%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM144+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.86s 0.31s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 248 ( 139 unt; 0 typ; 0 def)
% Number of atoms : 1762 (1100 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 3498 ( 886 ~; 554 |; 53 &;1940 @)
% ( 0 <=>; 65 =>; 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 : 30 ( 27 usr; 11 con; 0-3 aty)
% Number of variables : 1266 ( 0 ^;1266 !; 0 ?;1266 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Vx,type,
sK1_Vx: $i ).
thf(tp_sK2_SY69,type,
sK2_SY69: $i ).
thf(tp_sK3_SY73,type,
sK3_SY73: $i ).
thf(tp_sK4_SY76,type,
sK4_SY76: $i ).
thf(tp_sK5_SY78,type,
sK5_SY78: $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,
! [VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ve1 )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ve1 @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Preservation-T-abs-IH') ).
thf(17,axiom,
! [Vx: $i,VS: $i,Ve: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce1) ).
thf(19,axiom,
! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeExp0) ).
thf(20,axiom,
! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1) ).
thf(22,axiom,
! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
thf(23,axiom,
! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someExp') ).
thf(28,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst3) ).
thf(33,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(34,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate') ).
thf(49,axiom,
! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).
thf(53,axiom,
! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0) ).
thf(54,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).
thf(56,axiom,
! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs') ).
thf(58,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-abs') ).
thf(60,conjecture,
! [Vx: $i,VS: $i,VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ( vabs @ Vx @ VS @ ve1 ) )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ( vabs @ Vx @ VS @ ve1 ) @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Preservation-T-abs') ).
thf(61,negated_conjecture,
( ( ! [Vx: $i,VS: $i,VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ( vabs @ Vx @ VS @ ve1 ) )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ( vabs @ Vx @ VS @ ve1 ) @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[60]) ).
thf(62,plain,
( ( ! [Vx: $i,VS: $i,VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ( vabs @ Vx @ VS @ ve1 ) )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ( vabs @ Vx @ VS @ ve1 ) @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ) )
= $false ),
inference(unfold_def,[status(thm)],[61]) ).
thf(63,plain,
( ( ! [VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ve1 )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ve1 @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(64,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)],[17]) ).
thf(65,plain,
( ( ! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(66,plain,
( ( ! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(67,plain,
( ( ! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(68,plain,
( ( ! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(69,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(70,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(72,plain,
( ( ! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(73,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(74,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(75,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(76,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(77,plain,
( ( ! [SY69: $i,SY70: $i,SY71: $i,SY72: $i] :
( ( ( ( vreduce @ ( vabs @ sK1_Vx @ SY69 @ ve1 ) )
= ( vsomeExp @ SY71 ) )
& ( vtcheck @ SY70 @ ( vabs @ sK1_Vx @ SY69 @ ve1 ) @ SY72 ) )
=> ( vtcheck @ SY70 @ SY71 @ SY72 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(78,plain,
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ( ( ( vreduce @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) )
= ( vsomeExp @ SY74 ) )
& ( vtcheck @ SY73 @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) @ SY75 ) )
=> ( vtcheck @ SY73 @ SY74 @ SY75 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(79,plain,
( ( ! [SY76: $i,SY77: $i] :
( ( ( ( vreduce @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) )
= ( vsomeExp @ SY76 ) )
& ( vtcheck @ sK3_SY73 @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) @ SY77 ) )
=> ( vtcheck @ sK3_SY73 @ SY76 @ SY77 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( ! [SY78: $i] :
( ( ( ( vreduce @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) )
= ( vsomeExp @ sK4_SY76 ) )
& ( vtcheck @ sK3_SY73 @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) @ SY78 ) )
=> ( vtcheck @ sK3_SY73 @ sK4_SY76 @ SY78 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(81,plain,
( ( ( ( ( vreduce @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) )
= ( vsomeExp @ sK4_SY76 ) )
& ( vtcheck @ sK3_SY73 @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) @ sK5_SY78 ) )
=> ( vtcheck @ sK3_SY73 @ sK4_SY76 @ sK5_SY78 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[80]) ).
thf(82,plain,
( ( ( vreduce @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) )
= ( vsomeExp @ sK4_SY76 ) )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(83,plain,
( ( vtcheck @ sK3_SY73 @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) @ sK5_SY78 )
= $true ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(84,plain,
( ( vtcheck @ sK3_SY73 @ sK4_SY76 @ sK5_SY78 )
= $false ),
inference(standard_cnf,[status(thm)],[81]) ).
thf(85,plain,
( ( ~ ( vtcheck @ sK3_SY73 @ sK4_SY76 @ sK5_SY78 ) )
= $true ),
inference(polarity_switch,[status(thm)],[84]) ).
thf(86,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VVar1: $i,VTyp1: $i,VExp1: $i] :
( ( ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) )
=> ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) ) )
& ( ( ( VVar0 = VVar1 )
& ( VTyp0 = VTyp1 )
& ( VExp0 = VExp1 ) )
=> ( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
= ( vabs @ VVar1 @ VTyp1 @ VExp1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(87,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(88,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(89,plain,
( ( ! [Vx: $i,VS: $i,Ve: $i,VExp0: $i] :
( ( VExp0
= ( vabs @ Vx @ VS @ Ve ) )
=> ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(90,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)],[72]) ).
