%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM129+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:12:26 AM UTC 2026
% Result : Theorem 1.90s 0.51s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 297 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 2421 (1493 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 4007 (1171 ~; 832 |; 57 &;1862 @)
% ( 0 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 9 con; 0-3 aty)
% Number of variables : 1409 ( 0 ^;1409 !; 0 ?;1409 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Ve,type,
sK1_Ve: $i ).
thf(tp_sK2_SY73,type,
sK2_SY73: $i ).
thf(tp_sK3_SY76,type,
sK3_SY76: $i ).
thf(tp_sK4_SY78,type,
sK4_SY78: $i ).
thf(tp_vabs,type,
vabs: $i > $i > $i > $i ).
thf(tp_valphaEquivalent,type,
valphaEquivalent: $i > $i > $o ).
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(1,axiom,
! [Ve: $i,Ve1: $i,Vx: $i,Vfresh: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ( Vx != Vfresh ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-unequal-var-3') ).
thf(6,axiom,
! [Ve: $i,Vx: $i,Ve1: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( valphaEquivalent @ Ve @ Ve1 ) )
=> ~ ( visFreeVar @ Vx @ Ve1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-FreeVar') ).
thf(35,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst2) ).
thf(36,axiom,
! [Ve: $i,Vx: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Vy: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx != Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vvar @ Vy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst1) ).
thf(37,axiom,
! [Vx: $i,Vy: $i,VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vvar @ Vy ) ) )
=> ( ( Vx = Vy )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT = Ve ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst0) ).
thf(38,axiom,
! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
thf(54,axiom,
! [VVar0: $i,VExp0: $i,Ve1: $i,Vv: $i,Ve2: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar2) ).
thf(55,axiom,
! [VT: $i,VVar0: $i,VExp0: $i,Vx: $i,Vv: $i,Ve: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vabs @ Vx @ VT @ Ve ) ) )
=> ( ( ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( Vx != Vv )
& ( visFreeVar @ Vv @ Ve ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
thf(56,axiom,
! [VVar0: $i,VExp0: $i,Vx: $i,Vv: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vvar @ Vx ) ) )
=> ( ( ( Vx = Vv )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( Vx = Vv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar0) ).
thf(57,axiom,
! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
thf(58,axiom,
! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
thf(60,axiom,
! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-abs-app') ).
thf(61,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
thf(62,axiom,
! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-abs') ).
thf(63,axiom,
! [VExp0: $i,VExp1: $i,VExp2: $i,VExp3: $i] :
( ( ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) )
=> ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) ) )
& ( ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) )
=> ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-app') ).
thf(65,axiom,
! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-var') ).
thf(66,conjecture,
! [Ve: $i,Vx: $i,Vfresh: $i,Ve1: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ~ ( visFreeVar @ Vfresh @ Ve1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-free-2') ).
thf(67,negated_conjecture,
( ( ! [Ve: $i,Vx: $i,Vfresh: $i,Ve1: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ~ ( visFreeVar @ Vfresh @ Ve1 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[66]) ).
thf(68,plain,
( ( ! [Ve: $i,Vx: $i,Vfresh: $i,Ve1: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ~ ( visFreeVar @ Vfresh @ Ve1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[67]) ).
thf(69,plain,
( ( ! [Ve: $i,Ve1: $i,Vx: $i,Vfresh: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ( Vx != Vfresh ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(70,plain,
( ( ! [Ve: $i,Vx: $i,Ve1: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( valphaEquivalent @ Ve @ Ve1 ) )
=> ~ ( visFreeVar @ Vx @ Ve1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(71,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(72,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)],[36]) ).
thf(73,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)],[37]) ).
thf(74,plain,
( ( ! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(75,plain,
( ( ! [VVar0: $i,VExp0: $i,Ve1: $i,Vv: $i,Ve2: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(76,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)],[55]) ).
thf(77,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)],[56]) ).
thf(78,plain,
( ( ! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(79,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(80,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(81,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(82,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(83,plain,
( ( ! [VExp0: $i,VExp1: $i,VExp2: $i,VExp3: $i] :
( ( ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) )
=> ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) ) )
& ( ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) )
=> ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(84,plain,
( ( ! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(85,plain,
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ( SY74
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ SY75 ) @ ( vvar @ SY73 ) ) ) )
=> ~ ( visFreeVar @ SY74 @ SY75 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(86,plain,
( ( ! [SY76: $i,SY77: $i] :
( ( SY76
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ SY77 ) @ ( vvar @ sK2_SY73 ) ) ) )
=> ~ ( visFreeVar @ SY76 @ SY77 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(87,plain,
( ( ! [SY78: $i] :
( ( sK3_SY76
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ SY78 ) @ ( vvar @ sK2_SY73 ) ) ) )
=> ~ ( visFreeVar @ sK3_SY76 @ SY78 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ( sK3_SY76
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK4_SY78 ) @ ( vvar @ sK2_SY73 ) ) ) )
=> ~ ( visFreeVar @ sK3_SY76 @ sK4_SY78 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( sK3_SY76
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK4_SY78 ) @ ( vvar @ sK2_SY73 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(90,plain,
( ( ~ ( visFreeVar @ sK3_SY76 @ sK4_SY78 ) )
= $false ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(91,plain,
( ( visFreeVar @ sK3_SY76 @ sK4_SY78 )
= $true ),
inference(polarity_switch,[status(thm)],[90]) ).
thf(92,plain,
( ( ! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(93,plain,
( ( ! [VExp0: $i,VExp1: $i,VExp2: $i,VExp3: $i] :
( ( ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) )
=> ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) ) )
& ( ( ( VExp0 = VExp2 )
& ( VExp1 = VExp3 ) )
=> ( ( vapp @ VExp0 @ VExp1 )
= ( vapp @ VExp2 @ VExp3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(94,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(95,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(96,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(97,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(98,plain,
( ( ! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(99,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)],[77]) ).
