%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM146+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:12:28 AM UTC 2026
% Result : Theorem 2.47s 0.60s
% Output : CNFRefutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 218 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 1495 ( 988 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2401 ( 608 ~; 450 |; 37 &;1236 @)
% ( 0 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 9 con; 0-3 aty)
% Number of variables : 938 ( 0 ^; 938 !; 0 ?; 938 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Vx,type,
sK1_Vx: $i ).
thf(tp_sK2_SY58,type,
sK2_SY58: $i ).
thf(tp_sK3_SY61,type,
sK3_SY61: $i ).
thf(tp_sK4_SY63,type,
sK4_SY63: $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_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(17,axiom,
! [Vx: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce0) ).
thf(18,axiom,
! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeExp0) ).
thf(19,axiom,
! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1) ).
thf(21,axiom,
! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
thf(22,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(29,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst1) ).
thf(30,axiom,
! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst0) ).
thf(32,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).
thf(33,axiom,
! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx = Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vx @ VTx @ VC ) @ Ve @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate') ).
thf(49,axiom,
! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar0) ).
thf(51,axiom,
! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue1) ).
thf(54,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-app') ).
thf(55,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,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-var') ).
thf(59,conjecture,
! [Vx: $i,VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ( vvar @ Vx ) )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Preservation-T-var') ).
thf(60,negated_conjecture,
( ( ! [Vx: $i,VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ( vvar @ Vx ) )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[59]) ).
thf(61,plain,
( ( ! [Vx: $i,VC: $i,Veout: $i,VT: $i] :
( ( ( ( vreduce @ ( vvar @ Vx ) )
= ( vsomeExp @ Veout ) )
& ( vtcheck @ VC @ ( vvar @ Vx ) @ VT ) )
=> ( vtcheck @ VC @ Veout @ VT ) ) )
= $false ),
inference(unfold_def,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [Vx: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(63,plain,
( ( ! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(64,plain,
( ( ! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(65,plain,
( ( ! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(66,plain,
( ( ! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(67,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(69,plain,
( ( ! [Vy: $i,VTy: $i,Vx: $i,VTx: $i,VC: $i,Ve: $i,VT: $i] :
( ( ( Vx != Vy )
& ( vtcheck @ ( vbind @ Vx @ VTx @ ( vbind @ Vy @ VTy @ VC ) ) @ Ve @ VT ) )
=> ( vtcheck @ ( vbind @ Vy @ VTy @ ( vbind @ Vx @ VTx @ VC ) ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(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 @ Vx @ VTx @ VC ) @ Ve @ VT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(72,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(73,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(74,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(75,plain,
( ( ! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(76,plain,
( ( ! [SY58: $i,SY59: $i,SY60: $i] :
( ( ( ( vreduce @ ( vvar @ sK1_Vx ) )
= ( vsomeExp @ SY59 ) )
& ( vtcheck @ SY58 @ ( vvar @ sK1_Vx ) @ SY60 ) )
=> ( vtcheck @ SY58 @ SY59 @ SY60 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(77,plain,
( ( ! [SY61: $i,SY62: $i] :
( ( ( ( vreduce @ ( vvar @ sK1_Vx ) )
= ( vsomeExp @ SY61 ) )
& ( vtcheck @ sK2_SY58 @ ( vvar @ sK1_Vx ) @ SY62 ) )
=> ( vtcheck @ sK2_SY58 @ SY61 @ SY62 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(78,plain,
( ( ! [SY63: $i] :
( ( ( ( vreduce @ ( vvar @ sK1_Vx ) )
= ( vsomeExp @ sK3_SY61 ) )
& ( vtcheck @ sK2_SY58 @ ( vvar @ sK1_Vx ) @ SY63 ) )
=> ( vtcheck @ sK2_SY58 @ sK3_SY61 @ SY63 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(79,plain,
( ( ( ( ( vreduce @ ( vvar @ sK1_Vx ) )
= ( vsomeExp @ sK3_SY61 ) )
& ( vtcheck @ sK2_SY58 @ ( vvar @ sK1_Vx ) @ sK4_SY63 ) )
=> ( vtcheck @ sK2_SY58 @ sK3_SY61 @ sK4_SY63 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( ( vreduce @ ( vvar @ sK1_Vx ) )
= ( vsomeExp @ sK3_SY61 ) )
= $true ),
inference(standard_cnf,[status(thm)],[79]) ).
thf(81,plain,
( ( vtcheck @ sK2_SY58 @ ( vvar @ sK1_Vx ) @ sK4_SY63 )
= $true ),
inference(standard_cnf,[status(thm)],[79]) ).
thf(82,plain,
( ( vtcheck @ sK2_SY58 @ sK3_SY61 @ sK4_SY63 )
= $false ),
inference(standard_cnf,[status(thm)],[79]) ).