thf(91,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)],[71]) ).
thf(92,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)],[70]) ).
thf(93,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i,VT: $i,Ve1: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vabs @ Vy @ VT @ Ve1 ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vabs @ Vy @ VT @ Ve1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(94,plain,
( ( ! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(95,plain,
( ( ! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(96,plain,
( ( ! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(97,plain,
( ( ! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(98,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)],[64]) ).
thf(99,plain,
( ( ! [VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ve1 )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ve1 @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(100,plain,
( ( vtcheck @ sK3_SY73 @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) @ sK5_SY78 )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(101,plain,
( ( ( vreduce @ ( vabs @ sK1_Vx @ sK2_SY69 @ ve1 ) )
= ( vsomeExp @ sK4_SY76 ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(102,plain,
( ( ~ ( vtcheck @ sK3_SY73 @ sK4_SY76 @ sK5_SY78 ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(103,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)],[86]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(105,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)],[92]) ).
thf(106,plain,
( ( ! [SX0: $i] :
( vnoExp
!= ( vsomeExp @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(107,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)],[93]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SX1 ) )
| ~ ( vtcheck @ SX0 @ ve1 @ SX2 ) )
| ( vtcheck @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( vsomeExp @ SX2 ) )
| ( SX1
!= ( vgetSomeExp @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(110,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)],[91]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(112,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)],[90]) ).
thf(113,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)],[98]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( vsomeExp @ SX0 )
!= ( vsomeExp @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( vsomeExp @ SX0 )
= ( vsomeExp @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vsomeExp @ SX0 ) )
| ( visSomeExp @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vabs @ SX0 @ SX1 @ SX2 ) )
| ( visValue @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(117,plain,
( ( vtcheck @ sK3_SY73 @ sK4_SY76 @ sK5_SY78 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV1: $i] :
( ( ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i,SY83: $i] :
~ ( ~ ( ( ( vabs @ SV1 @ SY79 @ SY80 )
!= ( vabs @ SY81 @ SY82 @ SY83 ) )
| ~ ( ~ ~ ( ( SV1 != SY81 )
| ( SY79 != SY82 ) )
| ( SY80 != SY83 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SY81 )
| ( SY79 != SY82 ) )
| ( SY80 != SY83 ) )
| ( ( vabs @ SV1 @ SY79 @ SY80 )
= ( vabs @ SY81 @ SY82 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV2: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i,SY87: $i] :
( ( vabs @ SV2 @ SY84 @ SY85 )
!= ( vapp @ SY86 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV3: $i] :
( ( ! [SY88: $i,SY89: $i,SY90: $i,SY91: $i,SY92: $i,SY93: $i] :
( ~ ~ ( ~ ( ( SY89 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SY89 @ SY90 @ ( vbind @ SV3 @ SY88 @ SY91 ) ) @ SY92 @ SY93 ) )
| ( vtcheck @ ( vbind @ SV3 @ SY88 @ ( vbind @ SY89 @ SY90 @ SY91 ) ) @ SY92 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV4: $i] :
( ( vnoExp
!= ( vsomeExp @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV5: $i] :
( ( ! [SY94: $i,SY95: $i,SY96: $i,SY97: $i,SY98: $i,SY99: $i,SY100: $i,SY101: $i] :
( ~ ~ ( ~ ~ ( ( SY95 != SY94 )
| ( SY96 != SV5 ) )
| ( SY97
!= ( vabs @ SY99 @ SY100 @ SY101 ) ) )
| ( SY94 != SY99 )
| ( SY98
!= ( vsubst @ SY95 @ SY96 @ SY97 ) )
| ( SY98
= ( vabs @ SY99 @ SY100 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV6: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ~ ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SY102 ) )
| ~ ( vtcheck @ SV6 @ ve1 @ SY103 ) )
| ( vtcheck @ SV6 @ SY102 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV7: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ( SV7
!= ( vsomeExp @ SY105 ) )
| ( SY104
!= ( vgetSomeExp @ SV7 ) )
| ( SY104 = SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV8: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i,SY109: $i,SY110: $i,SY111: $i] :
( ~ ~ ( ( SY107 != SV8 )
| ~ ( vtcheck @ ( vbind @ SY107 @ SY108 @ ( vbind @ SV8 @ SY106 @ SY109 ) ) @ SY110 @ SY111 ) )
| ( vtcheck @ ( vbind @ SY107 @ SY108 @ SY109 ) @ SY110 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV9: $i] :
( ( ! [SY112: $i,SY113: $i,SY114: $i] :
( ( vvar @ SV9 )
!= ( vabs @ SY112 @ SY113 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV10: $i] :
( ( ! [SY115: $i,SY116: $i,SY117: $i,SY118: $i,SY119: $i] :
( ~ ~ ( ( SY115 != SY118 )
| ( SY116
!= ( vabs @ SY117 @ SV10 @ SY119 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY117 != SY118 ) )
| ~ ( visFreeVar @ SY118 @ SY119 ) )
| ( visFreeVar @ SY115 @ SY116 ) )
| ~ ( ~ ( visFreeVar @ SY115 @ SY116 )