thf(100,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)],[76]) ).
thf(101,plain,
( ( ! [VVar0: $i,VExp0: $i,Ve1: $i,Vv: $i,Ve2: $i] :
( ( ( VVar0 = Vv )
& ( VExp0
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) )
=> ( visFreeVar @ VVar0 @ VExp0 ) )
& ( ( visFreeVar @ VVar0 @ VExp0 )
=> ( ( visFreeVar @ Vv @ Ve1 )
| ( visFreeVar @ Vv @ Ve2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(102,plain,
( ( ! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(103,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)],[73]) ).
thf(104,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)],[72]) ).
thf(105,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i,RESULT: $i,Ve1: $i,Vx: $i,Ve: $i,Ve2: $i] :
( ( ( VVar0 = Vx )
& ( VExp0 = Ve )
& ( VExp1
= ( vapp @ Ve1 @ Ve2 ) ) )
=> ( ( RESULT
= ( vsubst @ VVar0 @ VExp0 @ VExp1 ) )
=> ( RESULT
= ( vapp @ ( vsubst @ Vx @ Ve @ Ve1 ) @ ( vsubst @ Vx @ Ve @ Ve2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(106,plain,
( ( ! [Ve: $i,Vx: $i,Ve1: $i] :
( ( ~ ( visFreeVar @ Vx @ Ve )
& ( valphaEquivalent @ Ve @ Ve1 ) )
=> ~ ( visFreeVar @ Vx @ Ve1 ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(107,plain,
( ( ! [Ve: $i,Ve1: $i,Vx: $i,Vfresh: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ( Vx != Vfresh ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(108,plain,
( ( sK3_SY76
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK4_SY78 ) @ ( vvar @ sK2_SY73 ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(109,plain,
( ( visFreeVar @ sK3_SY76 @ sK4_SY78 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( vvar @ SX0 )
!= ( vvar @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( vvar @ SX0 )
= ( vvar @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( vvar @ SX0 )
!= ( vapp @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ( ( vapp @ SX0 @ SX1 )
!= ( vapp @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) )
| ~ ( ~ ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) )
| ( ( vapp @ SX0 @ SX1 )
= ( vapp @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(113,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)],[99]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vvar @ SX0 ) )
| ~ ( visValue @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX3
!= ( vgensym @ ( vapp @ ( vapp @ SX0 @ SX1 ) @ ( vvar @ SX2 ) ) ) )
| ( SX2 != SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i] :
( ~ ~ ( ~ ~ ( ( SX0 != SX5 )
| ( SX1 != SX6 ) )
| ( SX2
!= ( vapp @ SX4 @ SX7 ) ) )
| ( SX3
!= ( vsubst @ SX0 @ SX1 @ SX2 ) )
| ( SX3
= ( vapp @ ( vsubst @ SX5 @ SX6 @ SX4 ) @ ( vsubst @ SX5 @ SX6 @ SX7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2
!= ( vapp @ SX0 @ SX1 ) )
| ~ ( visValue @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(118,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)],[100]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ( SX0 != SX3 )
| ( SX1
!= ( vapp @ SX2 @ SX4 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SX3 @ SX2 )
| ( visFreeVar @ SX3 @ SX4 ) )
| ( visFreeVar @ SX0 @ SX1 ) )
| ~ ( ~ ( visFreeVar @ SX0 @ SX1 )
| ( visFreeVar @ SX3 @ SX2 )
| ( visFreeVar @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SX1 @ SX0 )
| ~ ( valphaEquivalent @ SX0 @ SX2 ) )
| ~ ( visFreeVar @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( vgensym @ SX1 )
!= SX0 )
| ~ ( visFreeVar @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(124,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)],[103]) ).
thf(125,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)],[104]) ).
thf(126,plain,
! [SV1: $i] :
( ( ! [SY79: $i] :
~ ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SY79 ) )
| ( SV1 = SY79 ) )
| ~ ( ( SV1 != SY79 )
| ( ( vvar @ SV1 )
= ( vvar @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV2: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ( vvar @ SV2 )
!= ( vapp @ SY80 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV3: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i] :
~ ( ~ ( ( ( vapp @ SV3 @ SY82 )
!= ( vapp @ SY83 @ SY84 ) )
| ~ ( ( SV3 != SY83 )
| ( SY82 != SY84 ) ) )
| ~ ( ~ ~ ( ( SV3 != SY83 )
| ( SY82 != SY84 ) )
| ( ( vapp @ SV3 @ SY82 )
= ( vapp @ SY83 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV4: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ( SV4 != SY87 )
| ( SY85
!= ( vvar @ SY86 ) ) )
| ~ ( ~ ( ( SY86 != SY87 )
| ( visFreeVar @ SV4 @ SY85 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SY85 )
| ( SY86 = SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV5: $i] :
( ( ! [SY88: $i] :
( ( SY88
!= ( vvar @ SV5 ) )
| ~ ( visValue @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV6: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i] :
( ( SY91
!= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SY89 ) @ ( vvar @ SY90 ) ) ) )
| ( SY90 != SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV7: $i] :
( ( ! [SY92: $i,SY93: $i,SY94: $i,SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY96 )
| ( SY92 != SY97 ) )
| ( SY93
!= ( vapp @ SY95 @ SY98 ) ) )
| ( SY94
!= ( vsubst @ SV7 @ SY92 @ SY93 ) )
| ( SY94
= ( vapp @ ( vsubst @ SY96 @ SY97 @ SY95 ) @ ( vsubst @ SY96 @ SY97 @ SY98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV8: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ( SY100
!= ( vapp @ SV8 @ SY99 ) )
| ~ ( visValue @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV9: $i] :
( ( ! [SY101: $i,SY102: $i,SY103: $i,SY104: $i,SY105: $i] :
( ~ ~ ( ( SY101 != SY104 )
| ( SY102
!= ( vabs @ SY103 @ SV9 @ SY105 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY103 != SY104 ) )
| ~ ( visFreeVar @ SY104 @ SY105 ) )
| ( visFreeVar @ SY101 @ SY102 ) )
| ~ ( ~ ( visFreeVar @ SY101 @ SY102 )