thf(83,plain,
( ( ~ ( vtcheck @ sK2_SY58 @ sK3_SY61 @ sK4_SY63 ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(84,plain,
( ( ! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(85,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(86,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(87,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(88,plain,
( ( ! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(89,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)],[70]) ).
thf(90,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)],[69]) ).
thf(91,plain,
( ( ! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(92,plain,
( ( ! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(93,plain,
( ( ! [VExp0: $i,VExp1: $i] :
( ( ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) )
=> ( VExp0 = VExp1 ) )
& ( ( VExp0 = VExp1 )
=> ( ( vsomeExp @ VExp0 )
= ( vsomeExp @ VExp1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(94,plain,
( ( ! [VExp0: $i] :
( vnoExp
!= ( vsomeExp @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(95,plain,
( ( ! [Ve: $i,VOptExp0: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( visSomeExp @ VOptExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(96,plain,
( ( ! [VOptExp0: $i,RESULT: $i,Ve: $i] :
( ( VOptExp0
= ( vsomeExp @ Ve ) )
=> ( ( RESULT
= ( vgetSomeExp @ VOptExp0 ) )
=> ( RESULT = Ve ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(97,plain,
( ( ! [Vx: $i,VExp0: $i,RESULT: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ( ( RESULT
= ( vreduce @ VExp0 ) )
=> ( RESULT = vnoExp ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(98,plain,
( ( vtcheck @ sK2_SY58 @ ( vvar @ sK1_Vx ) @ sK4_SY63 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(99,plain,
( ( ( vreduce @ ( vvar @ sK1_Vx ) )
= ( vsomeExp @ sK3_SY61 ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(100,plain,
( ( ~ ( vtcheck @ sK2_SY58 @ sK3_SY61 @ sK4_SY63 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( vvar @ SX0 )
!= ( vapp @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ( SX0 != SX3 )
| ( SX1
!= ( vvar @ SX2 ) ) )
| ~ ( ~ ( ( SX2 != SX3 )
| ( visFreeVar @ SX0 @ SX1 ) )
| ~ ( ~ ( visFreeVar @ SX0 @ SX1 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX1 )
| ( SX3 != SX0 ) )
| ( SX4
!= ( vvar @ SX6 ) ) )
| ~ ( ( SX1 != SX6 ) )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5
= ( vvar @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vsomeExp @ SX0 ) )
| ( visSomeExp @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( vsomeExp @ SX0 )
!= ( vsomeExp @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( vsomeExp @ SX0 )
= ( vsomeExp @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1
!= ( vvar @ SX0 ) )
| ( SX2
!= ( vreduce @ SX1 ) )
| ( SX2 = vnoExp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ( SX2 != SX0 )
| ( SX3 != SX6 ) )
| ( SX4
!= ( vvar @ SX1 ) ) )
| ( SX0 != SX1 )
| ( SX5
!= ( vsubst @ SX2 @ SX3 @ SX4 ) )
| ( SX5 = SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( vvar @ SX0 )
!= ( vvar @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( vvar @ SX0 )
= ( vvar @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vvar @ SX0 ) )
| ~ ( visValue @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
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 @ SX0 @ SX1 @ ( vbind @ SX2 @ SX3 @ SX4 ) ) @ SX5 @ SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( vnoExp
!= ( vsomeExp @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( vsomeExp @ SX2 ) )
| ( SX1
!= ( vgetSomeExp @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(114,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)],[89]) ).
