%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM147+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 : n005.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 10:12:28 AM UTC 2026
% Result : Theorem 1.20s 0.43s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 32
% Syntax : Number of formulae : 548 ( 276 unt; 0 typ; 0 def)
% Number of atoms : 4404 (2689 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 8990 (2206 ~;1460 |; 102 &;5066 @)
% ( 0 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 9 con; 0-5 aty)
% Number of variables : 2923 ( 0 ^;2911 !; 12 ?;2923 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK10_SY516,type,
sK10_SY516: $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_VTin,type,
sK1_VTin: $i ).
thf(tp_sK2_SY151,type,
sK2_SY151: $i ).
thf(tp_sK3_SY154,type,
sK3_SY154: $i ).
thf(tp_sK4_SX1,type,
sK4_SX1: $i > $i ).
thf(tp_sK5_SY281,type,
sK5_SY281: $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_SY257,type,
sK6_SY257: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY511,type,
sK7_SY511: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY513,type,
sK8_SY513: $i > $i > $i > $i > $i > $i ).
thf(tp_sK9_SY515,type,
sK9_SY515: $i > $i > $i > $i > $i > $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_ve1,type,
ve1: $i ).
thf(tp_vempty,type,
vempty: $i ).
thf(tp_vgensym,type,
vgensym: $i > $i ).
thf(tp_vgetSomeExp,type,
vgetSomeExp: $i > $i ).
thf(tp_vgetSomeType,type,
vgetSomeType: $i > $i ).
thf(tp_visFreeVar,type,
visFreeVar: $i > $i > $o ).
thf(tp_visSomeExp,type,
visSomeExp: $i > $o ).
thf(tp_visSomeType,type,
visSomeType: $i > $o ).
thf(tp_visValue,type,
visValue: $i > $o ).
thf(tp_vlookup,type,
vlookup: $i > $i > $i ).
thf(tp_vnoExp,type,
vnoExp: $i ).
thf(tp_vnoType,type,
vnoType: $i ).
thf(tp_vreduce,type,
vreduce: $i > $i ).
thf(tp_vsomeExp,type,
vsomeExp: $i > $i ).
thf(tp_vsomeType,type,
vsomeType: $i > $i ).
thf(tp_vsubst,type,
vsubst: $i > $i > $i > $i ).
thf(tp_vtcheck,type,
vtcheck: $i > $i > $i > $o ).
thf(tp_vvar,type,
vvar: $i > $i ).
thf(1,axiom,
! [VT: $i] :
( ( ( vtcheck @ vempty @ ve1 @ VT )
& ~ ( visValue @ ve1 ) )
=> ? [Veout: $i] :
( ( vreduce @ ve1 )
= ( vsomeExp @ Veout ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Progress-T-abs-IH') ).
thf(2,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(3,axiom,
! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak') ).
thf(5,axiom,
! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-app') ).
thf(6,axiom,
! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-abs') ).
thf(7,axiom,
! [VC: $i,Vx: $i,VT: $i] :
( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
=> ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-var') ).
thf(10,axiom,
! [Ve2: $i,Ve1: $i,Ve1red: $i,VExp0: $i,RESULT: $i] :
( ( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
& ! [VVx0: $i,VVS0: $i,VVe10: $i] :
( Ve1
!= ( vabs @ VVx0 @ VVS0 @ VVe10 ) ) )
=> ( ( ( Ve1red
= ( vreduce @ Ve1 ) )
& ~ ( visSomeExp @ Ve1red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce6) ).
thf(11,axiom,
! [Ve1: $i,VExp0: $i,RESULT: $i,Ve1red: $i,Ve2: $i] :
( ( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
& ! [VVx0: $i,VVS0: $i,VVe10: $i] :
( Ve1
!= ( vabs @ VVx0 @ VVS0 @ VVe10 ) ) )
=> ( ( ( Ve1red
= ( vreduce @ Ve1 ) )
& ( visSomeExp @ Ve1red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ Ve1red ) @ Ve2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce5) ).
thf(12,axiom,
! [Vx: $i,VS: $i,Ve1: $i,Ve2red: $i,Ve2: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ~ ( visSomeExp @ Ve2red )
& ~ ( visValue @ Ve2 ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce4) ).
thf(13,axiom,
! [VS: $i,Ve2red: $i,VExp0: $i,RESULT: $i,Vx: $i,Ve2: $i,Ve1: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ~ ( visSomeExp @ Ve2red )
& ( visValue @ Ve2 ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vsubst @ Vx @ Ve2 @ Ve1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce3) ).
thf(14,axiom,
! [Ve2: $i,VExp0: $i,RESULT: $i,Vx: $i,VS: $i,Ve1: $i,Ve2red: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ( visSomeExp @ Ve2red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ ( vgetSomeExp @ Ve2red ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce2) ).
thf(15,axiom,
! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce1) ).
thf(16,axiom,
! [Vx: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce0) ).
thf(17,axiom,
! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeExp0) ).
thf(18,axiom,
! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp1) ).
thf(20,axiom,
! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
thf(21,axiom,
! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someExp') ).
thf(24,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(26,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst3) ).
thf(31,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(32,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Duplicate') ).
thf(36,axiom,
! [Vx: $i,VVar0: $i,VCtx0: $i,RESULT: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0 = vempty ) )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT = vnoType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup0) ).
thf(41,axiom,
! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
thf(45,axiom,
( ( ( vempty = vempty )
=> $true )
& ( $true
=> ( vempty = vempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-empty') ).
thf(47,axiom,
! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
thf(49,axiom,
! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
thf(50,axiom,
! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
thf(51,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(52,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(54,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(56,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-abs') ).
thf(58,conjecture,
! [VTin: $i,Vx: $i,VS: $i] :
( ( ( vtcheck @ vempty @ ( vabs @ Vx @ VS @ ve1 ) @ VTin )
& ~ ( visValue @ ( vabs @ Vx @ VS @ ve1 ) ) )
=> ? [Veout: $i] :
( ( vreduce @ ( vabs @ Vx @ VS @ ve1 ) )
= ( vsomeExp @ Veout ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Progress-T-abs') ).
thf(59,negated_conjecture,
( ( ! [VTin: $i,Vx: $i,VS: $i] :
( ( ( vtcheck @ vempty @ ( vabs @ Vx @ VS @ ve1 ) @ VTin )
& ~ ( visValue @ ( vabs @ Vx @ VS @ ve1 ) ) )
=> ? [Veout: $i] :
( ( vreduce @ ( vabs @ Vx @ VS @ ve1 ) )
= ( vsomeExp @ Veout ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[58]) ).
thf(60,plain,
( ( ! [VTin: $i,Vx: $i,VS: $i] :
( ( ( vtcheck @ vempty @ ( vabs @ Vx @ VS @ ve1 ) @ VTin )
& ~ ( visValue @ ( vabs @ Vx @ VS @ ve1 ) ) )
=> ? [Veout: $i] :
( ( vreduce @ ( vabs @ Vx @ VS @ ve1 ) )
= ( vsomeExp @ Veout ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [VT: $i] :
( ( ( vtcheck @ vempty @ ve1 @ VT )
& ~ ( visValue @ ve1 ) )
=> ? [Veout: $i] :
( ( vreduce @ ve1 )
= ( vsomeExp @ Veout ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(62,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)],[2]) ).
thf(63,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(65,plain,
( ( ! [VC: $i,Vx: $i,Ve: $i,VS: $i,VT: $i] :
( ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT )
=> ( vtcheck @ VC @ ( vabs @ Vx @ VS @ Ve ) @ ( varrow @ VS @ VT ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(66,plain,
( ( ! [VC: $i,Vx: $i,VT: $i] :
( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
=> ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(67,plain,
( ( ! [Ve2: $i,Ve1: $i,Ve1red: $i,VExp0: $i,RESULT: $i] :
( ( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
& ! [VVx0: $i,VVS0: $i,VVe10: $i] :
( Ve1
!= ( vabs @ VVx0 @ VVS0 @ VVe10 ) ) )
=> ( ( ( Ve1red
= ( vreduce @ Ve1 ) )
& ~ ( visSomeExp @ Ve1red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(68,plain,
( ( ! [Ve1: $i,VExp0: $i,RESULT: $i,Ve1red: $i,Ve2: $i] :
( ( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
& ! [VVx0: $i,VVS0: $i,VVe10: $i] :
( Ve1
!= ( vabs @ VVx0 @ VVS0 @ VVe10 ) ) )
=> ( ( ( Ve1red
= ( vreduce @ Ve1 ) )
& ( visSomeExp @ Ve1red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ Ve1red ) @ Ve2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(69,plain,
( ( ! [Vx: $i,VS: $i,Ve1: $i,Ve2red: $i,Ve2: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ~ ( visSomeExp @ Ve2red )
& ~ ( visValue @ Ve2 ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(70,plain,
( ( ! [VS: $i,Ve2red: $i,VExp0: $i,RESULT: $i,Vx: $i,Ve2: $i,Ve1: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ~ ( visSomeExp @ Ve2red )
& ( visValue @ Ve2 ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vsubst @ Vx @ Ve2 @ Ve1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(71,plain,
( ( ! [Ve2: $i,VExp0: $i,RESULT: $i,Vx: $i,VS: $i,Ve1: $i,Ve2red: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ( visSomeExp @ Ve2red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ ( vgetSomeExp @ Ve2red ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(72,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(73,plain,
( ( ! [Vx: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(74,plain,
( ( ! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(75,plain,
( ( ! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(76,plain,
( ( ! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(77,plain,
( ( ! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(78,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)],[24]) ).
thf(79,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(80,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(81,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(82,plain,
( ( ! [Vx: $i,VVar0: $i,VCtx0: $i,RESULT: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0 = vempty ) )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT = vnoType ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(83,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(84,plain,
( ( ( ( vempty = vempty )
=> $true )
& ( $true
=> ( vempty = vempty ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(85,plain,
( ( ! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(86,plain,
( ( ! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(87,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(88,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(89,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(90,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(91,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(92,plain,
( ( ! [SY151: $i,SY152: $i] :
( ( ( vtcheck @ vempty @ ( vabs @ SY151 @ SY152 @ ve1 ) @ sK1_VTin )
& ~ ( visValue @ ( vabs @ SY151 @ SY152 @ ve1 ) ) )
=> ? [Veout: $i] :
( ( vreduce @ ( vabs @ SY151 @ SY152 @ ve1 ) )
= ( vsomeExp @ Veout ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(93,plain,
( ( ! [SY154: $i] :
( ( ( vtcheck @ vempty @ ( vabs @ sK2_SY151 @ SY154 @ ve1 ) @ sK1_VTin )
& ~ ( visValue @ ( vabs @ sK2_SY151 @ SY154 @ ve1 ) ) )
=> ? [SY155: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ SY154 @ ve1 ) )
= ( vsomeExp @ SY155 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(94,plain,
( ( ( ( vtcheck @ vempty @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) @ sK1_VTin )
& ~ ( visValue @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) ) )
=> ? [SY156: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
= ( vsomeExp @ SY156 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(95,plain,
( ( vtcheck @ vempty @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) @ sK1_VTin )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(96,plain,
( ( ~ ( visValue @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(97,plain,
( ( ? [SY156: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
= ( vsomeExp @ SY156 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(98,plain,
( ( ~ ? [SY156: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
= ( vsomeExp @ SY156 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[97]) ).
thf(99,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(100,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(101,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(102,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(103,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(104,plain,
( ( ! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(105,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)],[85]) ).
thf(106,plain,
( ( ( ( vempty = vempty )
=> $true )
& ( $true
=> ( vempty = vempty ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(107,plain,
( ( ! [VVar0: $i,VTyp0: $i,VCtx0: $i] :
( vempty
!= ( vbind @ VVar0 @ VTyp0 @ VCtx0 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(108,plain,
( ( ! [Vx: $i,VVar0: $i,VCtx0: $i,RESULT: $i] :
( ( ( VVar0 = Vx )
& ( VCtx0 = vempty ) )
=> ( ( RESULT
= ( vlookup @ VVar0 @ VCtx0 ) )
=> ( RESULT = vnoType ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(109,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(110,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)],[80]) ).
thf(111,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(112,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Vx: $i,Ve: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( ( Vx != Vy )
& ~ ( visFreeVar @ Vy @ Ve ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ ( vsubst @ Vx @ Ve @ Ve1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(113,plain,
( ( ! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(114,plain,
( ( ! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(115,plain,
( ( ! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(116,plain,
( ( ! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(117,plain,
( ( ! [Vx: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(118,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(119,plain,
( ( ! [Ve2: $i,VExp0: $i,RESULT: $i,Vx: $i,VS: $i,Ve1: $i,Ve2red: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ( visSomeExp @ Ve2red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ ( vgetSomeExp @ Ve2red ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(120,plain,
( ( ! [VS: $i,Ve2red: $i,VExp0: $i,RESULT: $i,Vx: $i,Ve2: $i,Ve1: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ~ ( visSomeExp @ Ve2red )
& ( visValue @ Ve2 ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vsubst @ Vx @ Ve2 @ Ve1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(121,plain,
( ( ! [Vx: $i,VS: $i,Ve1: $i,Ve2red: $i,Ve2: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vapp @ ( vabs @ Vx @ VS @ Ve1 ) @ Ve2 ) )
=> ( ( ( Ve2red
= ( vreduce @ Ve2 ) )
& ~ ( visSomeExp @ Ve2red )
& ~ ( visValue @ Ve2 ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(122,plain,
( ( ! [Ve1: $i,VExp0: $i,RESULT: $i,Ve1red: $i,Ve2: $i] :
( ( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
& ! [VVx0: $i,VVS0: $i,VVe10: $i] :
( Ve1
!= ( vabs @ VVx0 @ VVS0 @ VVe10 ) ) )
=> ( ( ( Ve1red
= ( vreduce @ Ve1 ) )
& ( visSomeExp @ Ve1red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ Ve1red ) @ Ve2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(123,plain,
( ( ! [Ve2: $i,Ve1: $i,Ve1red: $i,VExp0: $i,RESULT: $i] :
( ( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
& ! [VVx0: $i,VVS0: $i,VVe10: $i] :
( Ve1
!= ( vabs @ VVx0 @ VVS0 @ VVe10 ) ) )
=> ( ( ( Ve1red
= ( vreduce @ Ve1 ) )
& ~ ( visSomeExp @ Ve1red ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(124,plain,
( ( ! [VC: $i,Vx: $i,VT: $i] :
( ( ( vlookup @ Vx @ VC )
= ( vsomeType @ VT ) )
=> ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(125,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)],[65]) ).