| ~ ( ~ ( ( SY117 != SY118 ) )
| ~ ( visFreeVar @ SY118 @ SY119 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV11: $i] :
( ( ! [SY120: $i,SY121: $i,SY122: $i,SY123: $i] :
( ( SY122
!= ( vabs @ SV11 @ SY120 @ SY121 ) )
| ( SY123
!= ( vreduce @ SY122 ) )
| ( SY123 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV12: $i] :
( ( ! [SY124: $i] :
~ ( ~ ( ( ( vsomeExp @ SV12 )
!= ( vsomeExp @ SY124 ) )
| ( SV12 = SY124 ) )
| ~ ( ( SV12 != SY124 )
| ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(130,plain,
! [SV13: $i] :
( ( ! [SY125: $i] :
( ( SY125
!= ( vsomeExp @ SV13 ) )
| ( visSomeExp @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(131,plain,
! [SV14: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i] :
( ( SY128
!= ( vabs @ SV14 @ SY126 @ SY127 ) )
| ( visValue @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV15: $i,SV1: $i] :
( ( ! [SY129: $i,SY130: $i,SY131: $i,SY132: $i] :
~ ( ~ ( ( ( vabs @ SV1 @ SV15 @ SY129 )
!= ( vabs @ SY130 @ SY131 @ SY132 ) )
| ~ ( ~ ~ ( ( SV1 != SY130 )
| ( SV15 != SY131 ) )
| ( SY129 != SY132 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SY130 )
| ( SV15 != SY131 ) )
| ( SY129 != SY132 ) )
| ( ( vabs @ SV1 @ SV15 @ SY129 )
= ( vabs @ SY130 @ SY131 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV16: $i,SV2: $i] :
( ( ! [SY133: $i,SY134: $i,SY135: $i] :
( ( vabs @ SV2 @ SV16 @ SY133 )
!= ( vapp @ SY134 @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV17: $i,SV3: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i,SY139: $i,SY140: $i] :
( ~ ~ ( ~ ( ( SY136 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SY136 @ SY137 @ ( vbind @ SV3 @ SV17 @ SY138 ) ) @ SY139 @ SY140 ) )
| ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SY136 @ SY137 @ SY138 ) ) @ SY139 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV4: $i] :
( ( vnoExp
= ( vsomeExp @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV5: $i,SV18: $i] :
( ( ! [SY141: $i,SY142: $i,SY143: $i,SY144: $i,SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ( SY141 != SV18 )
| ( SY142 != SV5 ) )
| ( SY143
!= ( vabs @ SY145 @ SY146 @ SY147 ) ) )
| ( SV18 != SY145 )
| ( SY144
!= ( vsubst @ SY141 @ SY142 @ SY143 ) )
| ( SY144
= ( vabs @ SY145 @ SY146 @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV6: $i,SV19: $i] :
( ( ! [SY148: $i] :
( ~ ~ ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SV19 ) )
| ~ ( vtcheck @ SV6 @ ve1 @ SY148 ) )
| ( vtcheck @ SV6 @ SV19 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY149: $i] :
( ( SV7
!= ( vsomeExp @ SY149 ) )
| ( SV20
!= ( vgetSomeExp @ SV7 ) )
| ( SV20 = SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i,SY153: $i,SY154: $i] :
( ~ ~ ( ( SY150 != SV8 )
| ~ ( vtcheck @ ( vbind @ SY150 @ SY151 @ ( vbind @ SV8 @ SV21 @ SY152 ) ) @ SY153 @ SY154 ) )
| ( vtcheck @ ( vbind @ SY150 @ SY151 @ SY152 ) @ SY153 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV22: $i,SV9: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ( vvar @ SV9 )
!= ( vabs @ SV22 @ SY155 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV10: $i,SV23: $i] :
( ( ! [SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ( SV23 != SY159 )
| ( SY157
!= ( vabs @ SY158 @ SV10 @ SY160 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY158 != SY159 ) )
| ~ ( visFreeVar @ SY159 @ SY160 ) )
| ( visFreeVar @ SV23 @ SY157 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SY157 )
| ~ ( ~ ( ( SY158 != SY159 ) )
| ~ ( visFreeVar @ SY159 @ SY160 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY161: $i,SY162: $i,SY163: $i] :
( ( SY162
!= ( vabs @ SV11 @ SV24 @ SY161 ) )
| ( SY163
!= ( vreduce @ SY162 ) )
| ( SY163 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV25: $i,SV12: $i] :
( ( ~ ( ~ ( ( ( vsomeExp @ SV12 )
!= ( vsomeExp @ SV25 ) )
| ( SV12 = SV25 ) )
| ~ ( ( SV12 != SV25 )
| ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV13: $i,SV26: $i] :
( ( ( SV26
!= ( vsomeExp @ SV13 ) )
| ( visSomeExp @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ( SY165
!= ( vabs @ SV14 @ SV27 @ SY164 ) )
| ( visValue @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV28: $i,SV15: $i,SV1: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i] :
~ ( ~ ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SY166 @ SY167 @ SY168 ) )
| ~ ( ~ ~ ( ( SV1 != SY166 )
| ( SV15 != SY167 ) )
| ( SV28 != SY168 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SY166 )
| ( SV15 != SY167 ) )
| ( SV28 != SY168 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SY166 @ SY167 @ SY168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV29: $i,SV16: $i,SV2: $i] :
( ( ! [SY169: $i,SY170: $i] :
( ( vabs @ SV2 @ SV16 @ SV29 )
!= ( vapp @ SY169 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV17: $i,SV3: $i,SV30: $i] :
( ( ! [SY171: $i,SY172: $i,SY173: $i,SY174: $i] :
( ~ ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SY171 @ ( vbind @ SV3 @ SV17 @ SY172 ) ) @ SY173 @ SY174 ) )
| ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SY171 @ SY172 ) ) @ SY173 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV5: $i,SV18: $i,SV31: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SY175 != SV5 ) )
| ( SY176
!= ( vabs @ SY178 @ SY179 @ SY180 ) ) )
| ( SV18 != SY178 )
| ( SY177
!= ( vsubst @ SV31 @ SY175 @ SY176 ) )
| ( SY177
= ( vabs @ SY178 @ SY179 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(150,plain,