| ~ ( ~ ( ( SY103 != SY104 ) )
| ~ ( visFreeVar @ SY104 @ SY105 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV10: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i] :
( ( vvar @ SV10 )
!= ( vabs @ SY106 @ SY107 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV11: $i] :
( ( ! [SY109: $i,SY110: $i,SY111: $i,SY112: $i] :
( ( vabs @ SV11 @ SY109 @ SY110 )
!= ( vapp @ SY111 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV12: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] :
( ~ ~ ( ( SV12 != SY115 )
| ( SY113
!= ( vapp @ SY114 @ SY116 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY115 @ SY114 )
| ( visFreeVar @ SY115 @ SY116 ) )
| ( visFreeVar @ SV12 @ SY113 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SY113 )
| ( visFreeVar @ SY115 @ SY114 )
| ( visFreeVar @ SY115 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV13: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SY117 @ SV13 )
| ~ ( valphaEquivalent @ SV13 @ SY118 ) )
| ~ ( visFreeVar @ SY117 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV14: $i] :
( ( ! [SY119: $i] :
( ( ( vgensym @ SY119 )
!= SV14 )
| ~ ( visFreeVar @ SV14 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV15: $i] :
( ( ! [SY120: $i,SY121: $i,SY122: $i,SY123: $i,SY124: $i,SY125: $i] :
( ~ ~ ( ~ ~ ( ( SY121 != SV15 )
| ( SY122 != SY125 ) )
| ( SY123
!= ( vvar @ SY120 ) ) )
| ( SV15 != SY120 )
| ( SY124
!= ( vsubst @ SY121 @ SY122 @ SY123 ) )
| ( SY124 = SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV16: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i,SY129: $i,SY130: $i,SY131: $i] :
( ~ ~ ( ~ ~ ( ( SY127 != SY126 )
| ( SY128 != SV16 ) )
| ( SY129
!= ( vvar @ SY131 ) ) )
| ~ ( ( SY126 != SY131 ) )
| ( SY130
!= ( vsubst @ SY127 @ SY128 @ SY129 ) )
| ( SY130
= ( vvar @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SV17 ) )
| ( SV1 = SV17 ) )
| ~ ( ( SV1 != SV17 )
| ( ( vvar @ SV1 )
= ( vvar @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY132: $i] :
( ( vvar @ SV2 )
!= ( vapp @ SV18 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY133: $i,SY134: $i] :
~ ( ~ ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SY133 @ SY134 ) )
| ~ ( ( SV3 != SY133 )
| ( SV19 != SY134 ) ) )
| ~ ( ~ ~ ( ( SV3 != SY133 )
| ( SV19 != SY134 ) )
| ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SY133 @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ~ ~ ( ( SV4 != SY136 )
| ( SV20
!= ( vvar @ SY135 ) ) )
| ~ ( ~ ( ( SY135 != SY136 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SY135 = SY136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV5: $i,SV21: $i] :
( ( ( SV21
!= ( vvar @ SV5 ) )
| ~ ( visValue @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(147,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ( SY138
!= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SV22 ) @ ( vvar @ SY137 ) ) ) )
| ( SY137 != SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY139: $i,SY140: $i,SY141: $i,SY142: $i,SY143: $i,SY144: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY142 )
| ( SV23 != SY143 ) )
| ( SY139
!= ( vapp @ SY141 @ SY144 ) ) )
| ( SY140
!= ( vsubst @ SV7 @ SV23 @ SY139 ) )
| ( SY140
= ( vapp @ ( vsubst @ SY142 @ SY143 @ SY141 ) @ ( vsubst @ SY142 @ SY143 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(149,plain,
! [SV24: $i,SV8: $i] :
( ( ! [SY145: $i] :
( ( SY145
!= ( vapp @ SV8 @ SV24 ) )
| ~ ( visValue @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV9: $i,SV25: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i,SY149: $i] :
( ~ ~ ( ( SV25 != SY148 )
| ( SY146
!= ( vabs @ SY147 @ SV9 @ SY149 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY147 != SY148 ) )
| ~ ( visFreeVar @ SY148 @ SY149 ) )
| ( visFreeVar @ SV25 @ SY146 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SY146 )
| ~ ( ~ ( ( SY147 != SY148 ) )
| ~ ( visFreeVar @ SY148 @ SY149 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY150: $i,SY151: $i] :
( ( vvar @ SV10 )
!= ( vabs @ SV26 @ SY150 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV27: $i,SV11: $i] :
( ( ! [SY152: $i,SY153: $i,SY154: $i] :
( ( vabs @ SV11 @ SV27 @ SY152 )
!= ( vapp @ SY153 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV28: $i,SV12: $i] :
( ( ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ( SV12 != SY156 )
| ( SV28
!= ( vapp @ SY155 @ SY157 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY156 @ SY155 )
| ( visFreeVar @ SY156 @ SY157 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SY156 @ SY155 )
| ( visFreeVar @ SY156 @ SY157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV13: $i,SV29: $i] :
( ( ! [SY158: $i] :
( ~ ~ ( ~ ~ ( visFreeVar @ SV29 @ SV13 )
| ~ ( valphaEquivalent @ SV13 @ SY158 ) )
| ~ ( visFreeVar @ SV29 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV14: $i,SV30: $i] :
( ( ( ( vgensym @ SV30 )
!= SV14 )
| ~ ( visFreeVar @ SV14 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV31: $i,SV15: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i,SY162: $i,SY163: $i] :
( ~ ~ ( ~ ~ ( ( SY159 != SV15 )
| ( SY160 != SY163 ) )
| ( SY161
!= ( vvar @ SV31 ) ) )
| ( SV15 != SV31 )
| ( SY162
!= ( vsubst @ SY159 @ SY160 @ SY161 ) )
| ( SY162 = SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV16: $i,SV32: $i] :
( ( ! [SY164: $i,SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ( SY164 != SV32 )
| ( SY165 != SV16 ) )
| ( SY166
!= ( vvar @ SY168 ) ) )
| ~ ( ( SV32 != SY168 ) )
| ( SY167
!= ( vsubst @ SY164 @ SY165 @ SY166 ) )
| ( SY167
= ( vvar @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SV17 ) )
| ( SV1 = SV17 ) )
| ~ ( ( SV1 != SV17 )
| ( ( vvar @ SV1 )
= ( vvar @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV33: $i,SV18: $i,SV2: $i] :
( ( ( vvar @ SV2 )