thf(126,plain,
( ( ! [VS: $i,VC: $i,Ve1: $i,Ve2: $i,VT: $i] :
( ( ( vtcheck @ VC @ Ve1 @ ( varrow @ VS @ VT ) )
& ( vtcheck @ VC @ Ve2 @ VS ) )
=> ( vtcheck @ VC @ ( vapp @ Ve1 @ Ve2 ) @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(127,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( ( vlookup @ Vx @ VC )
= vnoType )
& ( vtcheck @ VC @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VS @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(128,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)],[62]) ).
thf(129,plain,
( ( ! [VT: $i] :
( ( ( vtcheck @ vempty @ ve1 @ VT )
& ~ ( visValue @ ve1 ) )
=> ? [Veout: $i] :
( ( vreduce @ ve1 )
= ( vsomeExp @ Veout ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(130,plain,
( ( ~ ( visValue @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(131,plain,
( ( vtcheck @ vempty @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) @ sK1_VTin )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(132,plain,
( ( ~ ? [SY156: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
= ( vsomeExp @ SY156 ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vsomeExp @ SX0 ) )
| ( visSomeExp @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(134,plain,
( ( ! [SX0: $i] :
( vnoExp
!= ( vsomeExp @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vabs @ SX3 @ SX4 @ SX5 ) )
| ~ ( ~ ~ ( ( SX0 != SX3 )
| ( SX1 != SX4 ) )
| ( SX2 != SX5 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SX0 != SX3 )
| ( SX1 != SX4 ) )
| ( SX2 != SX5 ) )
| ( ( vabs @ SX0 @ SX1 @ SX2 )
= ( vabs @ SX3 @ SX4 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(136,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ( SX3
!= ( vapp @ SX1 @ SX0 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i] :
( SX1
!= ( vabs @ SX5 @ SX6 @ SX7 ) ) )
| ~ ~ ( ( SX2
!= ( vreduce @ SX1 ) )
| ~ ~ ( visSomeExp @ SX2 ) )
| ( SX4
!= ( vreduce @ SX3 ) )
| ( SX4 = vnoExp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ( SX0 != SX6 )
| ( SX1 != SX7 ) )
| ( SX2
!= ( vabs @ SX4 @ SX5 @ SX8 ) ) )
| ~ ~ ( ~ ( ( SX6 != SX4 ) )
| ~ ~ ( visFreeVar @ SX4 @ SX7 ) )
| ( SX3
!= ( vsubst @ SX0 @ SX1 @ SX2 ) )
| ( SX3
= ( vabs @ SX4 @ SX5 @ ( vsubst @ SX6 @ SX7 @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( vsomeExp @ SX0 )
!= ( vsomeExp @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( vsomeExp @ SX0 )
= ( vsomeExp @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( vsomeExp @ SX2 ) )
| ( SX1
!= ( vgetSomeExp @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( ( SX2 != SX0 ) )
| ~ ( vtcheck @ ( vbind @ SX2 @ SX3 @ ( vbind @ SX0 @ SX1 @ SX4 ) ) @ SX5 @ SX6 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ ( vbind @ SX2 @ SX3 @ SX4 ) ) @ SX5 @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(141,plain,
( ( ~ ~ ! [SX0: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
!= ( vsomeExp @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( vempty
!= ( vbind @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(143,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)],[109]) ).
thf(144,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)],[128]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( SX4
!= ( vreduce @ SX3 ) )
| ( SX4 = vnoExp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX1 )
| ( SX3 != SX0 ) )
| ( SX4
!= ( vabs @ SX6 @ SX7 @ SX8 ) ) )
| ( SX1 != SX6 )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5
= ( vabs @ SX6 @ SX7 @ SX8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(148,plain,
( ( ~ ( ~ ( ( vempty != vempty )
| $true )
| ~ ( ~ $true
| ( vempty = vempty ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ( SX1 != SX0 )
| ( SX2 != vempty ) )
| ( SX3
!= ( vlookup @ SX1 @ SX2 ) )
| ( SX3 = vnoType ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(150,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( vtcheck @ vempty @ ve1 @ SX0 )
| ~ ~ ( visValue @ ve1 ) )
| ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( vtcheck @ SX1 @ SX2 @ ( varrow @ SX0 @ SX4 ) )
| ~ ( vtcheck @ SX1 @ SX3 @ SX0 ) )
| ( vtcheck @ SX1 @ ( vapp @ SX2 @ SX3 ) @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( SX1
!= ( vapp @ ( vabs @ SX3 @ SX4 @ SX5 ) @ SX0 ) )
| ~ ~ ( ( SX6
!= ( vreduce @ SX0 ) )
| ~ ( visSomeExp @ SX6 ) )
| ( SX2
!= ( vreduce @ SX1 ) )
| ( SX2
= ( vsomeExp @ ( vapp @ ( vabs @ SX3 @ SX4 @ SX5 ) @ ( vgetSomeExp @ SX6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( SX2
!= ( vapp @ ( vabs @ SX4 @ SX0 @ SX6 ) @ SX5 ) )
| ~ ~ ( ~ ~ ( ( SX1
!= ( vreduce @ SX5 ) )
| ~ ~ ( visSomeExp @ SX1 ) )
| ~ ( visValue @ SX5 ) )
| ( SX3
!= ( vreduce @ SX2 ) )
| ( SX3
= ( vsomeExp @ ( vsubst @ SX4 @ SX5 @ SX6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ( ( vlookup @ SX0 @ SX2 )
!= vnoType )
| ~ ( vtcheck @ SX2 @ SX3 @ SX4 ) )
| ( vtcheck @ ( vbind @ SX0 @ SX1 @ SX2 ) @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1
!= ( vvar @ SX0 ) )
| ( SX2
!= ( vreduce @ SX1 ) )
| ( SX2 = vnoExp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(156,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)],[125]) ).
thf(157,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)],[105]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ( SX1
!= ( vapp @ SX0 @ SX4 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i] :
( SX0
!= ( vabs @ SX5 @ SX6 @ SX7 ) ) )
| ~ ~ ( ( SX3
!= ( vreduce @ SX0 ) )
| ~ ( visSomeExp @ SX3 ) )
| ( SX2
!= ( vreduce @ SX1 ) )
| ( SX2
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SX3 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( vlookup @ SX1 @ SX0 )
!= ( vsomeType @ SX2 ) )
| ( vtcheck @ SX0 @ ( vvar @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( SX5
!= ( vapp @ ( vabs @ SX0 @ SX1 @ SX2 ) @ SX4 ) )
| ~ ~ ( ~ ~ ( ( SX3
!= ( vreduce @ SX4 ) )
| ~ ~ ( visSomeExp @ SX3 ) )
| ~ ~ ( visValue @ SX4 ) )
| ( SX6
!= ( vreduce @ SX5 ) )
| ( SX6 = vnoExp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( visValue @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vvar @ SX0 ) )
| ~ ( visValue @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2
!= ( vapp @ SX0 @ SX1 ) )
| ~ ( visValue @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(165,plain,
( ( visValue @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(166,plain,
! [SV1: $i] :
( ( ! [SY157: $i] :
( ( SY157
!= ( vsomeExp @ SV1 ) )
| ( visSomeExp @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(167,plain,
! [SV2: $i] :
( ( vnoExp
!= ( vsomeExp @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(168,plain,
! [SV3: $i] :
( ( ! [SY158: $i,SY159: $i,SY160: $i,SY161: $i,SY162: $i] :
~ ( ~ ( ( ( vabs @ SV3 @ SY158 @ SY159 )
!= ( vabs @ SY160 @ SY161 @ SY162 ) )
| ~ ( ~ ~ ( ( SV3 != SY160 )
| ( SY158 != SY161 ) )
| ( SY159 != SY162 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SY160 )
| ( SY158 != SY161 ) )
| ( SY159 != SY162 ) )
| ( ( vabs @ SV3 @ SY158 @ SY159 )
= ( vabs @ SY160 @ SY161 @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(169,plain,
! [SV4: $i] :
( ( ! [SY163: $i,SY164: $i,SY165: $i,SY166: $i] :
( ~ ~ ( ( SY165
!= ( vapp @ SY163 @ SV4 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i] :
( SY163
!= ( vabs @ SX5 @ SX6 @ SX7 ) ) )
| ~ ~ ( ( SY164
!= ( vreduce @ SY163 ) )
| ~ ~ ( visSomeExp @ SY164 ) )
| ( SY166
!= ( vreduce @ SY165 ) )
| ( SY166 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(170,plain,
! [SV5: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i,SY173: $i,SY174: $i,SY175: $i,SY176: $i,SY177: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY175 )
| ( SY170 != SY176 ) )
| ( SY171
!= ( vabs @ SY173 @ SY174 @ SY177 ) ) )
| ~ ~ ( ~ ( ( SY175 != SY173 ) )
| ~ ~ ( visFreeVar @ SY173 @ SY176 ) )
| ( SY172
!= ( vsubst @ SV5 @ SY170 @ SY171 ) )
| ( SY172
= ( vabs @ SY173 @ SY174 @ ( vsubst @ SY175 @ SY176 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(171,plain,
! [SV6: $i] :
( ( ! [SY178: $i] :
~ ( ~ ( ( ( vsomeExp @ SV6 )
!= ( vsomeExp @ SY178 ) )
| ( SV6 = SY178 ) )
| ~ ( ( SV6 != SY178 )
| ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(172,plain,
! [SV7: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ( SV7
!= ( vsomeExp @ SY180 ) )
| ( SY179
!= ( vgetSomeExp @ SV7 ) )
| ( SY179 = SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(173,plain,
! [SV8: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i,SY185: $i,SY186: $i] :
( ~ ~ ( ~ ( ( SY182 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SY182 @ SY183 @ ( vbind @ SV8 @ SY181 @ SY184 ) ) @ SY185 @ SY186 ) )
| ( vtcheck @ ( vbind @ SV8 @ SY181 @ ( vbind @ SY182 @ SY183 @ SY184 ) ) @ SY185 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(174,plain,
( ( ~ ! [SX0: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
!= ( vsomeExp @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(175,plain,
! [SV9: $i] :
( ( ! [SY187: $i,SY188: $i] :
( vempty
!= ( vbind @ SV9 @ SY187 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(176,plain,
! [SV10: $i] :
( ( ! [SY189: $i,SY190: $i,SY191: $i,SY192: $i,SY193: $i,SY194: $i] :
( ~ ~ ( ( SY190 != SV10 )
| ~ ( vtcheck @ ( vbind @ SY190 @ SY191 @ ( vbind @ SV10 @ SY189 @ SY192 ) ) @ SY193 @ SY194 ) )
| ( vtcheck @ ( vbind @ SY190 @ SY191 @ SY192 ) @ SY193 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(177,plain,
! [SV11: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i,SY198: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SY197 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SY195 @ SY196 ) @ SY197 @ SY198 ) )
| ( vtcheck @ SY196 @ SY197 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(178,plain,
! [SV12: $i] :
( ( ! [SY199: $i,SY200: $i,SY201: $i,SY202: $i] :
( ( SY201
!= ( vabs @ SV12 @ SY199 @ SY200 ) )
| ( SY202
!= ( vreduce @ SY201 ) )
| ( SY202 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(179,plain,
! [SV13: $i] :
( ( ! [SY203: $i,SY204: $i,SY205: $i,SY206: $i] :
( ( vabs @ SV13 @ SY203 @ SY204 )
!= ( vapp @ SY205 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(180,plain,
! [SV14: $i] :
( ( ! [SY207: $i,SY208: $i,SY209: $i,SY210: $i,SY211: $i,SY212: $i,SY213: $i,SY214: $i] :
( ~ ~ ( ~ ~ ( ( SY208 != SY207 )
| ( SY209 != SV14 ) )
| ( SY210
!= ( vabs @ SY212 @ SY213 @ SY214 ) ) )
| ( SY207 != SY212 )
| ( SY211
!= ( vsubst @ SY208 @ SY209 @ SY210 ) )
| ( SY211
= ( vabs @ SY212 @ SY213 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(181,plain,
( ( ~ ( ( vempty != vempty )
| $true )
| ~ ( ~ $true
| ( vempty = vempty ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(182,plain,
! [SV15: $i] :
( ( ! [SY215: $i,SY216: $i,SY217: $i] :
( ~ ~ ( ( SY215 != SV15 )
| ( SY216 != vempty ) )
| ( SY217
!= ( vlookup @ SY215 @ SY216 ) )
| ( SY217 = vnoType ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(183,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ( vtcheck @ vempty @ ve1 @ SV16 )
| ~ ~ ( visValue @ ve1 ) )
| ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(184,plain,
! [SV17: $i] :
( ( ! [SY219: $i,SY220: $i,SY221: $i,SY222: $i] :
( ~ ~ ( ~ ( vtcheck @ SY219 @ SY220 @ ( varrow @ SV17 @ SY222 ) )
| ~ ( vtcheck @ SY219 @ SY221 @ SV17 ) )
| ( vtcheck @ SY219 @ ( vapp @ SY220 @ SY221 ) @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(185,plain,
! [SV18: $i] :
( ( ! [SY223: $i,SY224: $i,SY225: $i,SY226: $i,SY227: $i,SY228: $i] :
( ( SY223
!= ( vapp @ ( vabs @ SY225 @ SY226 @ SY227 ) @ SV18 ) )
| ~ ~ ( ( SY228
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SY228 ) )
| ( SY224
!= ( vreduce @ SY223 ) )
| ( SY224
= ( vsomeExp @ ( vapp @ ( vabs @ SY225 @ SY226 @ SY227 ) @ ( vgetSomeExp @ SY228 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(186,plain,
! [SV19: $i] :
( ( ! [SY229: $i,SY230: $i,SY231: $i,SY232: $i,SY233: $i,SY234: $i] :
( ( SY230
!= ( vapp @ ( vabs @ SY232 @ SV19 @ SY234 ) @ SY233 ) )
| ~ ~ ( ~ ~ ( ( SY229
!= ( vreduce @ SY233 ) )
| ~ ~ ( visSomeExp @ SY229 ) )
| ~ ( visValue @ SY233 ) )
| ( SY231
!= ( vreduce @ SY230 ) )
| ( SY231
= ( vsomeExp @ ( vsubst @ SY232 @ SY233 @ SY234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(187,plain,
! [SV20: $i] :
( ( ! [SY235: $i,SY236: $i,SY237: $i,SY238: $i] :
( ~ ~ ( ( ( vlookup @ SV20 @ SY236 )
!= vnoType )
| ~ ( vtcheck @ SY236 @ SY237 @ SY238 ) )
| ( vtcheck @ ( vbind @ SV20 @ SY235 @ SY236 ) @ SY237 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(188,plain,
! [SV21: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( SY239
!= ( vvar @ SV21 ) )
| ( SY240
!= ( vreduce @ SY239 ) )
| ( SY240 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(189,plain,
! [SV22: $i] :
( ( ! [SY241: $i,SY242: $i,SY243: $i,SY244: $i] :
( ~ ( vtcheck @ ( vbind @ SY241 @ SY243 @ SV22 ) @ SY242 @ SY244 )
| ( vtcheck @ SV22 @ ( vabs @ SY241 @ SY243 @ SY242 ) @ ( varrow @ SY243 @ SY244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(190,plain,
! [SV23: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i,SY248: $i,SY249: $i] :
( ~ ~ ( ( SY245 != SY248 )
| ( SY246
!= ( vabs @ SY247 @ SV23 @ SY249 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY247 != SY248 ) )
| ~ ( visFreeVar @ SY248 @ SY249 ) )
| ( visFreeVar @ SY245 @ SY246 ) )
| ~ ( ~ ( visFreeVar @ SY245 @ SY246 )
| ~ ( ~ ( ( SY247 != SY248 ) )
| ~ ( visFreeVar @ SY248 @ SY249 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(191,plain,
! [SV24: $i] :
( ( ! [SY250: $i,SY251: $i,SY252: $i] :
( ( vvar @ SV24 )
!= ( vabs @ SY250 @ SY251 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(192,plain,
! [SV25: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i,SY256: $i] :
( ~ ~ ( ( SY253
!= ( vapp @ SV25 @ SY256 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
| ~ ~ ( ( SY255
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SY255 ) )
| ( SY254
!= ( vreduce @ SY253 ) )
| ( SY254
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SY255 ) @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(193,plain,
! [SV26: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ( ( vlookup @ SY260 @ SV26 )
!= ( vsomeType @ SY261 ) )
| ( vtcheck @ SV26 @ ( vvar @ SY260 ) @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(194,plain,
! [SV27: $i] :
( ( ! [SY262: $i,SY263: $i,SY264: $i,SY265: $i,SY266: $i,SY267: $i] :
( ( SY266
!= ( vapp @ ( vabs @ SV27 @ SY262 @ SY263 ) @ SY265 ) )