thf(115,plain,
( ( vtcheck @ sK2_SY58 @ sK3_SY61 @ sK4_SY63 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV1: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( vvar @ SV1 )
!= ( vapp @ SY64 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV2: $i] :
( ( ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ( SV2 != SY68 )
| ( SY66
!= ( vvar @ SY67 ) ) )
| ~ ( ~ ( ( SY67 != SY68 )
| ( visFreeVar @ SV2 @ SY66 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SY66 )
| ( SY67 = SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV3: $i] :
( ( ! [SY69: $i,SY70: $i,SY71: $i,SY72: $i,SY73: $i,SY74: $i] :
( ~ ~ ( ~ ~ ( ( SY70 != SY69 )
| ( SY71 != SV3 ) )
| ( SY72
!= ( vvar @ SY74 ) ) )
| ~ ( ( SY69 != SY74 ) )
| ( SY73
!= ( vsubst @ SY70 @ SY71 @ SY72 ) )
| ( SY73
= ( vvar @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV4: $i] :
( ( ! [SY75: $i] :
( ( SY75
!= ( vsomeExp @ SV4 ) )
| ( visSomeExp @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV5: $i] :
( ( ! [SY76: $i] :
~ ( ~ ( ( ( vsomeExp @ SV5 )
!= ( vsomeExp @ SY76 ) )
| ( SV5 = SY76 ) )
| ~ ( ( SV5 != SY76 )
| ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV6: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ( SY77
!= ( vvar @ SV6 ) )
| ( SY78
!= ( vreduce @ SY77 ) )
| ( SY78 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV7: $i] :
( ( ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i,SY83: $i,SY84: $i] :
( ~ ~ ( ~ ~ ( ( SY80 != SV7 )
| ( SY81 != SY84 ) )
| ( SY82
!= ( vvar @ SY79 ) ) )
| ( SV7 != SY79 )
| ( SY83
!= ( vsubst @ SY80 @ SY81 @ SY82 ) )
| ( SY83 = SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV8: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ( ( vvar @ SV8 )
!= ( vvar @ SY85 ) )
| ( SV8 = SY85 ) )
| ~ ( ( SV8 != SY85 )
| ( ( vvar @ SV8 )
= ( vvar @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV9: $i] :
( ( ! [SY86: $i] :
( ( SY86
!= ( vvar @ SV9 ) )
| ~ ( visValue @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV10: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i,SY91: $i,SY92: $i] :
( ~ ~ ( ~ ( ( SY88 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SY88 @ SY89 @ ( vbind @ SV10 @ SY87 @ SY90 ) ) @ SY91 @ SY92 ) )
| ( vtcheck @ ( vbind @ SV10 @ SY87 @ ( vbind @ SY88 @ SY89 @ SY90 ) ) @ SY91 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV11: $i] :
( ( ! [SY93: $i,SY94: $i,SY95: $i] :
( ( vvar @ SV11 )
!= ( vabs @ SY93 @ SY94 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV12: $i] :
( ( vnoExp
!= ( vsomeExp @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV13: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ( SV13
!= ( vsomeExp @ SY97 ) )
| ( SY96
!= ( vgetSomeExp @ SV13 ) )
| ( SY96 = SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV14: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i,SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ( SY99 != SV14 )
| ~ ( vtcheck @ ( vbind @ SY99 @ SY100 @ ( vbind @ SV14 @ SY98 @ SY101 ) ) @ SY102 @ SY103 ) )
| ( vtcheck @ ( vbind @ SY99 @ SY100 @ SY101 ) @ SY102 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(130,plain,
! [SV15: $i,SV1: $i] :
( ( ! [SY104: $i] :
( ( vvar @ SV1 )
!= ( vapp @ SV15 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV16: $i,SV2: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ~ ( ( SV2 != SY106 )
| ( SV16
!= ( vvar @ SY105 ) ) )
| ~ ( ~ ( ( SY105 != SY106 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SY105 = SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV3: $i,SV17: $i] :
( ( ! [SY107: $i,SY108: $i,SY109: $i,SY110: $i,SY111: $i] :
( ~ ~ ( ~ ~ ( ( SY107 != SV17 )
| ( SY108 != SV3 ) )
| ( SY109
!= ( vvar @ SY111 ) ) )
| ~ ( ( SV17 != SY111 ) )
| ( SY110
!= ( vsubst @ SY107 @ SY108 @ SY109 ) )
| ( SY110
= ( vvar @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV4: $i,SV18: $i] :
( ( ( SV18
!= ( vsomeExp @ SV4 ) )
| ( visSomeExp @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( ~ ( ( ( vsomeExp @ SV5 )
!= ( vsomeExp @ SV19 ) )
| ( SV5 = SV19 ) )
| ~ ( ( SV5 != SV19 )
| ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV6: $i,SV20: $i] :
( ( ! [SY112: $i] :
( ( SV20
!= ( vvar @ SV6 ) )
| ( SY112
!= ( vreduce @ SV20 ) )
| ( SY112 = vnoExp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i,SY117: $i] :
( ~ ~ ( ~ ~ ( ( SY113 != SV7 )
| ( SY114 != SY117 ) )
| ( SY115
!= ( vvar @ SV21 ) ) )
| ( SV7 != SV21 )
| ( SY116
!= ( vsubst @ SY113 @ SY114 @ SY115 ) )
| ( SY116 = SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ~ ( ( ( vvar @ SV8 )
!= ( vvar @ SV22 ) )
| ( SV8 = SV22 ) )
| ~ ( ( SV8 != SV22 )
| ( ( vvar @ SV8 )
= ( vvar @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV9: $i,SV23: $i] :
( ( ( SV23
!= ( vvar @ SV9 ) )
| ~ ( visValue @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY118: $i,SY119: $i,SY120: $i,SY121: $i,SY122: $i] :