! [SV32: $i,SV6: $i,SV19: $i] :
( ( ~ ~ ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SV19 ) )
| ~ ( vtcheck @ SV6 @ ve1 @ SV32 ) )
| ( vtcheck @ SV6 @ SV19 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV20: $i,SV33: $i,SV7: $i] :
( ( ( SV7
!= ( vsomeExp @ SV33 ) )
| ( SV20
!= ( vgetSomeExp @ SV7 ) )
| ( SV20 = SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV21: $i,SV8: $i,SV34: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i] :
( ~ ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SY181 @ ( vbind @ SV8 @ SV21 @ SY182 ) ) @ SY183 @ SY184 ) )
| ( vtcheck @ ( vbind @ SV34 @ SY181 @ SY182 ) @ SY183 @ SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV35: $i,SV22: $i,SV9: $i] :
( ( ! [SY185: $i] :
( ( vvar @ SV9 )
!= ( vabs @ SV22 @ SV35 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV10: $i,SV36: $i,SV23: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i] :
( ~ ~ ( ( SV23 != SY187 )
| ( SV36
!= ( vabs @ SY186 @ SV10 @ SY188 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY186 != SY187 ) )
| ~ ( visFreeVar @ SY187 @ SY188 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SY186 != SY187 ) )
| ~ ( visFreeVar @ SY187 @ SY188 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV37: $i,SV24: $i,SV11: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ( SY189
!= ( vabs @ SV11 @ SV24 @ SV37 ) )
| ( SY190
!= ( vreduce @ SY189 ) )
| ( SY190 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV25: $i,SV12: $i] :
( ( ~ ( ( ( vsomeExp @ SV12 )
!= ( vsomeExp @ SV25 ) )
| ( SV12 = SV25 ) )
| ~ ( ( SV12 != SV25 )
| ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV13: $i,SV26: $i] :
( ( ( SV26
!= ( vsomeExp @ SV13 ) )
= $true )
| ( ( visSomeExp @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV38: $i,SV27: $i,SV14: $i] :
( ( ! [SY191: $i] :
( ( SY191
!= ( vabs @ SV14 @ SV27 @ SV38 ) )
| ( visValue @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ! [SY192: $i,SY193: $i] :
~ ( ~ ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SY192 @ SY193 ) )
| ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SY192 ) )
| ( SV28 != SY193 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SY192 ) )
| ( SV28 != SY193 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SY192 @ SY193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV40: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ! [SY194: $i] :
( ( vabs @ SV2 @ SV16 @ SV29 )
!= ( vapp @ SV40 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ~ ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SY195 ) ) @ SY196 @ SY197 ) )
| ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SY195 ) ) @ SY196 @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ! [SY198: $i,SY199: $i,SY200: $i,SY201: $i,SY202: $i] :
( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SY198
!= ( vabs @ SY200 @ SY201 @ SY202 ) ) )
| ( SV18 != SY200 )
| ( SY199
!= ( vsubst @ SV31 @ SV42 @ SY198 ) )
| ( SY199
= ( vabs @ SY200 @ SY201 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV32: $i,SV6: $i,SV19: $i] :
( ( ( ~ ~ ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SV19 ) )
| ~ ( vtcheck @ SV6 @ ve1 @ SV32 ) ) )
= $true )
| ( ( vtcheck @ SV6 @ SV19 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV20: $i,SV33: $i,SV7: $i] :
( ( ( SV7
!= ( vsomeExp @ SV33 ) )
= $true )
| ( ( ( SV20
!= ( vgetSomeExp @ SV7 ) )
| ( SV20 = SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ! [SY203: $i,SY204: $i,SY205: $i] :
( ~ ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SY203 ) ) @ SY204 @ SY205 ) )
| ( vtcheck @ ( vbind @ SV34 @ SV43 @ SY203 ) @ SY204 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV44: $i,SV35: $i,SV22: $i,SV9: $i] :
( ( ( vvar @ SV9 )
!= ( vabs @ SV22 @ SV35 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV10: $i,SV45: $i,SV36: $i,SV23: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ~ ~ ( ( SV23 != SY206 )
| ( SV36
!= ( vabs @ SV45 @ SV10 @ SY207 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SY206 ) )
| ~ ( visFreeVar @ SY206 @ SY207 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SY206 ) )
| ~ ( visFreeVar @ SY206 @ SY207 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV37: $i,SV24: $i,SV11: $i,SV46: $i] :
( ( ! [SY208: $i] :
( ( SV46
!= ( vabs @ SV11 @ SV24 @ SV37 ) )
| ( SY208
!= ( vreduce @ SV46 ) )
| ( SY208 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV25: $i,SV12: $i] :
( ( ~ ( ( ( vsomeExp @ SV12 )
!= ( vsomeExp @ SV25 ) )
| ( SV12 = SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV25: $i,SV12: $i] :
( ( ~ ( ( SV12 != SV25 )
| ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(171,plain,
! [SV13: $i,SV26: $i] :
( ( ( SV26
= ( vsomeExp @ SV13 ) )
= $false )
| ( ( visSomeExp @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(172,plain,
! [SV38: $i,SV27: $i,SV14: $i,SV47: $i] :
( ( ( SV47
!= ( vabs @ SV14 @ SV27 @ SV38 ) )
| ( visValue @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ! [SY209: $i] :
~ ( ~ ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SV48 @ SY209 ) )
| ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SY209 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SY209 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV49: $i,SV40: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ( vabs @ SV2 @ SV16 @ SV29 )