| ~ ~ ( ~ ~ ( ( SY264
!= ( vreduce @ SY265 ) )
| ~ ~ ( visSomeExp @ SY264 ) )
| ~ ~ ( visValue @ SY265 ) )
| ( SY267
!= ( vreduce @ SY266 ) )
| ( SY267 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(195,plain,
! [SV28: $i] :
( ( ! [SY268: $i,SY269: $i,SY270: $i] :
( ( SY270
!= ( vabs @ SV28 @ SY268 @ SY269 ) )
| ( visValue @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(196,plain,
! [SV29: $i] :
( ( ! [SY271: $i] :
( ( SY271
!= ( vvar @ SV29 ) )
| ~ ( visValue @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(197,plain,
! [SV30: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ( SY273
!= ( vapp @ SV30 @ SY272 ) )
| ~ ( visValue @ SY273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(198,plain,
! [SV1: $i,SV31: $i] :
( ( ( SV31
!= ( vsomeExp @ SV1 ) )
| ( visSomeExp @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(199,plain,
! [SV2: $i] :
( ( vnoExp
= ( vsomeExp @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(200,plain,
! [SV32: $i,SV3: $i] :
( ( ! [SY274: $i,SY275: $i,SY276: $i,SY277: $i] :
~ ( ~ ( ( ( vabs @ SV3 @ SV32 @ SY274 )
!= ( vabs @ SY275 @ SY276 @ SY277 ) )
| ~ ( ~ ~ ( ( SV3 != SY275 )
| ( SV32 != SY276 ) )
| ( SY274 != SY277 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SY275 )
| ( SV32 != SY276 ) )
| ( SY274 != SY277 ) )
| ( ( vabs @ SV3 @ SV32 @ SY274 )
= ( vabs @ SY275 @ SY276 @ SY277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(201,plain,
! [SV4: $i,SV33: $i] :
( ( ! [SY278: $i,SY279: $i,SY280: $i] :
( ~ ~ ( ( SY279
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
| ~ ~ ( ( SY278
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SY278 ) )
| ( SY280
!= ( vreduce @ SY279 ) )
| ( SY280 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(202,plain,
! [SV34: $i,SV5: $i] :
( ( ! [SY284: $i,SY285: $i,SY286: $i,SY287: $i,SY288: $i,SY289: $i,SY290: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY288 )
| ( SV34 != SY289 ) )
| ( SY284
!= ( vabs @ SY286 @ SY287 @ SY290 ) ) )
| ~ ~ ( ~ ( ( SY288 != SY286 ) )
| ~ ~ ( visFreeVar @ SY286 @ SY289 ) )
| ( SY285
!= ( vsubst @ SV5 @ SV34 @ SY284 ) )
| ( SY285
= ( vabs @ SY286 @ SY287 @ ( vsubst @ SY288 @ SY289 @ SY290 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(203,plain,
! [SV35: $i,SV6: $i] :
( ( ~ ( ~ ( ( ( vsomeExp @ SV6 )
!= ( vsomeExp @ SV35 ) )
| ( SV6 = SV35 ) )
| ~ ( ( SV6 != SV35 )
| ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(204,plain,
! [SV36: $i,SV7: $i] :
( ( ! [SY291: $i] :
( ( SV7
!= ( vsomeExp @ SY291 ) )
| ( SV36
!= ( vgetSomeExp @ SV7 ) )
| ( SV36 = SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(205,plain,
! [SV37: $i,SV8: $i] :
( ( ! [SY292: $i,SY293: $i,SY294: $i,SY295: $i,SY296: $i] :
( ~ ~ ( ~ ( ( SY292 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SY292 @ SY293 @ ( vbind @ SV8 @ SV37 @ SY294 ) ) @ SY295 @ SY296 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SY292 @ SY293 @ SY294 ) ) @ SY295 @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(206,plain,
( ( ! [SX0: $i] :
( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
!= ( vsomeExp @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(207,plain,
! [SV38: $i,SV9: $i] :
( ( ! [SY297: $i] :
( vempty
!= ( vbind @ SV9 @ SV38 @ SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(208,plain,
! [SV39: $i,SV10: $i] :
( ( ! [SY298: $i,SY299: $i,SY300: $i,SY301: $i,SY302: $i] :
( ~ ~ ( ( SY298 != SV10 )
| ~ ( vtcheck @ ( vbind @ SY298 @ SY299 @ ( vbind @ SV10 @ SV39 @ SY300 ) ) @ SY301 @ SY302 ) )
| ( vtcheck @ ( vbind @ SY298 @ SY299 @ SY300 ) @ SY301 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(209,plain,
! [SV40: $i,SV11: $i] :
( ( ! [SY303: $i,SY304: $i,SY305: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SY304 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SY303 ) @ SY304 @ SY305 ) )
| ( vtcheck @ SY303 @ SY304 @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(210,plain,
! [SV41: $i,SV12: $i] :
( ( ! [SY306: $i,SY307: $i,SY308: $i] :
( ( SY307
!= ( vabs @ SV12 @ SV41 @ SY306 ) )
| ( SY308
!= ( vreduce @ SY307 ) )
| ( SY308 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(211,plain,
! [SV42: $i,SV13: $i] :
( ( ! [SY309: $i,SY310: $i,SY311: $i] :
( ( vabs @ SV13 @ SV42 @ SY309 )
!= ( vapp @ SY310 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(212,plain,
! [SV14: $i,SV43: $i] :
( ( ! [SY312: $i,SY313: $i,SY314: $i,SY315: $i,SY316: $i,SY317: $i,SY318: $i] :
( ~ ~ ( ~ ~ ( ( SY312 != SV43 )
| ( SY313 != SV14 ) )
| ( SY314
!= ( vabs @ SY316 @ SY317 @ SY318 ) ) )
| ( SV43 != SY316 )
| ( SY315
!= ( vsubst @ SY312 @ SY313 @ SY314 ) )
| ( SY315
= ( vabs @ SY316 @ SY317 @ SY318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(213,plain,
( ( ~ ( ( vempty != vempty )
| $true ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(214,plain,
( ( ~ ( ~ $true
| ( vempty = vempty ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(215,plain,
! [SV15: $i,SV44: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ~ ( ( SV44 != SV15 )
| ( SY319 != vempty ) )
| ( SY320
!= ( vlookup @ SV44 @ SY319 ) )
| ( SY320 = vnoType ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(216,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ( vtcheck @ vempty @ ve1 @ SV16 )
| ~ ~ ( visValue @ ve1 ) ) )
= $true )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(217,plain,
! [SV17: $i,SV45: $i] :
( ( ! [SY321: $i,SY322: $i,SY323: $i] :
( ~ ~ ( ~ ( vtcheck @ SV45 @ SY321 @ ( varrow @ SV17 @ SY323 ) )
| ~ ( vtcheck @ SV45 @ SY322 @ SV17 ) )
| ( vtcheck @ SV45 @ ( vapp @ SY321 @ SY322 ) @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(218,plain,
! [SV18: $i,SV46: $i] :
( ( ! [SY324: $i,SY325: $i,SY326: $i,SY327: $i,SY328: $i] :
( ( SV46
!= ( vapp @ ( vabs @ SY325 @ SY326 @ SY327 ) @ SV18 ) )
| ~ ~ ( ( SY328
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SY328 ) )
| ( SY324
!= ( vreduce @ SV46 ) )
| ( SY324
= ( vsomeExp @ ( vapp @ ( vabs @ SY325 @ SY326 @ SY327 ) @ ( vgetSomeExp @ SY328 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(219,plain,
! [SV47: $i,SV19: $i] :
( ( ! [SY329: $i,SY330: $i,SY331: $i,SY332: $i,SY333: $i] :
( ( SY329
!= ( vapp @ ( vabs @ SY331 @ SV19 @ SY333 ) @ SY332 ) )
| ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SY332 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SY332 ) )
| ( SY330
!= ( vreduce @ SY329 ) )
| ( SY330
= ( vsomeExp @ ( vsubst @ SY331 @ SY332 @ SY333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(220,plain,
! [SV48: $i,SV20: $i] :
( ( ! [SY334: $i,SY335: $i,SY336: $i] :
( ~ ~ ( ( ( vlookup @ SV20 @ SY334 )
!= vnoType )
| ~ ( vtcheck @ SY334 @ SY335 @ SY336 ) )
| ( vtcheck @ ( vbind @ SV20 @ SV48 @ SY334 ) @ SY335 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(221,plain,
! [SV21: $i,SV49: $i] :
( ( ! [SY337: $i] :
( ( SV49
!= ( vvar @ SV21 ) )
| ( SY337
!= ( vreduce @ SV49 ) )
| ( SY337 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(222,plain,
! [SV22: $i,SV50: $i] :
( ( ! [SY338: $i,SY339: $i,SY340: $i] :
( ~ ( vtcheck @ ( vbind @ SV50 @ SY339 @ SV22 ) @ SY338 @ SY340 )
| ( vtcheck @ SV22 @ ( vabs @ SV50 @ SY339 @ SY338 ) @ ( varrow @ SY339 @ SY340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(223,plain,
! [SV23: $i,SV51: $i] :
( ( ! [SY341: $i,SY342: $i,SY343: $i,SY344: $i] :
( ~ ~ ( ( SV51 != SY343 )
| ( SY341
!= ( vabs @ SY342 @ SV23 @ SY344 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY342 != SY343 ) )
| ~ ( visFreeVar @ SY343 @ SY344 ) )
| ( visFreeVar @ SV51 @ SY341 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SY341 )
| ~ ( ~ ( ( SY342 != SY343 ) )
| ~ ( visFreeVar @ SY343 @ SY344 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(224,plain,
! [SV52: $i,SV24: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ( vvar @ SV24 )
!= ( vabs @ SV52 @ SY345 @ SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(225,plain,
! [SV25: $i,SV53: $i] :
( ( ! [SY347: $i,SY348: $i,SY349: $i] :
( ~ ~ ( ( SV53
!= ( vapp @ SV25 @ SY349 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
| ~ ~ ( ( SY348
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SY348 ) )
| ( SY347
!= ( vreduce @ SV53 ) )
| ( SY347
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SY348 ) @ SY349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(226,plain,
! [SV26: $i,SV54: $i] :
( ( ! [SY353: $i] :
( ( ( vlookup @ SV54 @ SV26 )
!= ( vsomeType @ SY353 ) )
| ( vtcheck @ SV26 @ ( vvar @ SV54 ) @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(227,plain,
! [SV55: $i,SV27: $i] :
( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i,SY358: $i] :
( ( SY357
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SY354 ) @ SY356 ) )
| ~ ~ ( ~ ~ ( ( SY355
!= ( vreduce @ SY356 ) )
| ~ ~ ( visSomeExp @ SY355 ) )
| ~ ~ ( visValue @ SY356 ) )
| ( SY358
!= ( vreduce @ SY357 ) )
| ( SY358 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(228,plain,
! [SV56: $i,SV28: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ( SY360
!= ( vabs @ SV28 @ SV56 @ SY359 ) )
| ( visValue @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(229,plain,
! [SV29: $i,SV57: $i] :
( ( ( SV57
!= ( vvar @ SV29 ) )
| ~ ( visValue @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(230,plain,
! [SV58: $i,SV30: $i] :
( ( ! [SY361: $i] :
( ( SY361
!= ( vapp @ SV30 @ SV58 ) )
| ~ ( visValue @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(231,plain,
! [SV1: $i,SV31: $i] :
( ( ( SV31
!= ( vsomeExp @ SV1 ) )
= $true )
| ( ( visSomeExp @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(232,plain,
! [SV59: $i,SV32: $i,SV3: $i] :
( ( ! [SY362: $i,SY363: $i,SY364: $i] :
~ ( ~ ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SY362 @ SY363 @ SY364 ) )
| ~ ( ~ ~ ( ( SV3 != SY362 )
| ( SV32 != SY363 ) )
| ( SV59 != SY364 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SY362 )
| ( SV32 != SY363 ) )
| ( SV59 != SY364 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SY362 @ SY363 @ SY364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(233,plain,
! [SV60: $i,SV4: $i,SV33: $i] :
( ( ! [SY365: $i,SY366: $i] :
( ~ ~ ( ( SY365
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
| ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SY366
!= ( vreduce @ SY365 ) )
| ( SY366 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(234,plain,
! [SV61: $i,SV34: $i,SV5: $i] :
( ( ! [SY370: $i,SY371: $i,SY372: $i,SY373: $i,SY374: $i,SY375: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY373 )
| ( SV34 != SY374 ) )
| ( SV61
!= ( vabs @ SY371 @ SY372 @ SY375 ) ) )
| ~ ~ ( ~ ( ( SY373 != SY371 ) )
| ~ ~ ( visFreeVar @ SY371 @ SY374 ) )
| ( SY370
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SY370
= ( vabs @ SY371 @ SY372 @ ( vsubst @ SY373 @ SY374 @ SY375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(235,plain,
! [SV35: $i,SV6: $i] :
( ( ~ ( ( ( vsomeExp @ SV6 )
!= ( vsomeExp @ SV35 ) )
| ( SV6 = SV35 ) )
| ~ ( ( SV6 != SV35 )
| ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(236,plain,
! [SV36: $i,SV62: $i,SV7: $i] :
( ( ( SV7
!= ( vsomeExp @ SV62 ) )
| ( SV36
!= ( vgetSomeExp @ SV7 ) )
| ( SV36 = SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(237,plain,
! [SV37: $i,SV8: $i,SV63: $i] :
( ( ! [SY376: $i,SY377: $i,SY378: $i,SY379: $i] :
( ~ ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SY376 @ ( vbind @ SV8 @ SV37 @ SY377 ) ) @ SY378 @ SY379 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SY376 @ SY377 ) ) @ SY378 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(238,plain,
! [SV64: $i] :
( ( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
!= ( vsomeExp @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(239,plain,
! [SV65: $i,SV38: $i,SV9: $i] :
( ( vempty
!= ( vbind @ SV9 @ SV38 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(240,plain,
! [SV39: $i,SV10: $i,SV66: $i] :
( ( ! [SY380: $i,SY381: $i,SY382: $i,SY383: $i] :
( ~ ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SY380 @ ( vbind @ SV10 @ SV39 @ SY381 ) ) @ SY382 @ SY383 ) )
| ( vtcheck @ ( vbind @ SV66 @ SY380 @ SY381 ) @ SY382 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(241,plain,
! [SV67: $i,SV40: $i,SV11: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SY384 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SY384 @ SY385 ) )
| ( vtcheck @ SV67 @ SY384 @ SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(242,plain,
! [SV68: $i,SV41: $i,SV12: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ( SY386
!= ( vabs @ SV12 @ SV41 @ SV68 ) )
| ( SY387
!= ( vreduce @ SY386 ) )
| ( SY387 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(243,plain,
! [SV69: $i,SV42: $i,SV13: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ( vabs @ SV13 @ SV42 @ SV69 )
!= ( vapp @ SY388 @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(244,plain,
! [SV14: $i,SV43: $i,SV70: $i] :
( ( ! [SY390: $i,SY391: $i,SY392: $i,SY393: $i,SY394: $i,SY395: $i] :
( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SY390 != SV14 ) )
| ( SY391
!= ( vabs @ SY393 @ SY394 @ SY395 ) ) )
| ( SV43 != SY393 )
| ( SY392
!= ( vsubst @ SV70 @ SY390 @ SY391 ) )
| ( SY392
= ( vabs @ SY393 @ SY394 @ SY395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(245,plain,
( ( ( vempty != vempty )
| $true )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(246,plain,
( ( ~ $true
| ( vempty = vempty ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(247,plain,
! [SV71: $i,SV15: $i,SV44: $i] :
( ( ! [SY396: $i] :
( ~ ~ ( ( SV44 != SV15 )
| ( SV71 != vempty ) )
| ( SY396
!= ( vlookup @ SV44 @ SV71 ) )
| ( SY396 = vnoType ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(248,plain,
! [SV16: $i] :
( ( ( ~ ( ~ ( vtcheck @ vempty @ ve1 @ SV16 )
| ~ ~ ( visValue @ ve1 ) ) )
= $false )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(249,plain,
! [SV17: $i,SV72: $i,SV45: $i] :
( ( ! [SY397: $i,SY398: $i] :
( ~ ~ ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SY398 ) )
| ~ ( vtcheck @ SV45 @ SY397 @ SV17 ) )
| ( vtcheck @ SV45 @ ( vapp @ SV72 @ SY397 ) @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(250,plain,
! [SV73: $i,SV18: $i,SV46: $i] :
( ( ! [SY399: $i,SY400: $i,SY401: $i,SY402: $i] :
( ( SV46
!= ( vapp @ ( vabs @ SY399 @ SY400 @ SY401 ) @ SV18 ) )
| ~ ~ ( ( SY402