( ~ ~ ( ~ ( ( SY118 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SY118 @ SY119 @ ( vbind @ SV10 @ SV24 @ SY120 ) ) @ SY121 @ SY122 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SY118 @ SY119 @ SY120 ) ) @ SY121 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ( vvar @ SV11 )
!= ( vabs @ SV25 @ SY123 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV12: $i] :
( ( vnoExp
= ( vsomeExp @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY125: $i] :
( ( SV13
!= ( vsomeExp @ SY125 ) )
| ( SV26
!= ( vgetSomeExp @ SV13 ) )
| ( SV26 = SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i,SY129: $i,SY130: $i] :
( ~ ~ ( ( SY126 != SV14 )
| ~ ( vtcheck @ ( vbind @ SY126 @ SY127 @ ( vbind @ SV14 @ SV27 @ SY128 ) ) @ SY129 @ SY130 ) )
| ( vtcheck @ ( vbind @ SY126 @ SY127 @ SY128 ) @ SY129 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV28: $i,SV15: $i,SV1: $i] :
( ( ( vvar @ SV1 )
!= ( vapp @ SV15 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV29: $i,SV16: $i,SV2: $i] :
( ( ! [SY131: $i] :
( ~ ~ ( ( SV2 != SY131 )
| ( SV16
!= ( vvar @ SV29 ) ) )
| ~ ( ~ ( ( SV29 != SY131 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SY131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV3: $i,SV17: $i,SV30: $i] :
( ( ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ~ ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SY132 != SV3 ) )
| ( SY133
!= ( vvar @ SY135 ) ) )
| ~ ( ( SV17 != SY135 ) )
| ( SY134
!= ( vsubst @ SV30 @ SY132 @ SY133 ) )
| ( SY134
= ( vvar @ SY135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV4: $i,SV18: $i] :
( ( ( SV18
!= ( vsomeExp @ SV4 ) )
= $true )
| ( ( visSomeExp @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( ( ( vsomeExp @ SV5 )
!= ( vsomeExp @ SV19 ) )
| ( SV5 = SV19 ) )
| ~ ( ( SV5 != SV19 )
| ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV31: $i,SV6: $i,SV20: $i] :
( ( ( SV20
!= ( vvar @ SV6 ) )
| ( SV31
!= ( vreduce @ SV20 ) )
| ( SV31 = vnoExp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV21: $i,SV7: $i,SV32: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i,SY139: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SY136 != SY139 ) )
| ( SY137
!= ( vvar @ SV21 ) ) )
| ( SV7 != SV21 )
| ( SY138
!= ( vsubst @ SV32 @ SY136 @ SY137 ) )
| ( SY138 = SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ( ( vvar @ SV8 )
!= ( vvar @ SV22 ) )
| ( SV8 = SV22 ) )
| ~ ( ( SV8 != SV22 )
| ( ( vvar @ SV8 )
= ( vvar @ SV22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV9: $i,SV23: $i] :
( ( ( SV23
!= ( vvar @ SV9 ) )
= $true )
| ( ( ~ ( visValue @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV24: $i,SV10: $i,SV33: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i,SY143: $i] :
( ~ ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SY140 @ ( vbind @ SV10 @ SV24 @ SY141 ) ) @ SY142 @ SY143 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SY140 @ SY141 ) ) @ SY142 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV34: $i,SV25: $i,SV11: $i] :
( ( ! [SY144: $i] :
( ( vvar @ SV11 )
!= ( vabs @ SV25 @ SV34 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV26: $i,SV35: $i,SV13: $i] :
( ( ( SV13
!= ( vsomeExp @ SV35 ) )
| ( SV26
!= ( vgetSomeExp @ SV13 ) )
| ( SV26 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV27: $i,SV14: $i,SV36: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i,SY148: $i] :
( ~ ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SY145 @ ( vbind @ SV14 @ SV27 @ SY146 ) ) @ SY147 @ SY148 ) )
| ( vtcheck @ ( vbind @ SV36 @ SY145 @ SY146 ) @ SY147 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV28: $i,SV15: $i,SV1: $i] :
( ( ( vvar @ SV1 )
= ( vapp @ SV15 @ SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV29: $i,SV16: $i,SV37: $i,SV2: $i] :
( ( ~ ~ ( ( SV2 != SV37 )
| ( SV16
!= ( vvar @ SV29 ) ) )
| ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ! [SY149: $i,SY150: $i,SY151: $i] :
( ~ ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SY149
!= ( vvar @ SY151 ) ) )
| ~ ( ( SV17 != SY151 ) )
| ( SY150
!= ( vsubst @ SV30 @ SV38 @ SY149 ) )
| ( SY150
= ( vvar @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV4: $i,SV18: $i] :
( ( ( SV18
= ( vsomeExp @ SV4 ) )
= $false )
| ( ( visSomeExp @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( ( ( vsomeExp @ SV5 )
!= ( vsomeExp @ SV19 ) )
| ( SV5 = SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(162,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( ( SV5 != SV19 )
| ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(163,plain,
! [SV31: $i,SV6: $i,SV20: $i] :
( ( ( SV20
!= ( vvar @ SV6 ) )
= $true )
| ( ( ( SV31
!= ( vreduce @ SV20 ) )
| ( SV31 = vnoExp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV21: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ! [SY152: $i,SY153: $i,SY154: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SY154 ) )