!= ( vapp @ SV18 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV34: $i,SV19: $i,SV3: $i] :
( ( ! [SY169: $i] :
~ ( ~ ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SV34 @ SY169 ) )
| ~ ( ( SV3 != SV34 )
| ( SV19 != SY169 ) ) )
| ~ ( ~ ~ ( ( SV3 != SV34 )
| ( SV19 != SY169 ) )
| ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SY169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV35: $i,SV20: $i,SV4: $i] :
( ( ! [SY170: $i] :
( ~ ~ ( ( SV4 != SY170 )
| ( SV20
!= ( vvar @ SV35 ) ) )
| ~ ( ~ ( ( SV35 != SY170 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SY170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(162,plain,
! [SV5: $i,SV21: $i] :
( ( ( SV21
!= ( vvar @ SV5 ) )
= $true )
| ( ( ~ ( visValue @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(163,plain,
! [SV36: $i,SV22: $i,SV6: $i] :
( ( ! [SY171: $i] :
( ( SY171
!= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SV22 ) @ ( vvar @ SV36 ) ) ) )
| ( SV36 != SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV37: $i,SV23: $i,SV7: $i] :
( ( ! [SY172: $i,SY173: $i,SY174: $i,SY175: $i,SY176: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY174 )
| ( SV23 != SY175 ) )
| ( SV37
!= ( vapp @ SY173 @ SY176 ) ) )
| ( SY172
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SY172
= ( vapp @ ( vsubst @ SY174 @ SY175 @ SY173 ) @ ( vsubst @ SY174 @ SY175 @ SY176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(165,plain,
! [SV24: $i,SV8: $i,SV38: $i] :
( ( ( SV38
!= ( vapp @ SV8 @ SV24 ) )
| ~ ( visValue @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(166,plain,
! [SV9: $i,SV39: $i,SV25: $i] :
( ( ! [SY177: $i,SY178: $i,SY179: $i] :
( ~ ~ ( ( SV25 != SY178 )
| ( SV39
!= ( vabs @ SY177 @ SV9 @ SY179 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SY177 != SY178 ) )
| ~ ( visFreeVar @ SY178 @ SY179 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SY177 != SY178 ) )
| ~ ( visFreeVar @ SY178 @ SY179 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(167,plain,
! [SV40: $i,SV26: $i,SV10: $i] :
( ( ! [SY180: $i] :
( ( vvar @ SV10 )
!= ( vabs @ SV26 @ SV40 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV41: $i,SV27: $i,SV11: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ( vabs @ SV11 @ SV27 @ SV41 )
!= ( vapp @ SY181 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV42: $i,SV28: $i,SV12: $i] :
( ( ! [SY183: $i,SY184: $i] :
( ~ ~ ( ( SV12 != SY183 )
| ( SV28
!= ( vapp @ SV42 @ SY184 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY183 @ SV42 )
| ( visFreeVar @ SY183 @ SY184 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SY183 @ SV42 )
| ( visFreeVar @ SY183 @ SY184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ~ ~ ( ~ ~ ( visFreeVar @ SV29 @ SV13 )
| ~ ( valphaEquivalent @ SV13 @ SV43 ) )
| ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV14: $i,SV30: $i] :
( ( ( ( vgensym @ SV30 )
!= SV14 )
= $true )
| ( ( ~ ( visFreeVar @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV31: $i,SV15: $i,SV44: $i] :
( ( ! [SY185: $i,SY186: $i,SY187: $i,SY188: $i] :
( ~ ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SY185 != SY188 ) )
| ( SY186
!= ( vvar @ SV31 ) ) )
| ( SV15 != SV31 )
| ( SY187
!= ( vsubst @ SV44 @ SY185 @ SY186 ) )
| ( SY187 = SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(173,plain,
! [SV16: $i,SV32: $i,SV45: $i] :
( ( ! [SY189: $i,SY190: $i,SY191: $i,SY192: $i] :
( ~ ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SY189 != SV16 ) )
| ( SY190
!= ( vvar @ SY192 ) ) )
| ~ ( ( SV32 != SY192 ) )
| ( SY191
!= ( vsubst @ SV45 @ SY189 @ SY190 ) )
| ( SY191
= ( vvar @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SV17 ) )
| ( SV1 = SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(175,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( ( SV1 != SV17 )
| ( ( vvar @ SV1 )
= ( vvar @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(176,plain,
! [SV33: $i,SV18: $i,SV2: $i] :
( ( ( vvar @ SV2 )
= ( vapp @ SV18 @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(177,plain,
! [SV46: $i,SV34: $i,SV19: $i,SV3: $i] :
( ( ~ ( ~ ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SV34 @ SV46 ) )
| ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
| ~ ( ~ ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) )
| ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV35: $i,SV20: $i,SV47: $i,SV4: $i] :
( ( ~ ~ ( ( SV4 != SV47 )
| ( SV20
!= ( vvar @ SV35 ) ) )
| ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV5: $i,SV21: $i] :
( ( ( SV21
= ( vvar @ SV5 ) )
= $false )
| ( ( ~ ( visValue @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV36: $i,SV22: $i,SV6: $i,SV48: $i] :
( ( ( SV48
!= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SV22 ) @ ( vvar @ SV36 ) ) ) )
| ( SV36 != SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV49: $i,SV37: $i,SV23: $i,SV7: $i] :
( ( ! [SY193: $i,SY194: $i,SY195: $i,SY196: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY194 )
| ( SV23 != SY195 ) )
| ( SV37
!= ( vapp @ SY193 @ SY196 ) ) )
| ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SY194 @ SY195 @ SY193 ) @ ( vsubst @ SY194 @ SY195 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(182,plain,
! [SV24: $i,SV8: $i,SV38: $i] :
( ( ( SV38
!= ( vapp @ SV8 @ SV24 ) )
= $true )
| ( ( ~ ( visValue @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(183,plain,
! [SV9: $i,SV50: $i,SV39: $i,SV25: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ~ ( ( SV25 != SY197 )
| ( SV39
!= ( vabs @ SV50 @ SV9 @ SY198 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SY197 ) )
| ~ ( visFreeVar @ SY197 @ SY198 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SY197 ) )
| ~ ( visFreeVar @ SY197 @ SY198 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(184,plain,