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SY402 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SY399 @ SY400 @ SY401 ) @ ( vgetSomeExp @ SY402 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(251,plain,
! [SV47: $i,SV19: $i,SV74: $i] :
( ( ! [SY403: $i,SY404: $i,SY405: $i,SY406: $i] :
( ( SV74
!= ( vapp @ ( vabs @ SY404 @ SV19 @ SY406 ) @ SY405 ) )
| ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SY405 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SY405 ) )
| ( SY403
!= ( vreduce @ SV74 ) )
| ( SY403
= ( vsomeExp @ ( vsubst @ SY404 @ SY405 @ SY406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(252,plain,
! [SV48: $i,SV75: $i,SV20: $i] :
( ( ! [SY407: $i,SY408: $i] :
( ~ ~ ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
| ~ ( vtcheck @ SV75 @ SY407 @ SY408 ) )
| ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SY407 @ SY408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(253,plain,
! [SV76: $i,SV21: $i,SV49: $i] :
( ( ( SV49
!= ( vvar @ SV21 ) )
| ( SV76
!= ( vreduce @ SV49 ) )
| ( SV76 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(254,plain,
! [SV77: $i,SV22: $i,SV50: $i] :
( ( ! [SY409: $i,SY410: $i] :
( ~ ( vtcheck @ ( vbind @ SV50 @ SY409 @ SV22 ) @ SV77 @ SY410 )
| ( vtcheck @ SV22 @ ( vabs @ SV50 @ SY409 @ SV77 ) @ ( varrow @ SY409 @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(255,plain,
! [SV23: $i,SV78: $i,SV51: $i] :
( ( ! [SY411: $i,SY412: $i,SY413: $i] :
( ~ ~ ( ( SV51 != SY412 )
| ( SV78
!= ( vabs @ SY411 @ SV23 @ SY413 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY411 != SY412 ) )
| ~ ( visFreeVar @ SY412 @ SY413 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SY411 != SY412 ) )
| ~ ( visFreeVar @ SY412 @ SY413 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(256,plain,
! [SV79: $i,SV52: $i,SV24: $i] :
( ( ! [SY414: $i] :
( ( vvar @ SV24 )
!= ( vabs @ SV52 @ SV79 @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(257,plain,
! [SV80: $i,SV25: $i,SV53: $i] :
( ( ! [SY415: $i,SY416: $i] :
( ~ ~ ( ( SV53
!= ( vapp @ SV25 @ SY416 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
| ~ ~ ( ( SY415
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SY415 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SY415 ) @ SY416 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(258,plain,
! [SV81: $i,SV26: $i,SV54: $i] :
( ( ( ( vlookup @ SV54 @ SV26 )
!= ( vsomeType @ SV81 ) )
| ( vtcheck @ SV26 @ ( vvar @ SV54 ) @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(259,plain,
! [SV82: $i,SV55: $i,SV27: $i] :
( ( ! [SY420: $i,SY421: $i,SY422: $i,SY423: $i] :
( ( SY422
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SY421 ) )
| ~ ~ ( ~ ~ ( ( SY420
!= ( vreduce @ SY421 ) )
| ~ ~ ( visSomeExp @ SY420 ) )
| ~ ~ ( visValue @ SY421 ) )
| ( SY423
!= ( vreduce @ SY422 ) )
| ( SY423 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(260,plain,
! [SV83: $i,SV56: $i,SV28: $i] :
( ( ! [SY424: $i] :
( ( SY424
!= ( vabs @ SV28 @ SV56 @ SV83 ) )
| ( visValue @ SY424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(261,plain,
! [SV29: $i,SV57: $i] :
( ( ( SV57
!= ( vvar @ SV29 ) )
= $true )
| ( ( ~ ( visValue @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(262,plain,
! [SV58: $i,SV30: $i,SV84: $i] :
( ( ( SV84
!= ( vapp @ SV30 @ SV58 ) )
| ~ ( visValue @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(263,plain,
! [SV1: $i,SV31: $i] :
( ( ( SV31
= ( vsomeExp @ SV1 ) )
= $false )
| ( ( visSomeExp @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(264,plain,
! [SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ! [SY425: $i,SY426: $i] :
~ ( ~ ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SY425 @ SY426 ) )
| ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SY425 ) )
| ( SV59 != SY426 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SY425 ) )
| ( SV59 != SY426 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SY425 @ SY426 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(265,plain,
! [SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ! [SY427: $i] :
( ~ ~ ( ( SV86
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
| ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SY427
!= ( vreduce @ SV86 ) )
| ( SY427 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(266,plain,
! [SV87: $i,SV61: $i,SV34: $i,SV5: $i] :
( ( ! [SY431: $i,SY432: $i,SY433: $i,SY434: $i,SY435: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY433 )
| ( SV34 != SY434 ) )
| ( SV61
!= ( vabs @ SY431 @ SY432 @ SY435 ) ) )
| ~ ~ ( ~ ( ( SY433 != SY431 ) )
| ~ ~ ( visFreeVar @ SY431 @ SY434 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SY431 @ SY432 @ ( vsubst @ SY433 @ SY434 @ SY435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(267,plain,
! [SV35: $i,SV6: $i] :
( ( ~ ( ( ( vsomeExp @ SV6 )
!= ( vsomeExp @ SV35 ) )
| ( SV6 = SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(268,plain,
! [SV35: $i,SV6: $i] :
( ( ~ ( ( SV6 != SV35 )
| ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(269,plain,
! [SV36: $i,SV62: $i,SV7: $i] :
( ( ( SV7
!= ( vsomeExp @ SV62 ) )
= $true )
| ( ( ( SV36
!= ( vgetSomeExp @ SV7 ) )
| ( SV36 = SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(270,plain,
! [SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ! [SY436: $i,SY437: $i,SY438: $i] :
( ~ ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SY436 ) ) @ SY437 @ SY438 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SY436 ) ) @ SY437 @ SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(271,plain,
! [SV64: $i] :
( ( ( vreduce @ ( vabs @ sK2_SY151 @ sK3_SY154 @ ve1 ) )
= ( vsomeExp @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(272,plain,
! [SV65: $i,SV38: $i,SV9: $i] :
( ( vempty
= ( vbind @ SV9 @ SV38 @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(273,plain,
! [SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ! [SY439: $i,SY440: $i,SY441: $i] :
( ~ ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SY439 ) ) @ SY440 @ SY441 ) )
| ( vtcheck @ ( vbind @ SV66 @ SV89 @ SY439 ) @ SY440 @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(274,plain,
! [SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ! [SY442: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SV90 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SY442 ) )
| ( vtcheck @ SV67 @ SV90 @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(275,plain,
! [SV68: $i,SV41: $i,SV12: $i,SV91: $i] :
( ( ! [SY443: $i] :
( ( SV91
!= ( vabs @ SV12 @ SV41 @ SV68 ) )
| ( SY443
!= ( vreduce @ SV91 ) )
| ( SY443 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(276,plain,
! [SV92: $i,SV69: $i,SV42: $i,SV13: $i] :
( ( ! [SY444: $i] :
( ( vabs @ SV13 @ SV42 @ SV69 )
!= ( vapp @ SV92 @ SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(277,plain,
! [SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ! [SY445: $i,SY446: $i,SY447: $i,SY448: $i,SY449: $i] :
( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SY445
!= ( vabs @ SY447 @ SY448 @ SY449 ) ) )
| ( SV43 != SY447 )
| ( SY446
!= ( vsubst @ SV70 @ SV93 @ SY445 ) )
| ( SY446
= ( vabs @ SY447 @ SY448 @ SY449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(278,plain,
( ( ( vempty != vempty )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(279,plain,
( ( ( ~ $true ) = $true )
| ( ( vempty = vempty )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(280,plain,
! [SV94: $i,SV71: $i,SV15: $i,SV44: $i] :
( ( ~ ~ ( ( SV44 != SV15 )
| ( SV71 != vempty ) )
| ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(281,plain,
! [SV16: $i] :
( ( ( ~ ( vtcheck @ vempty @ ve1 @ SV16 )
| ~ ~ ( visValue @ ve1 ) )
= $true )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(282,plain,
! [SV95: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ! [SY450: $i] :
( ~ ~ ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SY450 ) )
| ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) )
| ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SY450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(283,plain,
! [SV73: $i,SV18: $i,SV96: $i,SV46: $i] :
( ( ! [SY451: $i,SY452: $i,SY453: $i] :
( ( SV46
!= ( vapp @ ( vabs @ SV96 @ SY451 @ SY452 ) @ SV18 ) )
| ~ ~ ( ( SY453
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SY453 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SY451 @ SY452 ) @ ( vgetSomeExp @ SY453 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(284,plain,
! [SV97: $i,SV47: $i,SV19: $i,SV74: $i] :
( ( ! [SY454: $i,SY455: $i,SY456: $i] :
( ( SV74
!= ( vapp @ ( vabs @ SY454 @ SV19 @ SY456 ) @ SY455 ) )
| ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SY455 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SY455 ) )
| ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SY454 @ SY455 @ SY456 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(285,plain,
! [SV48: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ! [SY457: $i] :
( ~ ~ ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
| ~ ( vtcheck @ SV75 @ SV98 @ SY457 ) )
| ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(286,plain,
! [SV76: $i,SV21: $i,SV49: $i] :
( ( ( SV49
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV76
!= ( vreduce @ SV49 ) )
| ( SV76 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(287,plain,
! [SV77: $i,SV22: $i,SV99: $i,SV50: $i] :
( ( ! [SY458: $i] :
( ~ ( vtcheck @ ( vbind @ SV50 @ SV99 @ SV22 ) @ SV77 @ SY458 )
| ( vtcheck @ SV22 @ ( vabs @ SV50 @ SV99 @ SV77 ) @ ( varrow @ SV99 @ SY458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(288,plain,
! [SV23: $i,SV100: $i,SV78: $i,SV51: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ~ ( ( SV51 != SY459 )
| ( SV78
!= ( vabs @ SV100 @ SV23 @ SY460 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SY459 ) )
| ~ ( visFreeVar @ SY459 @ SY460 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SY459 ) )
| ~ ( visFreeVar @ SY459 @ SY460 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(289,plain,
! [SV101: $i,SV79: $i,SV52: $i,SV24: $i] :
( ( ( vvar @ SV24 )
!= ( vabs @ SV52 @ SV79 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(290,plain,
! [SV80: $i,SV102: $i,SV25: $i,SV53: $i] :
( ( ! [SY461: $i] :
( ~ ~ ( ( SV53
!= ( vapp @ SV25 @ SY461 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
| ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SY461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(291,plain,
! [SV81: $i,SV26: $i,SV54: $i] :
( ( ( ( vlookup @ SV54 @ SV26 )
!= ( vsomeType @ SV81 ) )
= $true )
| ( ( vtcheck @ SV26 @ ( vvar @ SV54 ) @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(292,plain,
! [SV103: $i,SV82: $i,SV55: $i,SV27: $i] :
( ( ! [SY465: $i,SY466: $i,SY467: $i] :
( ( SY466
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SY465 ) )
| ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SY465 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SY465 ) )
| ( SY467
!= ( vreduce @ SY466 ) )
| ( SY467 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(293,plain,
! [SV83: $i,SV56: $i,SV28: $i,SV104: $i] :
( ( ( SV104
!= ( vabs @ SV28 @ SV56 @ SV83 ) )
| ( visValue @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(294,plain,
! [SV29: $i,SV57: $i] :
( ( ( SV57
= ( vvar @ SV29 ) )
= $false )
| ( ( ~ ( visValue @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(295,plain,
! [SV58: $i,SV30: $i,SV84: $i] :
( ( ( SV84
!= ( vapp @ SV30 @ SV58 ) )
= $true )
| ( ( ~ ( visValue @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(296,plain,
! [SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ! [SY468: $i] :
~ ( ~ ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SV105 @ SY468 ) )
| ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SY468 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SY468 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SY468 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(297,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ~ ~ ( ( SV86
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
| ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(298,plain,
! [SV87: $i,SV107: $i,SV61: $i,SV34: $i,SV5: $i] :
( ( ! [SY472: $i,SY473: $i,SY474: $i,SY475: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY473 )
| ( SV34 != SY474 ) )
| ( SV61
!= ( vabs @ SV107 @ SY472 @ SY475 ) ) )
| ~ ~ ( ~ ( ( SY473 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SY474 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SY472 @ ( vsubst @ SY473 @ SY474 @ SY475 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(299,plain,
! [SV35: $i,SV6: $i] :
( ( ( ( vsomeExp @ SV6 )
!= ( vsomeExp @ SV35 ) )
| ( SV6 = SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(300,plain,
! [SV35: $i,SV6: $i] :
( ( ( SV6 != SV35 )
| ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(301,plain,
! [SV36: $i,SV62: $i,SV7: $i] :
( ( ( SV7
= ( vsomeExp @ SV62 ) )
= $false )
| ( ( ( SV36
!= ( vgetSomeExp @ SV7 ) )
| ( SV36 = SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(302,plain,
! [SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ! [SY476: $i,SY477: $i] :
( ~ ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SY476 @ SY477 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SY476 @ SY477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(303,plain,
! [SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ! [SY478: $i,SY479: $i] :
( ~ ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SY478 @ SY479 ) )
| ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SY478 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(304,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SV90 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) )
| ( vtcheck @ SV67 @ SV90 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(305,plain,
! [SV111: $i,SV68: $i,SV41: $i,SV12: $i,SV91: $i] :
( ( ( SV91
!= ( vabs @ SV12 @ SV41 @ SV68 ) )
| ( SV111
!= ( vreduce @ SV91 ) )
| ( SV111 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(306,plain,
! [SV112: $i,SV92: $i,SV69: $i,SV42: $i,SV13: $i] :
( ( ( vabs @ SV13 @ SV42 @ SV69 )
!= ( vapp @ SV92 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(307,plain,
! [SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ! [SY480: $i,SY481: $i,SY482: $i,SY483: $i] :
( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SY481 @ SY482 @ SY483 ) ) )