| ( SY152
!= ( vvar @ SV21 ) ) )
| ( SV7 != SV21 )
| ( SY153
!= ( vsubst @ SV32 @ SV39 @ SY152 ) )
| ( SY153 = SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ( ( vvar @ SV8 )
!= ( vvar @ SV22 ) )
| ( SV8 = SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(166,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( ( SV8 != SV22 )
| ( ( vvar @ SV8 )
= ( vvar @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(167,plain,
! [SV9: $i,SV23: $i] :
( ( ( SV23
= ( vvar @ SV9 ) )
= $false )
| ( ( ~ ( visValue @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SY155 ) ) @ SY156 @ SY157 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SY155 ) ) @ SY156 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV41: $i,SV34: $i,SV25: $i,SV11: $i] :
( ( ( vvar @ SV11 )
!= ( vabs @ SV25 @ SV34 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV26: $i,SV35: $i,SV13: $i] :
( ( ( SV13
!= ( vsomeExp @ SV35 ) )
= $true )
| ( ( ( SV26
!= ( vgetSomeExp @ SV13 ) )
| ( SV26 = SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SY158 ) ) @ SY159 @ SY160 ) )
| ( vtcheck @ ( vbind @ SV36 @ SV42 @ SY158 ) @ SY159 @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV29: $i,SV16: $i,SV37: $i,SV2: $i] :
( ( ( ~ ~ ( ( SV2 != SV37 )
| ( SV16
!= ( vvar @ SV29 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ~ ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SV43
!= ( vvar @ SY162 ) ) )
| ~ ( ( SV17 != SY162 ) )
| ( SY161
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SY161
= ( vvar @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV19: $i,SV5: $i] :
( ( ( ( vsomeExp @ SV5 )
!= ( vsomeExp @ SV19 ) )
| ( SV5 = SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(175,plain,
! [SV19: $i,SV5: $i] :
( ( ( SV5 != SV19 )
| ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(176,plain,
! [SV31: $i,SV6: $i,SV20: $i] :
( ( ( SV20
= ( vvar @ SV6 ) )
= $false )
| ( ( ( SV31
!= ( vreduce @ SV20 ) )
| ( SV31 = vnoExp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV21: $i,SV44: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SY164 ) )
| ( SV44
!= ( vvar @ SV21 ) ) )
| ( SV7 != SV21 )
| ( SY163
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SY163 = SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV22: $i,SV8: $i] :
( ( ( ( vvar @ SV8 )
!= ( vvar @ SV22 ) )
| ( SV8 = SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(179,plain,
! [SV22: $i,SV8: $i] :
( ( ( SV8 != SV22 )
| ( ( vvar @ SV8 )
= ( vvar @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(180,plain,
! [SV9: $i,SV23: $i] :
( ( ( visValue @ SV23 )
= $false )
| ( ( SV23
= ( vvar @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ! [SY165: $i,SY166: $i] :
( ~ ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SY165 @ SY166 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SY165 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV41: $i,SV34: $i,SV25: $i,SV11: $i] :
( ( ( vvar @ SV11 )
= ( vabs @ SV25 @ SV34 @ SV41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV26: $i,SV35: $i,SV13: $i] :
( ( ( SV13
= ( vsomeExp @ SV35 ) )
= $false )
| ( ( ( SV26
!= ( vgetSomeExp @ SV13 ) )
| ( SV26 = SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(184,plain,
! [SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SY167 @ SY168 ) )
| ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SY167 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV29: $i,SV16: $i,SV37: $i,SV2: $i] :
( ( ( ~ ( ( SV2 != SV37 )
| ( SV16
!= ( vvar @ SV29 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV47: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ! [SY169: $i] :
( ~ ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SV43
!= ( vvar @ SY169 ) ) )
| ~ ( ( SV17 != SY169 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(187,plain,
! [SV19: $i,SV5: $i] :
( ( ( ( vsomeExp @ SV5 )
!= ( vsomeExp @ SV19 ) )
= $true )
| ( ( SV5 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV19: $i,SV5: $i] :
( ( ( SV5 != SV19 )
= $true )
| ( ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV6: $i,SV20: $i,SV31: $i] :
( ( ( SV31
!= ( vreduce @ SV20 ) )
= $true )
| ( ( SV31 = vnoExp )
= $true )
| ( ( SV20
= ( vvar @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ! [SY170: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SY170 ) )
| ( SV44
!= ( vvar @ SV21 ) ) )
| ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(191,plain,
! [SV22: $i,SV8: $i] :
( ( ( ( vvar @ SV8 )
!= ( vvar @ SV22 ) )
= $true )
| ( ( SV8 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV22: $i,SV8: $i] :
( ( ( SV8 != SV22 )
= $true )
| ( ( ( vvar @ SV8 )
= ( vvar @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ! [SY171: $i] :