!= ( vapp @ SV40 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(175,plain,
! [SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ! [SY210: $i,SY211: $i] :
( ~ ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SY210 @ SY211 ) )
| ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SY210 @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(176,plain,
! [SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ! [SY212: $i,SY213: $i,SY214: $i,SY215: $i] :
( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SY213 @ SY214 @ SY215 ) ) )
| ( SV18 != SY213 )
| ( SY212
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SY212
= ( vabs @ SY213 @ SY214 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(177,plain,
! [SV32: $i,SV6: $i,SV19: $i] :
( ( ( ~ ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SV19 ) )
| ~ ( vtcheck @ SV6 @ ve1 @ SV32 ) ) )
= $false )
| ( ( vtcheck @ SV6 @ SV19 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(178,plain,
! [SV20: $i,SV33: $i,SV7: $i] :
( ( ( SV7
= ( vsomeExp @ SV33 ) )
= $false )
| ( ( ( SV20
!= ( vgetSomeExp @ SV7 ) )
| ( SV20 = SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(179,plain,
! [SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ~ ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SY216 @ SY217 ) )
| ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SY216 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(180,plain,
! [SV44: $i,SV35: $i,SV22: $i,SV9: $i] :
( ( ( vvar @ SV9 )
= ( vabs @ SV22 @ SV35 @ SV44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(181,plain,
! [SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ! [SY218: $i] :
( ~ ~ ( ( SV23 != SV53 )
| ( SV36
!= ( vabs @ SV45 @ SV10 @ SY218 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SY218 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SY218 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(182,plain,
! [SV54: $i,SV37: $i,SV24: $i,SV11: $i,SV46: $i] :
( ( ( SV46
!= ( vabs @ SV11 @ SV24 @ SV37 ) )
| ( SV54
!= ( vreduce @ SV46 ) )
| ( SV54 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(183,plain,
! [SV25: $i,SV12: $i] :
( ( ( ( vsomeExp @ SV12 )
!= ( vsomeExp @ SV25 ) )
| ( SV12 = SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(184,plain,
! [SV25: $i,SV12: $i] :
( ( ( SV12 != SV25 )
| ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(185,plain,
! [SV38: $i,SV27: $i,SV14: $i,SV47: $i] :
( ( ( SV47
!= ( vabs @ SV14 @ SV27 @ SV38 ) )
= $true )
| ( ( visValue @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV55: $i,SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ~ ( ~ ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SV48 @ SV55 ) )
| ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(187,plain,
! [SV49: $i,SV40: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ( vabs @ SV2 @ SV16 @ SV29 )
= ( vapp @ SV40 @ SV49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ! [SY219: $i] :
( ~ ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SY219 ) )
| ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV57: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ! [SY220: $i,SY221: $i,SY222: $i] :
( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SY220 @ SY221 @ SY222 ) ) )
| ( SV18 != SY220 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SY220 @ SY221 @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV32: $i,SV6: $i,SV19: $i] :
( ( ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SV19 ) )
| ~ ( vtcheck @ SV6 @ ve1 @ SV32 ) )
= $true )
| ( ( vtcheck @ SV6 @ SV19 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(191,plain,
! [SV33: $i,SV7: $i,SV20: $i] :
( ( ( SV20
!= ( vgetSomeExp @ SV7 ) )
= $true )
| ( ( SV20 = SV33 )
= $true )
| ( ( SV7
= ( vsomeExp @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ! [SY223: $i] :
( ~ ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SY223 ) )
| ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV59: $i,SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ~ ~ ( ( SV23 != SV53 )
| ( SV36
!= ( vabs @ SV45 @ SV10 @ SV59 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV54: $i,SV37: $i,SV24: $i,SV11: $i,SV46: $i] :
( ( ( SV46
!= ( vabs @ SV11 @ SV24 @ SV37 ) )
= $true )
| ( ( ( SV54
!= ( vreduce @ SV46 ) )
| ( SV54 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV25: $i,SV12: $i] :
( ( ( ( vsomeExp @ SV12 )
!= ( vsomeExp @ SV25 ) )
= $true )
| ( ( SV12 = SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV25: $i,SV12: $i] :
( ( ( SV12 != SV25 )
= $true )
| ( ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV38: $i,SV27: $i,SV14: $i,SV47: $i] :
( ( ( SV47
= ( vabs @ SV14 @ SV27 @ SV38 ) )
= $false )
| ( ( visValue @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(198,plain,
! [SV55: $i,SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ~ ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SV48 @ SV55 ) )
| ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(199,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ~ ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) )
| ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV57: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ! [SY224: $i,SY225: $i] :
( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SV61 @ SY224 @ SY225 ) ) )
| ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SY224 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV32: $i,SV6: $i,SV19: $i] :