| ( SV43 != SY481 )
| ( SY480
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SY480
= ( vabs @ SY481 @ SY482 @ SY483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(308,plain,
( ( ( vempty = vempty )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(309,plain,
( ( $true = $false )
| ( ( vempty = vempty )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(310,plain,
! [SV94: $i,SV71: $i,SV15: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44 != SV15 )
| ( SV71 != vempty ) ) )
= $true )
| ( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(311,plain,
! [SV16: $i] :
( ( ( ~ ( vtcheck @ vempty @ ve1 @ SV16 ) )
= $true )
| ( ( ~ ~ ( visValue @ ve1 ) )
= $true )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(312,plain,
! [SV95: $i,SV114: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ~ ~ ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) )
| ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) )
| ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(313,plain,
! [SV73: $i,SV18: $i,SV115: $i,SV96: $i,SV46: $i] :
( ( ! [SY484: $i,SY485: $i] :
( ( SV46
!= ( vapp @ ( vabs @ SV96 @ SV115 @ SY484 ) @ SV18 ) )
| ~ ~ ( ( SY485
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SY485 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SY484 ) @ ( vgetSomeExp @ SY485 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(314,plain,
! [SV97: $i,SV47: $i,SV19: $i,SV116: $i,SV74: $i] :
( ( ! [SY486: $i,SY487: $i] :
( ( SV74
!= ( vapp @ ( vabs @ SV116 @ SV19 @ SY487 ) @ SY486 ) )
| ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SY486 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SY486 ) )
| ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SY486 @ SY487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(315,plain,
! [SV48: $i,SV117: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ~ ~ ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
| ~ ( vtcheck @ SV75 @ SV98 @ SV117 ) )
| ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(316,plain,
! [SV76: $i,SV21: $i,SV49: $i] :
( ( ( SV49
= ( vvar @ SV21 ) )
= $false )
| ( ( ( SV76
!= ( vreduce @ SV49 ) )
| ( SV76 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(317,plain,
! [SV118: $i,SV77: $i,SV22: $i,SV99: $i,SV50: $i] :
( ( ~ ( vtcheck @ ( vbind @ SV50 @ SV99 @ SV22 ) @ SV77 @ SV118 )
| ( vtcheck @ SV22 @ ( vabs @ SV50 @ SV99 @ SV77 ) @ ( varrow @ SV99 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(318,plain,
! [SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ! [SY488: $i] :
( ~ ~ ( ( SV51 != SV119 )
| ( SV78
!= ( vabs @ SV100 @ SV23 @ SY488 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SY488 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SY488 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(319,plain,
! [SV101: $i,SV79: $i,SV52: $i,SV24: $i] :
( ( ( vvar @ SV24 )
= ( vabs @ SV52 @ SV79 @ SV101 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(320,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV25: $i,SV53: $i] :
( ( ~ ~ ( ( SV53
!= ( vapp @ SV25 @ SV120 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
| ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(321,plain,
! [SV81: $i,SV26: $i,SV54: $i] :
( ( ( ( vlookup @ SV54 @ SV26 )
= ( vsomeType @ SV81 ) )
= $false )
| ( ( vtcheck @ SV26 @ ( vvar @ SV54 ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(322,plain,
! [SV103: $i,SV121: $i,SV82: $i,SV55: $i,SV27: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ( SY492
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
| ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) )
| ( SY493
!= ( vreduce @ SY492 ) )
| ( SY493 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(323,plain,
! [SV83: $i,SV56: $i,SV28: $i,SV104: $i] :
( ( ( SV104
!= ( vabs @ SV28 @ SV56 @ SV83 ) )
= $true )
| ( ( visValue @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(324,plain,
! [SV29: $i,SV57: $i] :
( ( ( visValue @ SV57 )
= $false )
| ( ( SV57
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(325,plain,
! [SV58: $i,SV30: $i,SV84: $i] :
( ( ( SV84
= ( vapp @ SV30 @ SV58 ) )
= $false )
| ( ( ~ ( visValue @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(326,plain,
! [SV122: $i,SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ~ ( ~ ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SV105 @ SV122 ) )
| ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(327,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ( ~ ~ ( ( SV86
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) ) )
= $true )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(328,plain,
! [SV87: $i,SV123: $i,SV107: $i,SV61: $i,SV34: $i,SV5: $i] :
( ( ! [SY494: $i,SY495: $i,SY496: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SY494 )
| ( SV34 != SY495 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SY496 ) ) )
| ~ ~ ( ~ ( ( SY494 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SY495 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SY494 @ SY495 @ SY496 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(329,plain,
! [SV35: $i,SV6: $i] :
( ( ( ( vsomeExp @ SV6 )
!= ( vsomeExp @ SV35 ) )
= $true )
| ( ( SV6 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(330,plain,
! [SV35: $i,SV6: $i] :
( ( ( SV6 != SV35 )
= $true )
| ( ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(331,plain,
! [SV62: $i,SV7: $i,SV36: $i] :
( ( ( SV36
!= ( vgetSomeExp @ SV7 ) )
= $true )
| ( ( SV36 = SV62 )
= $true )
| ( ( SV7
= ( vsomeExp @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(332,plain,
! [SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ! [SY497: $i] :
( ~ ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SY497 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(333,plain,
! [SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ! [SY498: $i] :
( ~ ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SY498 ) )
| ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SY498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(334,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV11 @ SV90 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) ) )
= $true )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(335,plain,
! [SV111: $i,SV68: $i,SV41: $i,SV12: $i,SV91: $i] :
( ( ( SV91
!= ( vabs @ SV12 @ SV41 @ SV68 ) )
= $true )
| ( ( ( SV111
!= ( vreduce @ SV91 ) )
| ( SV111 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(336,plain,
! [SV112: $i,SV92: $i,SV69: $i,SV42: $i,SV13: $i] :
( ( ( vabs @ SV13 @ SV42 @ SV69 )
= ( vapp @ SV92 @ SV112 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(337,plain,
! [SV126: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ! [SY499: $i,SY500: $i,SY501: $i] :
( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SY499 @ SY500 @ SY501 ) ) )
| ( SV43 != SY499 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SY499 @ SY500 @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(338,plain,
! [SV94: $i,SV71: $i,SV15: $i,SV44: $i] :
( ( ( ~ ( ( SV44 != SV15 )
| ( SV71 != vempty ) ) )
= $false )
| ( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(339,plain,
! [SV16: $i] :
( ( ( vtcheck @ vempty @ ve1 @ SV16 )
= $false )
| ( ( ~ ~ ( visValue @ ve1 ) )
= $true )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(340,plain,
! [SV95: $i,SV114: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) )
| ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) ) )
= $true )
| ( ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(341,plain,
! [SV73: $i,SV18: $i,SV127: $i,SV115: $i,SV96: $i,SV46: $i] :
( ( ! [SY502: $i] :
( ( SV46
!= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
| ~ ~ ( ( SY502
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SY502 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SY502 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(342,plain,
! [SV97: $i,SV47: $i,SV128: $i,SV19: $i,SV116: $i,SV74: $i] :
( ( ! [SY503: $i] :
( ( SV74
!= ( vapp @ ( vabs @ SV116 @ SV19 @ SY503 ) @ SV128 ) )
| ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) )
| ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SY503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(343,plain,
! [SV48: $i,SV117: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ( ~ ~ ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
| ~ ( vtcheck @ SV75 @ SV98 @ SV117 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(344,plain,
! [SV21: $i,SV49: $i,SV76: $i] :
( ( ( SV76
!= ( vreduce @ SV49 ) )
= $true )
| ( ( SV76 = vnoExp )
= $true )
| ( ( SV49
= ( vvar @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(345,plain,
! [SV118: $i,SV77: $i,SV22: $i,SV99: $i,SV50: $i] :
( ( ( ~ ( vtcheck @ ( vbind @ SV50 @ SV99 @ SV22 ) @ SV77 @ SV118 ) )
= $true )
| ( ( vtcheck @ SV22 @ ( vabs @ SV50 @ SV99 @ SV77 ) @ ( varrow @ SV99 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(346,plain,
! [SV129: $i,SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ~ ~ ( ( SV51 != SV119 )
| ( SV78
!= ( vabs @ SV100 @ SV23 @ SV129 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(347,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV25: $i,SV53: $i] :
( ( ( ~ ~ ( ( SV53
!= ( vapp @ SV25 @ SV120 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) ) )
= $true )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(348,plain,
! [SV103: $i,SV121: $i,SV82: $i,SV55: $i,SV27: $i,SV130: $i] :
( ( ! [SY504: $i] :
( ( SV130
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
| ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) )
| ( SY504
!= ( vreduce @ SV130 ) )
| ( SY504 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(349,plain,
! [SV83: $i,SV56: $i,SV28: $i,SV104: $i] :
( ( ( SV104
= ( vabs @ SV28 @ SV56 @ SV83 ) )
= $false )
| ( ( visValue @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(350,plain,
! [SV58: $i,SV30: $i,SV84: $i] :
( ( ( visValue @ SV84 )
= $false )
| ( ( SV84
= ( vapp @ SV30 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(351,plain,
! [SV122: $i,SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ~ ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SV105 @ SV122 ) )
| ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(352,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ( ~ ( ( SV86
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) ) )
= $false )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(353,plain,
! [SV87: $i,SV123: $i,SV107: $i,SV61: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ! [SY505: $i,SY506: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SY505 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SY506 ) ) )
| ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SY505 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SY505 @ SY506 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(354,plain,
! [SV35: $i,SV6: $i] :
( ( ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) )
= $false )
| ( ( SV6 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(355,plain,
! [SV35: $i,SV6: $i] :
( ( ( SV6 = SV35 )
= $false )
| ( ( ( vsomeExp @ SV6 )
= ( vsomeExp @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(356,plain,
! [SV62: $i,SV7: $i,SV36: $i] :
( ( ( SV36
= ( vgetSomeExp @ SV7 ) )
= $false )
| ( ( SV36 = SV62 )
= $true )
| ( ( SV7
= ( vsomeExp @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(357,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ~ ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) )
| ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(358,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ~ ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 ) )
| ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(359,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV11 @ SV90 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) ) )
= $false )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(360,plain,
! [SV111: $i,SV68: $i,SV41: $i,SV12: $i,SV91: $i] :
( ( ( SV91
= ( vabs @ SV12 @ SV41 @ SV68 ) )
= $false )
| ( ( ( SV111
!= ( vreduce @ SV91 ) )
| ( SV111 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(361,plain,
! [SV126: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ! [SY507: $i,SY508: $i] :
( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SV134 @ SY507 @ SY508 ) ) )
| ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SY507 @ SY508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(362,plain,
! [SV94: $i,SV71: $i,SV15: $i,SV44: $i] :
( ( ( ( SV44 != SV15 )
| ( SV71 != vempty ) )
= $true )
| ( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(363,plain,
! [SV16: $i] :
( ( ( ~ ( visValue @ ve1 ) )
= $false )
| ( ( vtcheck @ vempty @ ve1 @ SV16 )
= $false )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(364,plain,
! [SV95: $i,SV114: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ( ~ ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) )
| ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) ) )
= $false )
| ( ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(365,plain,
! [SV73: $i,SV135: $i,SV18: $i,SV127: $i,SV115: $i,SV96: $i,SV46: $i] :
( ( ( SV46
!= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
| ~ ~ ( ( SV135
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SV135 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(366,plain,
! [SV97: $i,SV47: $i,SV128: $i,SV136: $i,SV19: $i,SV116: $i,SV74: $i] :
( ( ( SV74
!= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
| ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) )
| ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(367,plain,
! [SV48: $i,SV117: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ( ~ ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
| ~ ( vtcheck @ SV75 @ SV98 @ SV117 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(368,plain,
! [SV21: $i,SV49: $i,SV76: $i] :
( ( ( SV76
= ( vreduce @ SV49 ) )
= $false )
| ( ( SV76 = vnoExp )
= $true )
| ( ( SV49
= ( vvar @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(369,plain,
! [SV118: $i,SV77: $i,SV22: $i,SV99: $i,SV50: $i] :
( ( ( vtcheck @ ( vbind @ SV50 @ SV99 @ SV22 ) @ SV77 @ SV118 )
= $false )
| ( ( vtcheck @ SV22 @ ( vabs @ SV50 @ SV99 @ SV77 ) @ ( varrow @ SV99 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(370,plain,