( ~ ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SY171 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV35: $i,SV13: $i,SV26: $i] :
( ( ( SV26
!= ( vgetSomeExp @ SV13 ) )
= $true )
| ( ( SV26 = SV35 )
= $true )
| ( ( SV13
= ( vsomeExp @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ! [SY172: $i] :
( ~ ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SY172 ) )
| ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV29: $i,SV16: $i,SV37: $i,SV2: $i] :
( ( ( ( SV2 != SV37 )
| ( SV16
!= ( vvar @ SV29 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(197,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ~ ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SV43
!= ( vvar @ SV51 ) ) )
| ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV19: $i,SV5: $i] :
( ( ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) )
= $false )
| ( ( SV5 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV19: $i,SV5: $i] :
( ( ( SV5 = SV19 )
= $false )
| ( ( ( vsomeExp @ SV5 )
= ( vsomeExp @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV6: $i,SV20: $i,SV31: $i] :
( ( ( SV31
= ( vreduce @ SV20 ) )
= $false )
| ( ( SV31 = vnoExp )
= $true )
| ( ( SV20
= ( vvar @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ~ ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SV52 ) )
| ( SV44
!= ( vvar @ SV21 ) ) )
| ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV22: $i,SV8: $i] :
( ( ( ( vvar @ SV8 )
= ( vvar @ SV22 ) )
= $false )
| ( ( SV8 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(203,plain,
! [SV22: $i,SV8: $i] :
( ( ( SV8 = SV22 )
= $false )
| ( ( ( vvar @ SV8 )
= ( vvar @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(204,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ~ ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) )
| ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(205,plain,
! [SV35: $i,SV13: $i,SV26: $i] :
( ( ( SV26
= ( vgetSomeExp @ SV13 ) )
= $false )
| ( ( SV26 = SV35 )
= $true )
| ( ( SV13
= ( vsomeExp @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(206,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ~ ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 ) )
| ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(207,plain,
! [SV29: $i,SV16: $i,SV37: $i,SV2: $i] :
( ( ( SV2 != SV37 )
= $true )
| ( ( SV16
!= ( vvar @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(208,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SV43
!= ( vvar @ SV51 ) ) ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SV52 ) )
| ( SV44
!= ( vvar @ SV21 ) ) ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(211,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ( ~ ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 ) ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(212,plain,
! [SV29: $i,SV16: $i,SV37: $i,SV2: $i] :
( ( ( SV2 = SV37 )
= $false )
| ( ( SV16
!= ( vvar @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(213,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( ~ ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SV43
!= ( vvar @ SV51 ) ) ) )
= $false )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(214,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( ~ ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SV52 ) )
| ( SV44
!= ( vvar @ SV21 ) ) ) )
= $false )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(215,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ( ~ ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(216,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ( ~ ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 ) ) )
= $false )
| ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(217,plain,
! [SV37: $i,SV2: $i,SV29: $i,SV16: $i] :
( ( ( SV16
= ( vvar @ SV29 ) )
= $false )
| ( ( SV2 = SV37 )
= $false )
| ( ( ~ ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(218,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
| ( SV43
!= ( vvar @ SV51 ) ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(219,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SV52 ) )
| ( SV44
!= ( vvar @ SV21 ) ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(220,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ( ~ ( ( SV33 != SV10 ) )
| ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(221,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ( ( SV36 != SV14 )
| ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(222,plain,
! [SV16: $i,SV2: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) )
= $false )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(223,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( ~ ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) ) )
= $true )
| ( ( SV43
!= ( vvar @ SV51 ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(224,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( ~ ~ ( ( SV32 != SV7 )