( ( ( ( vreduce @ ve1 )
!= ( vsomeExp @ SV19 ) )
= $true )
| ( ( ~ ( vtcheck @ SV6 @ ve1 @ SV32 ) )
= $true )
| ( ( vtcheck @ SV6 @ SV19 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV33: $i,SV7: $i,SV20: $i] :
( ( ( SV20
= ( vgetSomeExp @ SV7 ) )
= $false )
| ( ( SV20 = SV33 )
= $true )
| ( ( SV7
= ( vsomeExp @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(203,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ~ ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 ) )
| ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(204,plain,
! [SV59: $i,SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ( ~ ~ ( ( SV23 != SV53 )
| ( SV36
!= ( vabs @ SV45 @ SV10 @ SV59 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(205,plain,
! [SV54: $i,SV37: $i,SV24: $i,SV11: $i,SV46: $i] :
( ( ( SV46
= ( vabs @ SV11 @ SV24 @ SV37 ) )
= $false )
| ( ( ( SV54
!= ( vreduce @ SV46 ) )
| ( SV54 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(206,plain,
! [SV25: $i,SV12: $i] :
( ( ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) )
= $false )
| ( ( SV12 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(207,plain,
! [SV25: $i,SV12: $i] :
( ( ( SV12 = SV25 )
= $false )
| ( ( ( vsomeExp @ SV12 )
= ( vsomeExp @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(208,plain,
! [SV55: $i,SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ~ ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SV48 @ SV55 ) )
| ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(209,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(210,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV57: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ! [SY226: $i] :
( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SV61 @ SV63 @ SY226 ) ) )
| ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV32: $i,SV6: $i,SV19: $i] :
( ( ( ( vreduce @ ve1 )
= ( vsomeExp @ SV19 ) )
= $false )
| ( ( ~ ( vtcheck @ SV6 @ ve1 @ SV32 ) )
= $true )
| ( ( vtcheck @ SV6 @ SV19 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ( ~ ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV59: $i,SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ( ~ ( ( SV23 != SV53 )
| ( SV36
!= ( vabs @ SV45 @ SV10 @ SV59 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV37: $i,SV24: $i,SV11: $i,SV46: $i,SV54: $i] :
( ( ( SV54
!= ( vreduce @ SV46 ) )
= $true )
| ( ( SV54 = vnoExp )
= $true )
| ( ( SV46
= ( vabs @ SV11 @ SV24 @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV55: $i,SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SV48 @ SV55 ) )
| ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(217,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) )
| ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(218,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ( ~ ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
| ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV19: $i,SV32: $i,SV6: $i] :
( ( ( vtcheck @ SV6 @ ve1 @ SV32 )
= $false )
| ( ( ( vreduce @ ve1 )
= ( vsomeExp @ SV19 ) )
= $false )
| ( ( vtcheck @ SV6 @ SV19 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ( ~ ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(222,plain,
! [SV59: $i,SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ( ( SV23 != SV53 )
| ( SV36
!= ( vabs @ SV45 @ SV10 @ SV59 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(223,plain,
! [SV37: $i,SV24: $i,SV11: $i,SV46: $i,SV54: $i] :
( ( ( SV54
= ( vreduce @ SV46 ) )
= $false )
| ( ( SV54 = vnoExp )
= $true )
| ( ( SV46
= ( vabs @ SV11 @ SV24 @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV55: $i,SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ( ( vabs @ SV1 @ SV15 @ SV28 )
!= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ( ~ ( ( SV30 != SV3 ) )
| ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(227,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) ) ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ( ( SV34 != SV8 )
| ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(229,plain,
! [SV59: $i,SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ( SV23 != SV53 )
= $true )
| ( ( SV36
!= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV55: $i,SV48: $i,SV39: $i,SV28: $i,SV15: $i,SV1: $i] :
( ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(231,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) ) )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ( ~ ( ( SV30 != SV3 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) ) ) )
= $false )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ( SV34 != SV8 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(235,plain,
! [SV59: $i,SV10: $i,SV45: $i,SV36: $i,SV53: $i,SV23: $i] :
( ( ( SV23 = SV53 )
= $false )
| ( ( SV36
!= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(236,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(237,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
| ( SV28 != SV55 ) )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(238,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ( SV30 != SV3 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(239,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
| ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(240,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV43: $i,SV8: $i,SV34: $i] :