! [SV129: $i,SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ( ~ ~ ( ( SV51 != SV119 )
| ( SV78
!= ( vabs @ SV100 @ SV23 @ SV129 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(371,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV25: $i,SV53: $i] :
( ( ( ~ ( ( SV53
!= ( vapp @ SV25 @ SV120 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) ) )
= $false )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(372,plain,
! [SV137: $i,SV103: $i,SV121: $i,SV82: $i,SV55: $i,SV27: $i,SV130: $i] :
( ( ( SV130
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
| ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) )
| ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(373,plain,
! [SV122: $i,SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ~ ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SV105 @ SV122 ) )
| ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(374,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(375,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ( ( SV86
!= ( vapp @ SV33 @ SV4 ) )
| ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
= $true )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(376,plain,
! [SV87: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ! [SY509: $i] :
( ~ ~ ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SY509 ) ) )
| ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SY509 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(377,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(378,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ( ~ ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(379,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ( ~ ~ ( visFreeVar @ SV11 @ SV90 )
| ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) )
= $true )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(380,plain,
! [SV68: $i,SV41: $i,SV12: $i,SV91: $i,SV111: $i] :
( ( ( SV111
!= ( vreduce @ SV91 ) )
= $true )
| ( ( SV111 = vnoExp )
= $true )
| ( ( SV91
= ( vabs @ SV12 @ SV41 @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(381,plain,
! [SV126: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ! [SY510: $i] :
( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SV134 @ SV139 @ SY510 ) ) )
| ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SY510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(382,plain,
! [SV94: $i,SV71: $i,SV15: $i,SV44: $i] :
( ( ( SV44 != SV15 )
= $true )
| ( ( SV71 != vempty )
= $true )
| ( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(383,plain,
! [SV16: $i] :
( ( ( visValue @ ve1 )
= $true )
| ( ( vtcheck @ vempty @ ve1 @ SV16 )
= $false )
| ( ( ~ ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(384,plain,
! [SV95: $i,SV114: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) )
| ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) )
= $true )
| ( ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(385,plain,
! [SV73: $i,SV135: $i,SV18: $i,SV127: $i,SV115: $i,SV96: $i,SV46: $i] :
( ( ( SV46
!= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $true )
| ( ( ~ ~ ( ( SV135
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SV135 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(386,plain,
! [SV97: $i,SV47: $i,SV128: $i,SV136: $i,SV19: $i,SV116: $i,SV74: $i] :
( ( ( SV74
!= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) )
| ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(387,plain,
! [SV48: $i,SV117: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
| ~ ( vtcheck @ SV75 @ SV98 @ SV117 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(388,plain,
! [SV129: $i,SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ( ~ ( ( SV51 != SV119 )
| ( SV78
!= ( vabs @ SV100 @ SV23 @ SV129 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(389,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV25: $i,SV53: $i] :
( ( ( ( SV53
!= ( vapp @ SV25 @ SV120 ) )
| ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
= $true )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(390,plain,
! [SV137: $i,SV103: $i,SV121: $i,SV82: $i,SV55: $i,SV27: $i,SV130: $i] :
( ( ( SV130
!= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) )
| ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(391,plain,
! [SV122: $i,SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SV105 @ SV122 ) )
| ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(392,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) )
| ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(393,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ( SV86
!= ( vapp @ SV33 @ SV4 ) )
= $true )
| ( ( ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
= $true )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(394,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) ) )
| ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(395,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ( ~ ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(396,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ( ~ ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(397,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ( ~ ~ ( visFreeVar @ SV11 @ SV90 ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) )
= $true )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(398,plain,
! [SV68: $i,SV41: $i,SV12: $i,SV91: $i,SV111: $i] :
( ( ( SV111
= ( vreduce @ SV91 ) )
= $false )
| ( ( SV111 = vnoExp )
= $true )
| ( ( SV91
= ( vabs @ SV12 @ SV41 @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(399,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
| ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(400,plain,
! [SV94: $i,SV71: $i,SV15: $i,SV44: $i] :
( ( ( SV44 = SV15 )
= $false )
| ( ( SV71 != vempty )
= $true )
| ( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(401,plain,
! [SV16: $i] :
( ( ( ! [SX1: $i] :
( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) ) )
= $false )
| ( ( vtcheck @ vempty @ ve1 @ SV16 )
= $false )
| ( ( visValue @ ve1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(402,plain,
! [SV95: $i,SV114: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ( ~ ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) ) )
= $true )
| ( ( ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) )
= $true )
| ( ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(403,plain,
! [SV73: $i,SV135: $i,SV18: $i,SV127: $i,SV115: $i,SV96: $i,SV46: $i] :
( ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false )
| ( ( ~ ~ ( ( SV135
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SV135 ) )
| ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(404,plain,
! [SV97: $i,SV47: $i,SV128: $i,SV136: $i,SV19: $i,SV116: $i,SV74: $i] :
( ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) )
| ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(405,plain,
! [SV48: $i,SV117: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ( ( vlookup @ SV20 @ SV75 )
!= vnoType )
= $true )
| ( ( ~ ( vtcheck @ SV75 @ SV98 @ SV117 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(406,plain,
! [SV129: $i,SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ( ( SV51 != SV119 )
| ( SV78
!= ( vabs @ SV100 @ SV23 @ SV129 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(407,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV25: $i,SV53: $i] :
( ( ( SV53
!= ( vapp @ SV25 @ SV120 ) )
= $true )
| ( ( ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
= $true )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(408,plain,
! [SV137: $i,SV103: $i,SV121: $i,SV82: $i,SV55: $i,SV27: $i,SV130: $i] :
( ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) )
| ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(409,plain,
! [SV122: $i,SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ( ( vabs @ SV3 @ SV32 @ SV59 )
!= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(410,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(411,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV33: $i,SV86: $i] :
( ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( ~ ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
= $true )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(412,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(413,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ( ~ ( ( SV63 != SV8 ) )
| ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(414,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ( ( SV66 != SV10 )
| ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(415,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ( ~ ( visFreeVar @ SV11 @ SV90 ) )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) )
= $true )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(416,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) ) ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(417,plain,
! [SV94: $i,SV15: $i,SV44: $i,SV71: $i] :
( ( ( SV71 = vempty )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
| ( SV94 = vnoType ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(418,plain,
! [SV16: $i] :
( ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ ( sK4_SX1 @ SV16 ) ) )
= $false )
| ( ( vtcheck @ vempty @ ve1 @ SV16 )
= $false )
| ( ( visValue @ ve1 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[401]) ).
thf(419,plain,
! [SV95: $i,SV114: $i,SV17: $i,SV72: $i,SV45: $i] :
( ( ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) )
= $false )
| ( ( ~ ( vtcheck @ SV45 @ SV95 @ SV17 ) )
= $true )
| ( ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(420,plain,
! [SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i,SV18: $i,SV135: $i] :
( ( ( ~ ~ ( ( SV135
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SV135 ) ) )
= $true )
| ( ( ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(421,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(422,plain,
! [SV48: $i,SV117: $i,SV98: $i,SV75: $i,SV20: $i] :
( ( ( ( vlookup @ SV20 @ SV75 )
= vnoType )
= $false )
| ( ( ~ ( vtcheck @ SV75 @ SV98 @ SV117 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(423,plain,
! [SV129: $i,SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ( SV51 != SV119 )
= $true )
| ( ( SV78
!= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(424,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV25: $i,SV53: $i] :
( ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( ~ ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
= $true )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(425,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(426,plain,
! [SV122: $i,SV105: $i,SV85: $i,SV59: $i,SV32: $i,SV3: $i] :
( ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(427,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) ) )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(428,plain,
! [SV106: $i,SV60: $i,SV4: $i,SV86: $i,SV33: $i] :
( ( ( ! [SY281: $i,SY282: $i,SY283: $i] :
( SV33
!= ( vabs @ SY281 @ SY282 @ SY283 ) ) )
= $false )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(429,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(430,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ( ~ ( ( SV63 != SV8 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(431,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ( SV66 != SV10 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(432,plain,
! [SV110: $i,SV67: $i,SV40: $i,SV90: $i,SV11: $i] :
( ( ( visFreeVar @ SV11 @ SV90 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 ) )
= $true )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(433,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( ~ ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) ) ) )
= $false )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(434,plain,
! [SV15: $i,SV71: $i,SV44: $i,SV94: $i] :
( ( ( SV94
!= ( vlookup @ SV44 @ SV71 ) )
= $true )
| ( ( SV94 = vnoType )
= $true )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV71 = vempty )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(435,plain,
! [SV16: $i] :
( ( ( ( vreduce @ ve1 )
= ( vsomeExp @ ( sK4_SX1 @ SV16 ) ) )
= $true )
| ( ( vtcheck @ vempty @ ve1 @ SV16 )
= $false )
| ( ( visValue @ ve1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(436,plain,
! [SV114: $i,SV72: $i,SV17: $i,SV95: $i,SV45: $i] :
( ( ( vtcheck @ SV45 @ SV95 @ SV17 )
= $false )
| ( ( vtcheck @ SV45 @ SV72 @ ( varrow @ SV17 @ SV114 ) )
= $false )
| ( ( vtcheck @ SV45 @ ( vapp @ SV72 @ SV95 ) @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(437,plain,
! [SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i,SV18: $i,SV135: $i] :
( ( ( ~ ( ( SV135
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SV135 ) ) )
= $false )
| ( ( ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(438,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ~ ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) ) )
= $false )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(439,plain,
! [SV48: $i,SV20: $i,SV117: $i,SV98: $i,SV75: $i] :
( ( ( vtcheck @ SV75 @ SV98 @ SV117 )
= $false )
| ( ( ( vlookup @ SV20 @ SV75 )
= vnoType )
= $false )
| ( ( vtcheck @ ( vbind @ SV20 @ SV48 @ SV75 ) @ SV98 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(440,plain,
! [SV129: $i,SV23: $i,SV100: $i,SV78: $i,SV119: $i,SV51: $i] :
( ( ( SV51 = SV119 )
= $false )
| ( ( SV78
!= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(441,plain,
! [SV80: $i,SV102: $i,SV120: $i,SV53: $i,SV25: $i] :
( ( ( ! [SY257: $i,SY258: $i,SY259: $i] :
( SV25
!= ( vabs @ SY257 @ SY258 @ SY259 ) ) )
= $false )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(442,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ~ ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) ) )
= $false )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(443,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(444,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
| ( SV59 != SV122 ) )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(445,plain,
! [SV86: $i,SV4: $i,SV60: $i,SV106: $i,SV33: $i] :
( ( ( ! [SY511: $i,SY512: $i] :
( SV33
!= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ SY511 @ SY512 ) ) )
= $false )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[428]) ).