| ( SV39 != SV52 ) ) )
= $true )
| ( ( SV44
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(225,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ( ~ ( ( SV33 != SV10 ) ) )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ( SV36 != SV14 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV16: $i,SV2: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) ) )
= $false )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(228,plain,
! [SV37: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) ) )
= $false )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(229,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( ~ ( ( SV30 != SV17 )
| ( SV38 != SV3 ) ) )
= $false )
| ( ( SV43
!= ( vvar @ SV51 ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(230,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( ~ ( ( SV32 != SV7 )
| ( SV39 != SV52 ) ) )
= $false )
| ( ( SV44
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(231,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ( SV33 != SV10 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV42: $i,SV14: $i,SV36: $i] :
( ( ( SV36 = SV14 )
= $false )
| ( ( ~ ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV16: $i,SV2: $i,SV37: $i,SV29: $i] :
( ( ( ( SV29 != SV37 )
| ( visFreeVar @ SV2 @ SV16 ) )
= $true )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(234,plain,
! [SV37: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( visFreeVar @ SV2 @ SV16 )
| ( SV29 = SV37 ) )
= $true )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(235,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( ( SV30 != SV17 )
| ( SV38 != SV3 ) )
= $true )
| ( ( SV43
!= ( vvar @ SV51 ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(236,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( ( SV32 != SV7 )
| ( SV39 != SV52 ) )
= $true )
| ( ( SV44
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(237,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV40: $i,SV10: $i,SV33: $i] :
( ( ( SV33 = SV10 )
= $true )
| ( ( ~ ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 ) )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(238,plain,
! [SV54: $i,SV50: $i,SV46: $i,SV27: $i,SV14: $i,SV42: $i,SV36: $i] :
( ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ ( vbind @ SV14 @ SV27 @ SV46 ) ) @ SV50 @ SV54 )
= $false )
| ( ( SV36 = SV14 )
= $false )
| ( ( vtcheck @ ( vbind @ SV36 @ SV42 @ SV46 ) @ SV50 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(239,plain,
! [SV16: $i,SV2: $i,SV37: $i,SV29: $i] :
( ( ( SV29 != SV37 )
= $true )
| ( ( visFreeVar @ SV2 @ SV16 )
= $true )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(240,plain,
! [SV37: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( visFreeVar @ SV2 @ SV16 ) )
= $true )
| ( ( SV29 = SV37 )
= $true )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(241,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( SV30 != SV17 )
= $true )
| ( ( SV38 != SV3 )
= $true )
| ( ( SV43
!= ( vvar @ SV51 ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(242,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( SV32 != SV7 )
= $true )
| ( ( SV39 != SV52 )
= $true )
| ( ( SV44
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(243,plain,
! [SV53: $i,SV49: $i,SV45: $i,SV24: $i,SV10: $i,SV40: $i,SV33: $i] :
( ( ( vtcheck @ ( vbind @ SV33 @ SV40 @ ( vbind @ SV10 @ SV24 @ SV45 ) ) @ SV49 @ SV53 )
= $false )
| ( ( SV33 = SV10 )
= $true )
| ( ( vtcheck @ ( vbind @ SV10 @ SV24 @ ( vbind @ SV33 @ SV40 @ SV45 ) ) @ SV49 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(244,plain,
! [SV16: $i,SV2: $i,SV37: $i,SV29: $i] :
( ( ( SV29 = SV37 )
= $false )
| ( ( visFreeVar @ SV2 @ SV16 )
= $true )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV37: $i,SV29: $i,SV16: $i,SV2: $i] :
( ( ( visFreeVar @ SV2 @ SV16 )
= $false )
| ( ( SV29 = SV37 )
= $true )
| ( ( SV2 = SV37 )
= $false )
| ( ( SV16
= ( vvar @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i] :
( ( ( SV30 = SV17 )
= $false )
| ( ( SV38 != SV3 )
= $true )
| ( ( SV43
!= ( vvar @ SV51 ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(247,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i] :
( ( ( SV32 = SV7 )
= $false )
| ( ( SV39 != SV52 )
= $true )
| ( ( SV44
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(248,plain,
! [SV47: $i,SV51: $i,SV43: $i,SV17: $i,SV30: $i,SV3: $i,SV38: $i] :
( ( ( SV38 = SV3 )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV43
!= ( vvar @ SV51 ) )
= $true )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(249,plain,
! [SV48: $i,SV21: $i,SV44: $i,SV7: $i,SV32: $i,SV52: $i,SV39: $i] :
( ( ( SV39 = SV52 )
= $false )
| ( ( SV32 = SV7 )
= $false )
| ( ( SV44
!= ( vvar @ SV21 ) )
= $true )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(250,plain,