( ( ( SV34 = SV8 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(241,plain,
! [SV53: $i,SV23: $i,SV59: $i,SV10: $i,SV45: $i,SV36: $i] :
( ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(242,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) ) )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(243,plain,
! [SV48: $i,SV39: $i,SV15: $i,SV1: $i,SV55: $i,SV28: $i] :
( ( ( SV28 != SV55 )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(244,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) ) )
= $true )
| ( ( SV28 != SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(245,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV41: $i,SV3: $i,SV30: $i] :
( ( ( SV30 = SV3 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(246,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( ~ ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) ) )
= $true )
| ( ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(247,plain,
! [SV62: $i,SV58: $i,SV52: $i,SV21: $i,SV8: $i,SV43: $i,SV34: $i] :
( ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ ( vbind @ SV8 @ SV21 @ SV52 ) ) @ SV58 @ SV62 )
= $false )
| ( ( SV34 = SV8 )
= $false )
| ( ( vtcheck @ ( vbind @ SV34 @ SV43 @ SV52 ) @ SV58 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(248,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
| ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(249,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) ) )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(250,plain,
! [SV48: $i,SV39: $i,SV15: $i,SV1: $i,SV55: $i,SV28: $i] :
( ( ( SV28 = SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(251,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ~ ( ( SV1 != SV39 )
| ( SV15 != SV48 ) ) )
= $false )
| ( ( SV28 != SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(252,plain,
! [SV60: $i,SV56: $i,SV50: $i,SV17: $i,SV3: $i,SV41: $i,SV30: $i] :
( ( ( vtcheck @ ( vbind @ SV30 @ SV41 @ ( vbind @ SV3 @ SV17 @ SV50 ) ) @ SV56 @ SV60 )
= $false )
| ( ( SV30 = SV3 )
= $true )
| ( ( vtcheck @ ( vbind @ SV3 @ SV17 @ ( vbind @ SV30 @ SV41 @ SV50 ) ) @ SV56 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(253,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( ~ ( ( SV31 != SV18 )
| ( SV42 != SV5 ) ) )
= $false )
| ( ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(254,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) ) )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(255,plain,
! [SV10: $i,SV59: $i,SV53: $i,SV45: $i,SV36: $i,SV23: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(256,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(257,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( ( SV1 != SV39 )
| ( SV15 != SV48 ) )
= $true )
| ( ( SV28 != SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(258,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( ( SV31 != SV18 )
| ( SV42 != SV5 ) )
= $true )
| ( ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(259,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV23 @ SV36 ) )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(260,plain,
! [SV10: $i,SV59: $i,SV53: $i,SV45: $i,SV36: $i,SV23: $i] :
( ( ( ~ ( visFreeVar @ SV23 @ SV36 )
| ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(261,plain,
! [SV55: $i,SV48: $i,SV28: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( SV1 != SV39 )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(262,plain,
! [SV55: $i,SV39: $i,SV28: $i,SV1: $i,SV48: $i,SV15: $i] :
( ( ( SV15 != SV48 )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(263,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( SV1 != SV39 )
= $true )
| ( ( SV15 != SV48 )
= $true )
| ( ( SV28 != SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(264,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( SV31 != SV18 )
= $true )
| ( ( SV42 != SV5 )
= $true )
| ( ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(265,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(266,plain,
! [SV10: $i,SV59: $i,SV53: $i,SV45: $i,SV36: $i,SV23: $i] :
( ( ( ~ ( visFreeVar @ SV23 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(267,plain,
! [SV55: $i,SV48: $i,SV28: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( SV1 = SV39 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(268,plain,
! [SV55: $i,SV39: $i,SV28: $i,SV1: $i,SV48: $i,SV15: $i] :
( ( ( SV15 = SV48 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(269,plain,
! [SV55: $i,SV28: $i,SV48: $i,SV15: $i,SV39: $i,SV1: $i] :
( ( ( SV1 = SV39 )
= $false )
| ( ( SV15 != SV48 )
= $true )
| ( ( SV28 != SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i] :
( ( ( SV31 = SV18 )
= $false )
| ( ( SV42 != SV5 )
= $true )
| ( ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(271,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) )
= $false )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(272,plain,
! [SV10: $i,SV59: $i,SV53: $i,SV45: $i,SV36: $i,SV23: $i] :
( ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( ~ ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) ) )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV55: $i,SV28: $i,SV39: $i,SV1: $i,SV48: $i,SV15: $i] :
( ( ( SV15 = SV48 )
= $false )
| ( ( SV1 = SV39 )
= $false )
| ( ( SV28 != SV55 )
= $true )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(274,plain,