! [SV51: $i,SV40: $i,SV26: $i,SV10: $i] :
( ( ( vvar @ SV10 )
!= ( vabs @ SV26 @ SV40 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV52: $i,SV41: $i,SV27: $i,SV11: $i] :
( ( ! [SY199: $i] :
( ( vabs @ SV11 @ SV27 @ SV41 )
!= ( vapp @ SV52 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ! [SY200: $i] :
( ~ ~ ( ( SV12 != SV53 )
| ( SV28
!= ( vapp @ SV42 @ SY200 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SY200 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( visFreeVar @ SV29 @ SV13 )
| ~ ( valphaEquivalent @ SV13 @ SV43 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV14: $i,SV30: $i] :
( ( ( ( vgensym @ SV30 )
= SV14 )
= $false )
| ( ( ~ ( visFreeVar @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV31: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ! [SY201: $i,SY202: $i,SY203: $i] :
( ~ ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SY203 ) )
| ( SY201
!= ( vvar @ SV31 ) ) )
| ( SV15 != SV31 )
| ( SY202
!= ( vsubst @ SV44 @ SV54 @ SY201 ) )
| ( SY202 = SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i] :
( ~ ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SY204
!= ( vvar @ SY206 ) ) )
| ~ ( ( SV32 != SY206 ) )
| ( SY205
!= ( vsubst @ SV45 @ SV55 @ SY204 ) )
| ( SY205
= ( vvar @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV17: $i,SV1: $i] :
( ( ( ( vvar @ SV1 )
!= ( vvar @ SV17 ) )
| ( SV1 = SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(192,plain,
! [SV17: $i,SV1: $i] :
( ( ( SV1 != SV17 )
| ( ( vvar @ SV1 )
= ( vvar @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(193,plain,
! [SV46: $i,SV34: $i,SV19: $i,SV3: $i] :
( ( ~ ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SV34 @ SV46 ) )
| ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
| ~ ( ~ ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) )
| ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV35: $i,SV20: $i,SV47: $i,SV4: $i] :
( ( ( ~ ~ ( ( SV4 != SV47 )
| ( SV20
!= ( vvar @ SV35 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV5: $i,SV21: $i] :
( ( ( visValue @ SV21 )
= $false )
| ( ( SV21
= ( vvar @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV36: $i,SV22: $i,SV6: $i,SV48: $i] :
( ( ( SV48
!= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SV22 ) @ ( vvar @ SV36 ) ) ) )
= $true )
| ( ( SV36 != SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV49: $i,SV56: $i,SV37: $i,SV23: $i,SV7: $i] :
( ( ! [SY207: $i,SY208: $i,SY209: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SY207 )
| ( SV23 != SY208 ) )
| ( SV37
!= ( vapp @ SV56 @ SY209 ) ) )
| ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SY207 @ SY208 @ SV56 ) @ ( vsubst @ SY207 @ SY208 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV24: $i,SV8: $i,SV38: $i] :
( ( ( SV38
= ( vapp @ SV8 @ SV24 ) )
= $false )
| ( ( ~ ( visValue @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ! [SY210: $i] :
( ~ ~ ( ( SV25 != SV57 )
| ( SV39
!= ( vabs @ SV50 @ SV9 @ SY210 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SY210 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SY210 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(200,plain,
! [SV51: $i,SV40: $i,SV26: $i,SV10: $i] :
( ( ( vvar @ SV10 )
= ( vabs @ SV26 @ SV40 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(201,plain,
! [SV58: $i,SV52: $i,SV41: $i,SV27: $i,SV11: $i] :
( ( ( vabs @ SV11 @ SV27 @ SV41 )
!= ( vapp @ SV52 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(202,plain,
! [SV59: $i,SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ~ ~ ( ( SV12 != SV53 )
| ( SV28
!= ( vapp @ SV42 @ SV59 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(203,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( visFreeVar @ SV29 @ SV13 )
| ~ ( valphaEquivalent @ SV13 @ SV43 ) ) )
= $false )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV30: $i,SV14: $i] :
( ( ( visFreeVar @ SV14 @ SV30 )
= $false )
| ( ( ( vgensym @ SV30 )
= SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV31: $i,SV60: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SY212 ) )
| ( SV60
!= ( vvar @ SV31 ) ) )
| ( SV15 != SV31 )
| ( SY211
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SY211 = SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(206,plain,
! [SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ~ ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SV61
!= ( vvar @ SY214 ) ) )
| ~ ( ( SV32 != SY214 ) )
| ( SY213
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SY213
= ( vvar @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(207,plain,
! [SV17: $i,SV1: $i] :
( ( ( ( vvar @ SV1 )
!= ( vvar @ SV17 ) )
= $true )
| ( ( SV1 = SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(208,plain,
! [SV17: $i,SV1: $i] :
( ( ( SV1 != SV17 )
= $true )
| ( ( ( vvar @ SV1 )
= ( vvar @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(209,plain,
! [SV46: $i,SV34: $i,SV19: $i,SV3: $i] :
( ( ~ ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SV34 @ SV46 ) )
| ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(210,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) )
| ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(211,plain,
! [SV35: $i,SV20: $i,SV47: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != SV47 )
| ( SV20
!= ( vvar @ SV35 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV36: $i,SV22: $i,SV6: $i,SV48: $i] :
( ( ( SV48
= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SV22 ) @ ( vvar @ SV36 ) ) ) )
= $false )
| ( ( SV36 != SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(213,plain,
! [SV49: $i,SV56: $i,SV37: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SY215 ) )
| ( SV37
!= ( vapp @ SV56 @ SY216 ) ) )
| ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SY215 @ SV56 ) @ ( vsubst @ SV62 @ SY215 @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(214,plain,
! [SV24: $i,SV8: $i,SV38: $i] :
( ( ( visValue @ SV38 )
= $false )
| ( ( SV38
= ( vapp @ SV8 @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(215,plain,
! [SV63: $i,SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ~ ~ ( ( SV25 != SV57 )
| ( SV39
!= ( vabs @ SV50 @ SV9 @ SV63 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(216,plain,
! [SV58: $i,SV52: $i,SV41: $i,SV27: $i,SV11: $i] :
( ( ( vabs @ SV11 @ SV27 @ SV41 )
= ( vapp @ SV52 @ SV58 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV59: $i,SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12 != SV53 )
| ( SV28
!= ( vapp @ SV42 @ SV59 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(218,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ( ~ ~ ( visFreeVar @ SV29 @ SV13 )
| ~ ( valphaEquivalent @ SV13 @ SV43 ) )
= $true )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(219,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ! [SY217: $i] :
( ~ ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SY217 ) )
| ( SV60
!= ( vvar @ SV31 ) ) )
| ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(220,plain,
! [SV65: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ! [SY218: $i] :
( ~ ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SV61
!= ( vvar @ SY218 ) ) )
| ~ ( ( SV32 != SY218 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SY218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(221,plain,
! [SV17: $i,SV1: $i] :
( ( ( ( vvar @ SV1 )
= ( vvar @ SV17 ) )
= $false )
| ( ( SV1 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(222,plain,
! [SV17: $i,SV1: $i] :
( ( ( SV1 = SV17 )
= $false )
| ( ( ( vvar @ SV1 )
= ( vvar @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(223,plain,
! [SV46: $i,SV34: $i,SV19: $i,SV3: $i] :
( ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SV34 @ SV46 ) )
| ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(224,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ~ ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) )
| ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(225,plain,
! [SV35: $i,SV20: $i,SV47: $i,SV4: $i] :
( ( ( ( SV4 != SV47 )
| ( SV20
!= ( vvar @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(226,plain,
! [SV22: $i,SV6: $i,SV48: $i,SV36: $i] :
( ( ( SV36 = SV48 )
= $false )
| ( ( SV48
= ( vgensym @ ( vapp @ ( vapp @ SV6 @ SV22 ) @ ( vvar @ SV36 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(227,plain,
! [SV49: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ! [SY219: $i] :
( ~ ~ ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) )
| ( SV37
!= ( vapp @ SV56 @ SY219 ) ) )
| ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(228,plain,
! [SV63: $i,SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ( ~ ~ ( ( SV25 != SV57 )
| ( SV39
!= ( vabs @ SV50 @ SV9 @ SV63 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(229,plain,
! [SV59: $i,SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV53 )
| ( SV28
!= ( vapp @ SV42 @ SV59 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ( ~ ~ ( visFreeVar @ SV29 @ SV13 ) )
= $true )
| ( ( ~ ( valphaEquivalent @ SV13 @ SV43 ) )
= $true )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ~ ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SV67 ) )
| ( SV60
!= ( vvar @ SV31 ) ) )
| ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ~ ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SV61
!= ( vvar @ SV68 ) ) )
| ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV46: $i,SV34: $i,SV19: $i,SV3: $i] :
( ( ( ( vapp @ SV3 @ SV19 )
!= ( vapp @ SV34 @ SV46 ) )
= $true )
| ( ( ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(234,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
= $true )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(235,plain,
! [SV35: $i,SV20: $i,SV47: $i,SV4: $i] :
( ( ( SV4 != SV47 )
= $true )
| ( ( SV20
!= ( vvar @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(236,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) )
| ( SV37
!= ( vapp @ SV56 @ SV69 ) ) )
| ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(237,plain,
! [SV63: $i,SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ( ~ ( ( SV25 != SV57 )
| ( SV39
!= ( vabs @ SV50 @ SV9 @ SV63 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(238,plain,
! [SV59: $i,SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ( ( SV12 != SV53 )
| ( SV28
!= ( vapp @ SV42 @ SV59 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(239,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ( ~ ( visFreeVar @ SV29 @ SV13 ) )
= $false )
| ( ( ~ ( valphaEquivalent @ SV13 @ SV43 ) )
= $true )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(240,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SV67 ) )
| ( SV60
!= ( vvar @ SV31 ) ) ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(241,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SV61
!= ( vvar @ SV68 ) ) ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(242,plain,
! [SV46: $i,SV34: $i,SV19: $i,SV3: $i] :
( ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $false )
| ( ( ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(243,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV34 )
| ( SV19 != SV46 ) ) )
= $false )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV35: $i,SV20: $i,SV47: $i,SV4: $i] :
( ( ( SV4 = SV47 )
= $false )
| ( ( SV20
!= ( vvar @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) )
| ( SV37
!= ( vapp @ SV56 @ SV69 ) ) ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(246,plain,