thf(446,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) )
| ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(447,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ( SV63 != SV8 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(448,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV89: $i,SV10: $i,SV66: $i] :
( ( ( SV66 = SV10 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(449,plain,
! [SV110: $i,SV90: $i,SV67: $i,SV40: $i,SV11: $i] :
( ( ( vtcheck @ ( vbind @ SV11 @ SV40 @ SV67 ) @ SV90 @ SV110 )
= $false )
| ( ( visFreeVar @ SV11 @ SV90 )
= $true )
| ( ( vtcheck @ SV67 @ SV90 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(450,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
| ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(451,plain,
! [SV15: $i,SV71: $i,SV44: $i,SV94: $i] :
( ( ( SV94
= ( vlookup @ SV44 @ SV71 ) )
= $false )
| ( ( SV94 = vnoType )
= $true )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV71 = vempty )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(452,plain,
! [SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i,SV18: $i,SV135: $i] :
( ( ( ( SV135
!= ( vreduce @ SV18 ) )
| ~ ( visSomeExp @ SV135 ) )
= $true )
| ( ( ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(453,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
| ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(454,plain,
! [SV119: $i,SV51: $i,SV129: $i,SV23: $i,SV100: $i,SV78: $i] :
( ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(455,plain,
! [SV53: $i,SV120: $i,SV102: $i,SV80: $i,SV25: $i] :
( ( ( ! [SY513: $i,SY514: $i] :
( SV25
!= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ SY513 @ SY514 ) ) )
= $false )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[441]) ).
thf(456,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
| ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(457,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) ) )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(458,plain,
! [SV105: $i,SV85: $i,SV32: $i,SV3: $i,SV122: $i,SV59: $i] :
( ( ( SV59 != SV122 )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(459,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) ) )
= $true )
| ( ( SV59 != SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(460,plain,
! [SV86: $i,SV4: $i,SV60: $i,SV106: $i,SV33: $i] :
( ( ( ! [SY515: $i] :
( SV33
!= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ SY515 ) ) )
= $false )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[445]) ).
thf(461,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) ) )
= $true )
| ( ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(462,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV88: $i,SV8: $i,SV63: $i] :
( ( ( SV63 = SV8 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(463,plain,
! [SV133: $i,SV125: $i,SV109: $i,SV39: $i,SV10: $i,SV89: $i,SV66: $i] :
( ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ ( vbind @ SV10 @ SV39 @ SV109 ) ) @ SV125 @ SV133 )
= $false )
| ( ( SV66 = SV10 )
= $false )
| ( ( vtcheck @ ( vbind @ SV66 @ SV89 @ SV109 ) @ SV125 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(464,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( ~ ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) ) )
= $true )
| ( ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(465,plain,
! [SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i,SV18: $i,SV135: $i] :
( ( ( SV135
!= ( vreduce @ SV18 ) )
= $true )
| ( ( ~ ( visSomeExp @ SV135 ) )
= $true )
| ( ( ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(466,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ~ ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) ) )
= $true )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(467,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
| ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(468,plain,
! [SV53: $i,SV120: $i,SV102: $i,SV80: $i,SV25: $i] :
( ( ( ! [SY516: $i] :
( SV25
!= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ SY516 ) ) )
= $false )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[455]) ).
thf(469,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ~ ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) ) )
= $true )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(470,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) ) )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(471,plain,
! [SV105: $i,SV85: $i,SV32: $i,SV3: $i,SV122: $i,SV59: $i] :
( ( ( SV59 = SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(472,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV85 )
| ( SV32 != SV105 ) ) )
= $false )
| ( ( SV59 != SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(473,plain,
! [SV86: $i,SV4: $i,SV60: $i,SV106: $i,SV33: $i] :
( ( ( SV33
!= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $false )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[460]) ).
thf(474,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV131 )
| ( SV34 != SV138 ) ) )
= $false )
| ( ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(475,plain,
! [SV132: $i,SV124: $i,SV108: $i,SV37: $i,SV8: $i,SV88: $i,SV63: $i] :
( ( ( vtcheck @ ( vbind @ SV63 @ SV88 @ ( vbind @ SV8 @ SV37 @ SV108 ) ) @ SV124 @ SV132 )
= $false )
| ( ( SV63 = SV8 )
= $true )
| ( ( vtcheck @ ( vbind @ SV8 @ SV37 @ ( vbind @ SV63 @ SV88 @ SV108 ) ) @ SV124 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(476,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( ~ ( ( SV70 != SV43 )
| ( SV93 != SV14 ) ) )
= $false )
| ( ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(477,plain,
! [SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i,SV18: $i,SV135: $i] :
( ( ( SV135
= ( vreduce @ SV18 ) )
= $false )
| ( ( ~ ( visSomeExp @ SV135 ) )
= $true )
| ( ( ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(478,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ~ ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) ) )
= $false )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(479,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) ) )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(480,plain,
! [SV23: $i,SV129: $i,SV119: $i,SV100: $i,SV78: $i,SV51: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) ) )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(481,plain,
! [SV53: $i,SV120: $i,SV102: $i,SV80: $i,SV25: $i] :
( ( ( SV25
!= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $false )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[468]) ).
thf(482,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ~ ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) ) )
= $false )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(483,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(484,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( ( SV3 != SV85 )
| ( SV32 != SV105 ) )
= $true )
| ( ( SV59 != SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(485,plain,
! [SV86: $i,SV4: $i,SV60: $i,SV106: $i,SV33: $i] :
( ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
| ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(486,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( ( SV5 != SV131 )
| ( SV34 != SV138 ) )
= $true )
| ( ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(487,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( ( SV70 != SV43 )
| ( SV93 != SV14 ) )
= $true )
| ( ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(488,plain,
! [SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i,SV18: $i,SV135: $i] :
( ( ( visSomeExp @ SV135 )
= $false )
| ( ( SV135
= ( vreduce @ SV18 ) )
= $false )
| ( ( ( SV73
!= ( vreduce @ SV46 ) )
| ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) ) )
= $true )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(489,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ( SV47
!= ( vreduce @ SV128 ) )
| ~ ~ ( visSomeExp @ SV47 ) )
= $true )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(490,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
| ( visFreeVar @ SV51 @ SV78 ) )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(491,plain,
! [SV23: $i,SV129: $i,SV119: $i,SV100: $i,SV78: $i,SV51: $i] :
( ( ( ~ ( visFreeVar @ SV51 @ SV78 )
| ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(492,plain,
! [SV53: $i,SV120: $i,SV102: $i,SV80: $i,SV25: $i] :
( ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
| ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(493,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ( SV103
!= ( vreduce @ SV121 ) )
| ~ ~ ( visSomeExp @ SV103 ) )
= $true )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(494,plain,
! [SV122: $i,SV105: $i,SV59: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( SV3 != SV85 )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(495,plain,
! [SV122: $i,SV85: $i,SV59: $i,SV3: $i,SV105: $i,SV32: $i] :
( ( ( SV32 != SV105 )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(496,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( SV3 != SV85 )
= $true )
| ( ( SV32 != SV105 )
= $true )
| ( ( SV59 != SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(497,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( ~ ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) ) )
= $true )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(498,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( SV5 != SV131 )
= $true )
| ( ( SV34 != SV138 )
= $true )
| ( ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(499,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( SV70 != SV43 )
= $true )
| ( ( SV93 != SV14 )
= $true )
| ( ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(500,plain,
! [SV18: $i,SV135: $i,SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i] :
( ( ( SV73
!= ( vreduce @ SV46 ) )
= $true )
| ( ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( vreduce @ SV18 ) )
= $false )
| ( ( visSomeExp @ SV135 )
= $false )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(501,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( SV47
!= ( vreduce @ SV128 ) )
= $true )
| ( ( ~ ~ ( visSomeExp @ SV47 ) )
= $true )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(502,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(503,plain,
! [SV23: $i,SV129: $i,SV119: $i,SV100: $i,SV78: $i,SV51: $i] :
( ( ( ~ ( visFreeVar @ SV51 @ SV78 ) )
= $true )
| ( ( ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(504,plain,
! [SV120: $i,SV53: $i,SV80: $i,SV25: $i,SV102: $i] :
( ( ( ~ ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) ) )
= $true )
| ( ( ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(505,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( SV103
!= ( vreduce @ SV121 ) )
= $true )
| ( ( ~ ~ ( visSomeExp @ SV103 ) )
= $true )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(506,plain,
! [SV122: $i,SV105: $i,SV59: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( SV3 = SV85 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(507,plain,
! [SV122: $i,SV85: $i,SV59: $i,SV3: $i,SV105: $i,SV32: $i] :
( ( ( SV32 = SV105 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(508,plain,
! [SV122: $i,SV59: $i,SV105: $i,SV32: $i,SV85: $i,SV3: $i] :
( ( ( SV3 = SV85 )
= $false )
| ( ( SV32 != SV105 )
= $true )
| ( ( SV59 != SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(509,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( ~ ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) ) )
= $false )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(510,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i] :
( ( ( SV5 = SV131 )
= $false )
| ( ( SV34 != SV138 )
= $true )
| ( ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(511,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i] :
( ( ( SV70 = SV43 )
= $false )
| ( ( SV93 != SV14 )
= $true )
| ( ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(512,plain,
! [SV18: $i,SV135: $i,SV127: $i,SV115: $i,SV96: $i,SV46: $i,SV73: $i] :
( ( ( SV73
= ( vreduce @ SV46 ) )
= $false )
| ( ( SV73
= ( vsomeExp @ ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ ( vgetSomeExp @ SV135 ) ) ) )
= $true )
| ( ( SV135
= ( vreduce @ SV18 ) )
= $false )
| ( ( visSomeExp @ SV135 )
= $false )
| ( ( SV46
= ( vapp @ ( vabs @ SV96 @ SV115 @ SV127 ) @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(513,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( SV47
= ( vreduce @ SV128 ) )
= $false )
| ( ( ~ ~ ( visSomeExp @ SV47 ) )
= $true )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(514,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) )
= $false )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(515,plain,
! [SV23: $i,SV129: $i,SV119: $i,SV100: $i,SV78: $i,SV51: $i] :
( ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( ~ ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) ) )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(516,plain,
! [SV120: $i,SV53: $i,SV80: $i,SV25: $i,SV102: $i] :
( ( ( ~ ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) ) )
= $false )
| ( ( ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(517,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( ~ ~ ( visSomeExp @ SV103 ) )
= $true )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(518,plain,
! [SV122: $i,SV59: $i,SV85: $i,SV3: $i,SV105: $i,SV32: $i] :
( ( ( SV32 = SV105 )
= $false )
| ( ( SV3 = SV85 )
= $false )
| ( ( SV59 != SV122 )
= $true )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(519,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( ( SV60
!= ( vreduce @ SV33 ) )
| ~ ~ ( visSomeExp @ SV60 ) )
= $true )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(520,plain,
! [SV87: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i,SV131: $i,SV5: $i,SV138: $i,SV34: $i] :
( ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
!= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(521,plain,
! [SV126: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV43: $i,SV70: $i,SV14: $i,SV93: $i] :
( ( ( SV93 = SV14 )
= $false )
| ( ( SV70 = SV43 )
= $false )
| ( ( SV113
!= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(522,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( ~ ( visSomeExp @ SV47 ) )
= $false )
| ( ( SV47
= ( vreduce @ SV128 ) )
= $false )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(523,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(524,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != SV119 ) )
| ~ ( visFreeVar @ SV119 @ SV129 ) )
= $false )
| ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(525,plain,
! [SV120: $i,SV53: $i,SV80: $i,SV25: $i,SV102: $i] :
( ( ( ( SV102
!= ( vreduce @ SV25 ) )
| ~ ( visSomeExp @ SV102 ) )
= $true )
| ( ( ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(526,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( ~ ( visSomeExp @ SV103 ) )
= $false )
| ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(527,plain,
! [SV105: $i,SV32: $i,SV85: $i,SV3: $i,SV122: $i,SV59: $i] :
( ( ( SV59 = SV122 )
= $false )
| ( ( SV3 = SV85 )
= $false )
| ( ( SV32 = SV105 )
= $false )
| ( ( ( vabs @ SV3 @ SV32 @ SV59 )
= ( vabs @ SV85 @ SV105 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(528,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( SV60
!= ( vreduce @ SV33 ) )
= $true )
| ( ( ~ ~ ( visSomeExp @ SV60 ) )
= $true )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(529,plain,
! [SV87: $i,SV138: $i,SV34: $i,SV131: $i,SV5: $i,SV140: $i,SV123: $i,SV107: $i,SV61: $i] :
( ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV34 = SV138 )
= $false )
| ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
| ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(530,plain,
! [SV126: $i,SV14: $i,SV93: $i,SV43: $i,SV70: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i] :
( ( ( SV113
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $false )
| ( ( SV70 = SV43 )
= $false )
| ( ( SV93 = SV14 )
= $false )
| ( ( ( SV43 != SV134 )
| ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(531,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV128: $i,SV47: $i] :
( ( ( visSomeExp @ SV47 )
= $true )
| ( ( SV47
= ( vreduce @ SV128 ) )
= $false )
| ( ( ~ ( visValue @ SV128 ) )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(532,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != SV119 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV119 @ SV129 ) )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(533,plain,
! [SV129: $i,SV23: $i,SV78: $i,SV51: $i,SV119: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != SV119 ) ) )
= $false )
| ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(534,plain,
! [SV23: $i,SV100: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i] :
( ( ( ~ ( visFreeVar @ SV119 @ SV129 ) )
= $false )
| ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(535,plain,
! [SV120: $i,SV53: $i,SV80: $i,SV25: $i,SV102: $i] :
( ( ( SV102
!= ( vreduce @ SV25 ) )
= $true )
| ( ( ~ ( visSomeExp @ SV102 ) )
= $true )
| ( ( ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(536,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV121: $i,SV103: $i] :
( ( ( visSomeExp @ SV103 )
= $true )
| ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( ~ ~ ( visValue @ SV121 ) )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(537,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( SV60
= ( vreduce @ SV33 ) )
= $false )
| ( ( ~ ~ ( visSomeExp @ SV60 ) )
= $true )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(538,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV138: $i,SV107: $i,SV131: $i] :
( ( ( ~ ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) ) )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(539,plain,
! [SV14: $i,SV141: $i,SV139: $i,SV113: $i,SV93: $i,SV70: $i,SV126: $i,SV134: $i,SV43: $i] :
( ( ( SV43 != SV134 )
= $true )
| ( ( ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true )
| ( ( SV93 = SV14 )
= $false )
| ( ( SV70 = SV43 )
= $false )
| ( ( SV113
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(540,plain,
! [SV19: $i,SV136: $i,SV116: $i,SV74: $i,SV97: $i,SV47: $i,SV128: $i] :
( ( ( visValue @ SV128 )
= $false )
| ( ( SV47
= ( vreduce @ SV128 ) )
= $false )
| ( ( visSomeExp @ SV47 )
= $true )
| ( ( ( SV97
!= ( vreduce @ SV74 ) )
| ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) ) )
= $true )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(541,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( SV100 != SV119 )
= $false )
| ( ( ~ ( visFreeVar @ SV119 @ SV129 ) )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(542,plain,
! [SV129: $i,SV23: $i,SV78: $i,SV51: $i,SV119: $i,SV100: $i] :
( ( ( SV100 != SV119 )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(543,plain,
! [SV23: $i,SV100: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i] :
( ( ( visFreeVar @ SV119 @ SV129 )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(544,plain,
! [SV120: $i,SV53: $i,SV80: $i,SV25: $i,SV102: $i] :
( ( ( SV102
= ( vreduce @ SV25 ) )
= $false )
| ( ( ~ ( visSomeExp @ SV102 ) )
= $true )
| ( ( ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(545,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV103: $i,SV121: $i] :
( ( ( ~ ( visValue @ SV121 ) )
= $false )
| ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( visSomeExp @ SV103 )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(546,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( ~ ( visSomeExp @ SV60 ) )
= $false )
| ( ( SV60
= ( vreduce @ SV33 ) )
= $false )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(547,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV138: $i,SV107: $i,SV131: $i] :
( ( ( ~ ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) ) )
= $false )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(548,plain,
! [SV14: $i,SV141: $i,SV139: $i,SV113: $i,SV93: $i,SV70: $i,SV126: $i,SV134: $i,SV43: $i] :
( ( ( SV43 = SV134 )
= $false )
| ( ( ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
| ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) ) )
= $true )
| ( ( SV93 = SV14 )
= $false )
| ( ( SV70 = SV43 )
= $false )
| ( ( SV113
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(549,plain,
! [SV19: $i,SV47: $i,SV136: $i,SV128: $i,SV116: $i,SV74: $i,SV97: $i] :
( ( ( SV97
!= ( vreduce @ SV74 ) )
= $true )
| ( ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) )
= $true )
| ( ( visSomeExp @ SV47 )
= $true )
| ( ( SV47
= ( vreduce @ SV128 ) )
= $false )
| ( ( visValue @ SV128 )
= $false )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(550,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV129: $i,SV119: $i,SV100: $i] :
( ( ( SV100 = SV119 )
= $true )
| ( ( ~ ( visFreeVar @ SV119 @ SV129 ) )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(551,plain,
! [SV129: $i,SV23: $i,SV78: $i,SV51: $i,SV119: $i,SV100: $i] :
( ( ( SV100 = SV119 )
= $false )
| ( ( visFreeVar @ SV51 @ SV78 )
= $false )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(552,plain,
! [SV120: $i,SV53: $i,SV80: $i,SV25: $i,SV102: $i] :
( ( ( visSomeExp @ SV102 )
= $false )
| ( ( SV102
= ( vreduce @ SV25 ) )
= $false )
| ( ( ( SV80
!= ( vreduce @ SV53 ) )
| ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) ) )
= $true )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(553,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV130: $i,SV137: $i,SV103: $i,SV121: $i] :
( ( ( visValue @ SV121 )
= $true )
| ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( visSomeExp @ SV103 )
= $true )
| ( ( ( SV137
!= ( vreduce @ SV130 ) )
| ( SV137 = vnoExp ) )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(554,plain,
! [SV4: $i,SV86: $i,SV106: $i,SV33: $i,SV60: $i] :
( ( ( visSomeExp @ SV60 )
= $true )
| ( ( SV60
= ( vreduce @ SV33 ) )
= $false )
| ( ( ( SV106
!= ( vreduce @ SV86 ) )
| ( SV106 = vnoExp ) )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(555,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV138: $i,SV107: $i,SV131: $i] :
( ( ( ~ ( ( SV131 != SV107 ) )
| ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(556,plain,
! [SV14: $i,SV43: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV93: $i,SV70: $i,SV126: $i] :
( ( ( SV126
!= ( vsubst @ SV70 @ SV93 @ SV113 ) )
= $true )
| ( ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( SV43 = SV134 )
= $false )
| ( ( SV93 = SV14 )
= $false )
| ( ( SV70 = SV43 )
= $false )
| ( ( SV113
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(557,plain,
! [SV19: $i,SV47: $i,SV136: $i,SV128: $i,SV116: $i,SV74: $i,SV97: $i] :
( ( ( SV97
= ( vreduce @ SV74 ) )
= $false )
| ( ( SV97
= ( vsomeExp @ ( vsubst @ SV116 @ SV128 @ SV136 ) ) )
= $true )
| ( ( visSomeExp @ SV47 )
= $true )
| ( ( SV47
= ( vreduce @ SV128 ) )
= $false )
| ( ( visValue @ SV128 )
= $false )
| ( ( SV74
= ( vapp @ ( vabs @ SV116 @ SV19 @ SV136 ) @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(558,plain,
! [SV23: $i,SV78: $i,SV51: $i,SV100: $i,SV129: $i,SV119: $i] :
( ( ( visFreeVar @ SV119 @ SV129 )
= $false )
| ( ( SV100 = SV119 )
= $true )
| ( ( visFreeVar @ SV51 @ SV78 )
= $true )
| ( ( SV51 = SV119 )
= $false )
| ( ( SV78
= ( vabs @ SV100 @ SV23 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(559,plain,
! [SV25: $i,SV120: $i,SV102: $i,SV53: $i,SV80: $i] :
( ( ( SV80
!= ( vreduce @ SV53 ) )
= $true )
| ( ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) )
= $true )
| ( ( SV102
= ( vreduce @ SV25 ) )
= $false )
| ( ( visSomeExp @ SV102 )
= $false )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(560,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV121: $i,SV103: $i,SV130: $i,SV137: $i] :
( ( ( SV137
!= ( vreduce @ SV130 ) )
= $true )
| ( ( SV137 = vnoExp )
= $true )
| ( ( visSomeExp @ SV103 )
= $true )
| ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( visValue @ SV121 )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(561,plain,
! [SV4: $i,SV33: $i,SV60: $i,SV86: $i,SV106: $i] :
( ( ( SV106
!= ( vreduce @ SV86 ) )
= $true )
| ( ( SV106 = vnoExp )
= $true )
| ( ( SV60
= ( vreduce @ SV33 ) )
= $false )
| ( ( visSomeExp @ SV60 )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(562,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV138: $i,SV107: $i,SV131: $i] :
( ( ( ~ ( ( SV131 != SV107 ) ) )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(563,plain,
! [SV14: $i,SV43: $i,SV141: $i,SV139: $i,SV134: $i,SV113: $i,SV93: $i,SV70: $i,SV126: $i] :
( ( ( SV126
= ( vsubst @ SV70 @ SV93 @ SV113 ) )
= $false )
| ( ( SV126
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $true )
| ( ( SV43 = SV134 )
= $false )
| ( ( SV93 = SV14 )
= $false )
| ( ( SV70 = SV43 )
= $false )
| ( ( SV113
= ( vabs @ SV134 @ SV139 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(564,plain,
! [SV25: $i,SV120: $i,SV102: $i,SV53: $i,SV80: $i] :
( ( ( SV80
= ( vreduce @ SV53 ) )
= $false )
| ( ( SV80
= ( vsomeExp @ ( vapp @ ( vgetSomeExp @ SV102 ) @ SV120 ) ) )
= $true )
| ( ( SV102
= ( vreduce @ SV25 ) )
= $false )
| ( ( visSomeExp @ SV102 )
= $false )
| ( ( SV53
= ( vapp @ SV25 @ SV120 ) )
= $false )
| ( ( SV25
= ( vabs @ ( sK6_SY257 @ SV80 @ SV102 @ SV120 @ SV53 @ SV25 ) @ ( sK8_SY513 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) @ ( sK10_SY516 @ SV53 @ SV120 @ SV102 @ SV80 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(565,plain,
! [SV82: $i,SV55: $i,SV27: $i,SV121: $i,SV103: $i,SV130: $i,SV137: $i] :
( ( ( SV137
= ( vreduce @ SV130 ) )
= $false )
| ( ( SV137 = vnoExp )
= $true )
| ( ( visSomeExp @ SV103 )
= $true )
| ( ( SV103
= ( vreduce @ SV121 ) )
= $false )
| ( ( visValue @ SV121 )
= $true )
| ( ( SV130
= ( vapp @ ( vabs @ SV27 @ SV55 @ SV82 ) @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(566,plain,
! [SV4: $i,SV33: $i,SV60: $i,SV86: $i,SV106: $i] :
( ( ( SV106
= ( vreduce @ SV86 ) )
= $false )
| ( ( SV106 = vnoExp )
= $true )
| ( ( SV60
= ( vreduce @ SV33 ) )
= $false )
| ( ( visSomeExp @ SV60 )
= $true )
| ( ( SV86
= ( vapp @ SV33 @ SV4 ) )
= $false )
| ( ( SV33
= ( vabs @ ( sK5_SY281 @ SV106 @ SV60 @ SV4 @ SV86 @ SV33 ) @ ( sK7_SY511 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) @ ( sK9_SY515 @ SV86 @ SV4 @ SV60 @ SV106 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(567,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV138: $i,SV107: $i,SV131: $i] :
( ( ( SV131 != SV107 )
= $false )
| ( ( ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(568,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV138: $i,SV107: $i,SV131: $i] :
( ( ( SV131 = SV107 )
= $true )
| ( ( ~ ~ ( visFreeVar @ SV107 @ SV138 ) )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(569,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV131: $i,SV138: $i,SV107: $i] :
( ( ( ~ ( visFreeVar @ SV107 @ SV138 ) )
= $false )
| ( ( SV131 = SV107 )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(570,plain,
! [SV140: $i,SV123: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i,SV131: $i,SV138: $i,SV107: $i] :
( ( ( visFreeVar @ SV107 @ SV138 )
= $true )
| ( ( SV131 = SV107 )
= $true )
| ( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
| ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) ) )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(571,plain,
! [SV140: $i,SV138: $i,SV131: $i,SV123: $i,SV107: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i] :
( ( ( SV87
!= ( vsubst @ SV5 @ SV34 @ SV61 ) )
= $true )
| ( ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) )
= $true )
| ( ( SV131 = SV107 )
= $true )
| ( ( visFreeVar @ SV107 @ SV138 )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(572,plain,
! [SV140: $i,SV138: $i,SV131: $i,SV123: $i,SV107: $i,SV61: $i,SV34: $i,SV5: $i,SV87: $i] :
( ( ( SV87
= ( vsubst @ SV5 @ SV34 @ SV61 ) )
= $false )
| ( ( SV87
= ( vabs @ SV107 @ SV123 @ ( vsubst @ SV131 @ SV138 @ SV140 ) ) )
= $true )
| ( ( SV131 = SV107 )
= $true )
| ( ( visFreeVar @ SV107 @ SV138 )
= $true )
| ( ( SV34 = SV138 )
= $false )
| ( ( SV5 = SV131 )
= $false )
| ( ( SV61
= ( vabs @ SV107 @ SV123 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(573,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[131,572,566,565,564,563,558,557,551,543,527,512,507,506,475,471,463,451,449,439,436,435,398,369,368,356,355,354,350,349,336,324,321,319,309,308,272,271,263,199,165]) ).
thf(574,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM147+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
% 0.08/0.16 % Computer : n005.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 18:38:53 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/0.43
% 1.20/0.43 No.of.Axioms: 31
% 1.20/0.43
% 1.20/0.43 Length.of.Defs: 0
% 1.20/0.43
% 1.20/0.43 Contains.Choice.Funs: false
% 1.20/0.43 ...........................
% 1.20/0.43
% 1.20/0.43 ********************************
% 1.20/0.43 * All subproblems solved! *
% 1.20/0.43 ********************************
% 1.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:33,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:573,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.20/0.43
% 1.20/0.43 %**** Beginning of derivation protocol ****
% 1.20/0.43 % SZS output start CNFRefutation
% See solution above
% 1.20/0.43
% 1.20/0.43 %**** End of derivation protocol ****
% 1.20/0.43 %**** no. of clauses in derivation: 548 ****
% 1.20/0.43 %**** clause counter: 573 ****
% 1.20/0.43
% 1.20/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:33,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:573,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------