! [SV57: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV18: $i,SV31: $i,SV5: $i,SV42: $i] :
( ( ( SV42 = SV5 )
= $false )
| ( ( SV31 = SV18 )
= $false )
| ( ( SV51
!= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(275,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(276,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ( SV45 != SV53 ) )
| ~ ( visFreeVar @ SV53 @ SV59 ) )
= $false )
| ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(277,plain,
! [SV48: $i,SV15: $i,SV39: $i,SV1: $i,SV55: $i,SV28: $i] :
( ( ( SV28 = SV55 )
= $false )
| ( ( SV1 = SV39 )
= $false )
| ( ( SV15 = SV48 )
= $false )
| ( ( ( vabs @ SV1 @ SV15 @ SV28 )
= ( vabs @ SV39 @ SV48 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(278,plain,
! [SV57: $i,SV5: $i,SV42: $i,SV18: $i,SV31: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i] :
( ( ( SV51
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $false )
| ( ( SV31 = SV18 )
= $false )
| ( ( SV42 = SV5 )
= $false )
| ( ( ( SV18 != SV61 )
| ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(279,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ( SV45 != SV53 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(280,plain,
! [SV59: $i,SV10: $i,SV36: $i,SV23: $i,SV53: $i,SV45: $i] :
( ( ( ~ ( ( SV45 != SV53 ) ) )
= $false )
| ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(281,plain,
! [SV10: $i,SV45: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i] :
( ( ( ~ ( visFreeVar @ SV53 @ SV59 ) )
= $false )
| ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(282,plain,
! [SV5: $i,SV64: $i,SV63: $i,SV51: $i,SV42: $i,SV31: $i,SV57: $i,SV61: $i,SV18: $i] :
( ( ( SV18 != SV61 )
= $true )
| ( ( ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true )
| ( ( SV42 = SV5 )
= $false )
| ( ( SV31 = SV18 )
= $false )
| ( ( SV51
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( SV45 != SV53 )
= $false )
| ( ( ~ ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(284,plain,
! [SV59: $i,SV10: $i,SV36: $i,SV23: $i,SV53: $i,SV45: $i] :
( ( ( SV45 != SV53 )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(285,plain,
! [SV10: $i,SV45: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i] :
( ( ( visFreeVar @ SV53 @ SV59 )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(286,plain,
! [SV5: $i,SV64: $i,SV63: $i,SV51: $i,SV42: $i,SV31: $i,SV57: $i,SV61: $i,SV18: $i] :
( ( ( SV18 = SV61 )
= $false )
| ( ( ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
| ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) ) )
= $true )
| ( ( SV42 = SV5 )
= $false )
| ( ( SV31 = SV18 )
= $false )
| ( ( SV51
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(287,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV59: $i,SV53: $i,SV45: $i] :
( ( ( SV45 = SV53 )
= $true )
| ( ( ~ ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(288,plain,
! [SV59: $i,SV10: $i,SV36: $i,SV23: $i,SV53: $i,SV45: $i] :
( ( ( SV45 = SV53 )
= $false )
| ( ( visFreeVar @ SV23 @ SV36 )
= $false )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(289,plain,
! [SV5: $i,SV18: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV42: $i,SV31: $i,SV57: $i] :
( ( ( SV57
!= ( vsubst @ SV31 @ SV42 @ SV51 ) )
= $true )
| ( ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( SV18 = SV61 )
= $false )
| ( ( SV42 = SV5 )
= $false )
| ( ( SV31 = SV18 )
= $false )
| ( ( SV51
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(290,plain,
! [SV10: $i,SV36: $i,SV23: $i,SV45: $i,SV59: $i,SV53: $i] :
( ( ( visFreeVar @ SV53 @ SV59 )
= $false )
| ( ( SV45 = SV53 )
= $true )
| ( ( visFreeVar @ SV23 @ SV36 )
= $true )
| ( ( SV23 = SV53 )
= $false )
| ( ( SV36
= ( vabs @ SV45 @ SV10 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(291,plain,
! [SV5: $i,SV18: $i,SV64: $i,SV63: $i,SV61: $i,SV51: $i,SV42: $i,SV31: $i,SV57: $i] :
( ( ( SV57
= ( vsubst @ SV31 @ SV42 @ SV51 ) )
= $false )
| ( ( SV57
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $true )
| ( ( SV18 = SV61 )
= $false )
| ( ( SV42 = SV5 )
= $false )
| ( ( SV31 = SV18 )
= $false )
| ( ( SV51
= ( vabs @ SV61 @ SV63 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(292,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[100,291,290,288,285,277,268,267,252,250,247,223,220,207,206,202,197,187,180,171,135,117,101]) ).
thf(293,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM144+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 18:38:39 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.86/0.31
% 0.86/0.31 No.of.Axioms: 14
% 0.86/0.31
% 0.86/0.31 Length.of.Defs: 0
% 0.86/0.31
% 0.86/0.31 Contains.Choice.Funs: false
% 0.86/0.31 ............
% 0.86/0.31
% 0.86/0.31 ********************************
% 0.86/0.31 * All subproblems solved! *
% 0.86/0.31 ********************************
% 0.86/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:292,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.86/0.31
% 0.86/0.31 %**** Beginning of derivation protocol ****
% 0.86/0.31 % SZS output start CNFRefutation
% See solution above
% 0.86/0.31
% 0.86/0.31 %**** End of derivation protocol ****
% 0.86/0.31 %**** no. of clauses in derivation: 248 ****
% 0.86/0.31 %**** clause counter: 292 ****
% 0.86/0.31
% 0.86/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,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:292,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------