! [SV63: $i,SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ( ( SV25 != SV57 )
| ( SV39
!= ( vabs @ SV50 @ SV9 @ SV63 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(247,plain,
! [SV59: $i,SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ( SV12 != SV53 )
= $true )
| ( ( SV28
!= ( vapp @ SV42 @ SV59 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(248,plain,
! [SV43: $i,SV13: $i,SV29: $i] :
( ( ( visFreeVar @ SV29 @ SV13 )
= $true )
| ( ( ~ ( valphaEquivalent @ SV13 @ SV43 ) )
= $true )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(249,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( ~ ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SV67 ) )
| ( SV60
!= ( vvar @ SV31 ) ) ) )
= $false )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(250,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SV61
!= ( vvar @ SV68 ) ) ) )
= $false )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(251,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( ( SV3 != SV34 )
| ( SV19 != SV46 ) )
= $false )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(252,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( ( SV3 != SV34 )
| ( SV19 != SV46 ) )
= $true )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(253,plain,
! [SV47: $i,SV4: $i,SV35: $i,SV20: $i] :
( ( ( SV20
= ( vvar @ SV35 ) )
= $false )
| ( ( SV4 = SV47 )
= $false )
| ( ( ~ ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(254,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) )
| ( SV37
!= ( vapp @ SV56 @ SV69 ) ) ) )
= $false )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(255,plain,
! [SV63: $i,SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ( SV25 != SV57 )
= $true )
| ( ( SV39
!= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(256,plain,
! [SV59: $i,SV42: $i,SV28: $i,SV53: $i,SV12: $i] :
( ( ( SV12 = SV53 )
= $false )
| ( ( SV28
!= ( vapp @ SV42 @ SV59 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(257,plain,
! [SV29: $i,SV43: $i,SV13: $i] :
( ( ( valphaEquivalent @ SV13 @ SV43 )
= $false )
| ( ( visFreeVar @ SV29 @ SV13 )
= $true )
| ( ( ~ ( visFreeVar @ SV29 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(258,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SV67 ) )
| ( SV60
!= ( vvar @ SV31 ) ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(259,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
| ( SV61
!= ( vvar @ SV68 ) ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(260,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( SV3 != SV34 )
= $false )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(261,plain,
! [SV34: $i,SV3: $i,SV46: $i,SV19: $i] :
( ( ( SV19 != SV46 )
= $false )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(262,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( SV3 != SV34 )
= $true )
| ( ( SV19 != SV46 )
= $true )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV20: $i,SV4: $i,SV47: $i,SV35: $i] :
( ( ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
| ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) )
= $false )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(264,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) )
| ( SV37
!= ( vapp @ SV56 @ SV69 ) ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(265,plain,
! [SV63: $i,SV9: $i,SV50: $i,SV39: $i,SV57: $i,SV25: $i] :
( ( ( SV25 = SV57 )
= $false )
| ( ( SV39
!= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(266,plain,
! [SV53: $i,SV12: $i,SV59: $i,SV42: $i,SV28: $i] :
( ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false )
| ( ( SV12 = SV53 )
= $false )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(267,plain,
! [SV13: $i,SV43: $i,SV29: $i] :
( ( ( visFreeVar @ SV29 @ SV43 )
= $false )
| ( ( visFreeVar @ SV29 @ SV13 )
= $true )
| ( ( valphaEquivalent @ SV13 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(268,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( ~ ~ ( ( SV44 != SV15 )
| ( SV54 != SV67 ) ) )
= $true )
| ( ( SV60
!= ( vvar @ SV31 ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(269,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( ~ ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) ) )
= $true )
| ( ( SV61
!= ( vvar @ SV68 ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(270,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( SV3 = SV34 )
= $true )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(271,plain,
! [SV34: $i,SV3: $i,SV46: $i,SV19: $i] :
( ( ( SV19 = SV46 )
= $true )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(272,plain,
! [SV46: $i,SV19: $i,SV34: $i,SV3: $i] :
( ( ( SV3 = SV34 )
= $false )
| ( ( SV19 != SV46 )
= $true )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(273,plain,
! [SV20: $i,SV4: $i,SV47: $i,SV35: $i] :
( ( ( ~ ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) ) )
= $false )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(274,plain,
! [SV47: $i,SV35: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) ) )
= $false )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(275,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( ~ ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) ) )
= $true )
| ( ( SV37
!= ( vapp @ SV56 @ SV69 ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV57: $i,SV25: $i,SV63: $i,SV9: $i,SV50: $i,SV39: $i] :
( ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( ~ ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV28: $i,SV12: $i,SV59: $i,SV42: $i,SV53: $i] :
( ( ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) )
= $false )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(278,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( ~ ( ( SV44 != SV15 )
| ( SV54 != SV67 ) ) )
= $false )
| ( ( SV60
