plain,
! [SV98: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV36: $i,SV55: $i,SV16: $i,SV73: $i] :
( ( ( SV73 = SV16 )
= $false )
| ( ( SV55 = SV36 )
= $false )
| ( ( SV87
!= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(438,plain,
! [SV17: $i,SV37: $i,SV104: $i,SV99: $i,SV74: $i,SV56: $i,SV88: $i] :
( ( ( SV88
= ( vlookup @ SV56 @ SV74 ) )
= $false )
| ( ( SV88
= ( vlookup @ SV99 @ SV104 ) )
= $true )
| ( ( SV99 = SV37 )
= $true )
| ( ( SV56 = SV99 )
= $false )
| ( ( SV74
= ( vbind @ SV37 @ SV17 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(439,plain,
! [SV79: $i,SV22: $i,SV61: $i,SV2: $i,SV92: $i,SV42: $i] :
( ( ( SV42 = SV92 )
= $false )
| ( ( SV2 = SV61 )
= $false )
| ( ( SV22 = SV79 )
= $false )
| ( ( ( vabs @ SV2 @ SV22 @ SV42 )
= ( vabs @ SV61 @ SV79 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(440,plain,
! [SV66: $i,SV107: $i,SV27: $i,SV102: $i,SV7: $i,SV109: $i,SV94: $i,SV82: $i,SV47: $i] :
( ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV27 = SV107 )
= $false )
| ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
| ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(441,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV83 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV83 @ SV95 ) )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(442,plain,
! [SV95: $i,SV9: $i,SV48: $i,SV29: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV83 ) ) )
= $false )
| ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(443,plain,
! [SV9: $i,SV67: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i] :
( ( ( ~ ( visFreeVar @ SV83 @ SV95 ) )
= $false )
| ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(444,plain,
! [SV84: $i,SV30: $i,SV68: $i,SV10: $i,SV96: $i,SV49: $i] :
( ( ( SV49 = SV96 )
= $false )
| ( ( SV10 = SV68 )
= $false )
| ( ( SV30 = SV84 )
= $false )
| ( ( ( vbind @ SV10 @ SV30 @ SV49 )
= ( vbind @ SV68 @ SV84 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(445,plain,
! [SV98: $i,SV16: $i,SV73: $i,SV36: $i,SV55: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i] :
( ( ( SV87
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $false )
| ( ( SV55 = SV36 )
= $false )
| ( ( SV73 = SV16 )
= $false )
| ( ( ( SV36 != SV103 )
| ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(446,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV107: $i,SV82: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) ) )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(447,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( SV67 != SV83 )
= $false )
| ( ( ~ ( visFreeVar @ SV83 @ SV95 ) )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(448,plain,
! [SV95: $i,SV9: $i,SV48: $i,SV29: $i,SV83: $i,SV67: $i] :
( ( ( SV67 != SV83 )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(449,plain,
! [SV9: $i,SV67: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i] :
( ( ( visFreeVar @ SV83 @ SV95 )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(450,plain,
! [SV16: $i,SV110: $i,SV108: $i,SV87: $i,SV73: $i,SV55: $i,SV98: $i,SV103: $i,SV36: $i] :
( ( ( SV36 != SV103 )
= $true )
| ( ( ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true )
| ( ( SV73 = SV16 )
= $false )
| ( ( SV55 = SV36 )
= $false )
| ( ( SV87
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(451,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV107: $i,SV82: $i,SV102: $i] :
( ( ( ~ ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) ) )
= $false )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(452,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV95: $i,SV83: $i,SV67: $i] :
( ( ( SV67 = SV83 )
= $true )
| ( ( ~ ( visFreeVar @ SV83 @ SV95 ) )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(453,plain,
! [SV95: $i,SV9: $i,SV48: $i,SV29: $i,SV83: $i,SV67: $i] :
( ( ( SV67 = SV83 )
= $false )
| ( ( visFreeVar @ SV29 @ SV48 )
= $false )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(454,plain,
! [SV16: $i,SV110: $i,SV108: $i,SV87: $i,SV73: $i,SV55: $i,SV98: $i,SV103: $i,SV36: $i] :
( ( ( SV36 = SV103 )
= $false )
| ( ( ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
| ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) ) )
= $true )
| ( ( SV73 = SV16 )
= $false )
| ( ( SV55 = SV36 )
= $false )
| ( ( SV87
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(455,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV107: $i,SV82: $i,SV102: $i] :
( ( ( ~ ( ( SV102 != SV82 ) )
| ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(456,plain,
! [SV9: $i,SV48: $i,SV29: $i,SV67: $i,SV95: $i,SV83: $i] :
( ( ( visFreeVar @ SV83 @ SV95 )
= $false )
| ( ( SV67 = SV83 )
= $true )
| ( ( visFreeVar @ SV29 @ SV48 )
= $true )
| ( ( SV29 = SV83 )
= $false )
| ( ( SV48
= ( vabs @ SV67 @ SV9 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(457,plain,
! [SV16: $i,SV36: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV73: $i,SV55: $i,SV98: $i] :
( ( ( SV98
!= ( vsubst @ SV55 @ SV73 @ SV87 ) )
= $true )
| ( ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( SV36 = SV103 )
= $false )
| ( ( SV73 = SV16 )
= $false )
| ( ( SV55 = SV36 )
= $false )
| ( ( SV87
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(458,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV107: $i,SV82: $i,SV102: $i] :
( ( ( ~ ( ( SV102 != SV82 ) ) )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(459,plain,
! [SV16: $i,SV36: $i,SV110: $i,SV108: $i,SV103: $i,SV87: $i,SV73: $i,SV55: $i,SV98: $i] :
( ( ( SV98
= ( vsubst @ SV55 @ SV73 @ SV87 ) )
= $false )
| ( ( SV98
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $true )
| ( ( SV36 = SV103 )
= $false )
| ( ( SV73 = SV16 )
= $false )
| ( ( SV55 = SV36 )
= $false )
| ( ( SV87
= ( vabs @ SV103 @ SV108 @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(460,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV107: $i,SV82: $i,SV102: $i] :
( ( ( SV102 != SV82 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(461,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV107: $i,SV82: $i,SV102: $i] :
( ( ( SV102 = SV82 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV82 @ SV107 ) )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(462,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV102: $i,SV107: $i,SV82: $i] :
( ( ( ~ ( visFreeVar @ SV82 @ SV107 ) )
= $false )
| ( ( SV102 = SV82 )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(463,plain,
! [SV109: $i,SV94: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i,SV102: $i,SV107: $i,SV82: $i] :
( ( ( visFreeVar @ SV82 @ SV107 )
= $true )
| ( ( SV102 = SV82 )
= $true )
| ( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
| ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) ) )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(464,plain,
! [SV109: $i,SV107: $i,SV102: $i,SV94: $i,SV82: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i] :
( ( ( SV66
!= ( vsubst @ SV7 @ SV27 @ SV47 ) )
= $true )
| ( ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) )
= $true )
| ( ( SV102 = SV82 )
= $true )
| ( ( visFreeVar @ SV82 @ SV107 )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(465,plain,
! [SV109: $i,SV107: $i,SV102: $i,SV94: $i,SV82: $i,SV47: $i,SV27: $i,SV7: $i,SV66: $i] :
( ( ( SV66
= ( vsubst @ SV7 @ SV27 @ SV47 ) )
= $false )
| ( ( SV66
= ( vabs @ SV82 @ SV94 @ ( vsubst @ SV102 @ SV107 @ SV109 ) ) )
= $true )
| ( ( SV102 = SV82 )
= $true )
| ( ( visFreeVar @ SV82 @ SV107 )
= $true )
| ( ( SV27 = SV107 )
= $false )
| ( ( SV7 = SV102 )
= $false )
| ( ( SV47
= ( vabs @ SV82 @ SV94 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(466,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[113,465,459,456,453,449,444,439,438,436,426,425,421,420,419,418,416,415,390,389,384,379,368,365,343,322,268,247,237,229,225,211,137,136]) ).
thf(467,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM125+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
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 18:37:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.29/0.62
% 2.29/0.62 No.of.Axioms: 20
% 2.29/0.62
% 2.29/0.62 Length.of.Defs: 0
% 2.29/0.62
% 2.29/0.62 Contains.Choice.Funs: false
% 2.29/0.62 .......................
% 2.29/0.62
% 2.29/0.62 ********************************
% 2.29/0.62 * All subproblems solved! *
% 2.29/0.62 ********************************
% 2.29/0.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:466,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.29/0.62
% 2.29/0.62 %**** Beginning of derivation protocol ****
% 2.29/0.62 % SZS output start CNFRefutation
% See solution above
% 2.29/0.62
% 2.29/0.62 %**** End of derivation protocol ****
% 2.29/0.62 %**** no. of clauses in derivation: 428 ****
% 2.29/0.62 %**** clause counter: 466 ****
% 2.29/0.62
% 2.29/0.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:466,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------