! [SV47: $i,SV3: $i,SV38: $i,SV17: $i,SV30: $i,SV51: $i,SV43: $i] :
( ( ( SV43
= ( vvar @ SV51 ) )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV38 = SV3 )
= $false )
| ( ( ~ ( ( SV17 != SV51 ) )
| ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(251,plain,
! [SV48: $i,SV52: $i,SV39: $i,SV7: $i,SV32: $i,SV21: $i,SV44: $i] :
( ( ( SV44
= ( vvar @ SV21 ) )
= $false )
| ( ( SV32 = SV7 )
= $false )
| ( ( SV39 = SV52 )
= $false )
| ( ( ( SV7 != SV21 )
| ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(252,plain,
! [SV3: $i,SV43: $i,SV38: $i,SV30: $i,SV47: $i,SV51: $i,SV17: $i] :
( ( ( ~ ( ( SV17 != SV51 ) ) )
= $true )
| ( ( ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true )
| ( ( SV38 = SV3 )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV43
= ( vvar @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(253,plain,
! [SV52: $i,SV44: $i,SV39: $i,SV32: $i,SV48: $i,SV21: $i,SV7: $i] :
( ( ( SV7 != SV21 )
= $true )
| ( ( ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true )
| ( ( SV39 = SV52 )
= $false )
| ( ( SV32 = SV7 )
= $false )
| ( ( SV44
= ( vvar @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(254,plain,
! [SV3: $i,SV43: $i,SV38: $i,SV30: $i,SV47: $i,SV51: $i,SV17: $i] :
( ( ( SV17 != SV51 )
= $false )
| ( ( ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true )
| ( ( SV38 = SV3 )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV43
= ( vvar @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(255,plain,
! [SV52: $i,SV44: $i,SV39: $i,SV32: $i,SV48: $i,SV21: $i,SV7: $i] :
( ( ( SV7 = SV21 )
= $false )
| ( ( ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
| ( SV48 = SV52 ) )
= $true )
| ( ( SV39 = SV52 )
= $false )
| ( ( SV32 = SV7 )
= $false )
| ( ( SV44
= ( vvar @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(256,plain,
! [SV3: $i,SV43: $i,SV38: $i,SV30: $i,SV47: $i,SV51: $i,SV17: $i] :
( ( ( SV17 = SV51 )
= $true )
| ( ( ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
| ( SV47
= ( vvar @ SV51 ) ) )
= $true )
| ( ( SV38 = SV3 )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV43
= ( vvar @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(257,plain,
! [SV21: $i,SV7: $i,SV52: $i,SV44: $i,SV39: $i,SV32: $i,SV48: $i] :
( ( ( SV48
!= ( vsubst @ SV32 @ SV39 @ SV44 ) )
= $true )
| ( ( SV48 = SV52 )
= $true )
| ( ( SV7 = SV21 )
= $false )
| ( ( SV39 = SV52 )
= $false )
| ( ( SV32 = SV7 )
= $false )
| ( ( SV44
= ( vvar @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(258,plain,
! [SV3: $i,SV17: $i,SV51: $i,SV43: $i,SV38: $i,SV30: $i,SV47: $i] :
( ( ( SV47
!= ( vsubst @ SV30 @ SV38 @ SV43 ) )
= $true )
| ( ( SV47
= ( vvar @ SV51 ) )
= $true )
| ( ( SV17 = SV51 )
= $true )
| ( ( SV38 = SV3 )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV43
= ( vvar @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(259,plain,
! [SV21: $i,SV7: $i,SV52: $i,SV44: $i,SV39: $i,SV32: $i,SV48: $i] :
( ( ( SV48
= ( vsubst @ SV32 @ SV39 @ SV44 ) )
= $false )
| ( ( SV48 = SV52 )
= $true )
| ( ( SV7 = SV21 )
= $false )
| ( ( SV39 = SV52 )
= $false )
| ( ( SV32 = SV7 )
= $false )
| ( ( SV44
= ( vvar @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(260,plain,
! [SV3: $i,SV17: $i,SV51: $i,SV43: $i,SV38: $i,SV30: $i,SV47: $i] :
( ( ( SV47
= ( vsubst @ SV30 @ SV38 @ SV43 ) )
= $false )
| ( ( SV47
= ( vvar @ SV51 ) )
= $true )
| ( ( SV17 = SV51 )
= $true )
| ( ( SV38 = SV3 )
= $false )
| ( ( SV30 = SV17 )
= $false )
| ( ( SV43
= ( vvar @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(261,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[98,260,259,245,244,243,238,205,203,202,200,199,198,182,180,160,157,141,115,99]) ).
thf(262,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM146+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n026.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 18:41:55 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.47/0.60
% 2.47/0.60 No.of.Axioms: 14
% 2.47/0.60
% 2.47/0.60 Length.of.Defs: 0
% 2.47/0.60
% 2.47/0.60 Contains.Choice.Funs: false
% 2.47/0.60 .........
% 2.47/0.60
% 2.47/0.60 ********************************
% 2.47/0.60 * All subproblems solved! *
% 2.47/0.60 ********************************
% 2.47/0.60 % 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:261,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.47/0.60
% 2.47/0.60 %**** Beginning of derivation protocol ****
% 2.47/0.60 % SZS output start CNFRefutation
% See solution above
% 2.47/0.60
% 2.47/0.60 %**** End of derivation protocol ****
% 2.47/0.60 %**** no. of clauses in derivation: 218 ****
% 2.47/0.60 %**** clause counter: 261 ****
% 2.47/0.60
% 2.47/0.60 % 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:261,loop_count:0,foatp_calls:1,translation:fof_full)
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