!= ( vvar @ SV31 ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(279,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( ( SV45 != SV32 )
| ( SV55 != SV16 ) ) )
= $false )
| ( ( SV61
!= ( vvar @ SV68 ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(280,plain,
! [SV34: $i,SV3: $i,SV46: $i,SV19: $i] :
( ( ( SV19 = SV46 )
= $false )
| ( ( SV3 = SV34 )
= $false )
| ( ( ( vapp @ SV3 @ SV19 )
= ( vapp @ SV34 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(281,plain,
! [SV20: $i,SV4: $i,SV47: $i,SV35: $i] :
( ( ( ( SV35 != SV47 )
| ( visFreeVar @ SV4 @ SV20 ) )
= $true )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(282,plain,
! [SV47: $i,SV35: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( visFreeVar @ SV4 @ SV20 )
| ( SV35 = SV47 ) )
= $true )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(283,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( ~ ( ( SV7 != SV62 )
| ( SV23 != SV66 ) ) )
= $false )
| ( ( SV37
!= ( vapp @ SV56 @ SV69 ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(284,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
| ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(285,plain,
! [SV28: $i,SV12: $i,SV59: $i,SV42: $i,SV53: $i] :
( ( ( ~ ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) ) )
= $false )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(286,plain,
! [SV59: $i,SV42: $i,SV53: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) )
= $false )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(287,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( ( SV44 != SV15 )
| ( SV54 != SV67 ) )
= $true )
| ( ( SV60
!= ( vvar @ SV31 ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(288,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( ( SV45 != SV32 )
| ( SV55 != SV16 ) )
= $true )
| ( ( SV61
!= ( vvar @ SV68 ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(289,plain,
! [SV20: $i,SV4: $i,SV47: $i,SV35: $i] :
( ( ( SV35 != SV47 )
= $true )
| ( ( visFreeVar @ SV4 @ SV20 )
= $true )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(290,plain,
! [SV47: $i,SV35: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( visFreeVar @ SV4 @ SV20 ) )
= $true )
| ( ( SV35 = SV47 )
= $true )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(291,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( ( SV7 != SV62 )
| ( SV23 != SV66 ) )
= $true )
| ( ( SV37
!= ( vapp @ SV56 @ SV69 ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(292,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) ) )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(293,plain,
! [SV9: $i,SV63: $i,SV57: $i,SV50: $i,SV39: $i,SV25: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) ) )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(294,plain,
! [SV28: $i,SV12: $i,SV59: $i,SV42: $i,SV53: $i] :
( ( ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
| ( visFreeVar @ SV12 @ SV28 ) )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(295,plain,
! [SV59: $i,SV42: $i,SV53: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( visFreeVar @ SV12 @ SV28 )
| ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(296,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( SV44 != SV15 )
= $true )
| ( ( SV54 != SV67 )
= $true )
| ( ( SV60
!= ( vvar @ SV31 ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(297,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( SV45 != SV32 )
= $true )
| ( ( SV55 != SV16 )
= $true )
| ( ( SV61
!= ( vvar @ SV68 ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(298,plain,
! [SV20: $i,SV4: $i,SV47: $i,SV35: $i] :
( ( ( SV35 = SV47 )
= $false )
| ( ( visFreeVar @ SV4 @ SV20 )
= $true )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(299,plain,
! [SV47: $i,SV35: $i,SV20: $i,SV4: $i] :
( ( ( visFreeVar @ SV4 @ SV20 )
= $false )
| ( ( SV35 = SV47 )
= $true )
| ( ( SV4 = SV47 )
= $false )
| ( ( SV20
= ( vvar @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(300,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( SV7 != SV62 )
= $true )
| ( ( SV23 != SV66 )
= $true )
| ( ( SV37
!= ( vapp @ SV56 @ SV69 ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(301,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
| ( visFreeVar @ SV25 @ SV39 ) )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(302,plain,
! [SV9: $i,SV63: $i,SV57: $i,SV50: $i,SV39: $i,SV25: $i] :
( ( ( ~ ( visFreeVar @ SV25 @ SV39 )
| ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(303,plain,
! [SV28: $i,SV12: $i,SV59: $i,SV42: $i,SV53: $i] :
( ( ( ~ ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) ) )
= $true )
| ( ( visFreeVar @ SV12 @ SV28 )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(304,plain,
! [SV59: $i,SV42: $i,SV53: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( visFreeVar @ SV12 @ SV28 ) )
= $true )
| ( ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(305,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i] :
( ( ( SV44 = SV15 )
= $false )
| ( ( SV54 != SV67 )
= $true )
| ( ( SV60
!= ( vvar @ SV31 ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(306,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i] :
( ( ( SV45 = SV32 )
= $false )
| ( ( SV55 != SV16 )
= $true )
| ( ( SV61
!= ( vvar @ SV68 ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(307,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i] :
( ( ( SV7 = SV62 )
= $false )
| ( ( SV23 != SV66 )
= $true )
| ( ( SV37
!= ( vapp @ SV56 @ SV69 ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(308,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(309,plain,
! [SV9: $i,SV63: $i,SV57: $i,SV50: $i,SV39: $i,SV25: $i] :
( ( ( ~ ( visFreeVar @ SV25 @ SV39 ) )
= $true )
| ( ( ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(310,plain,
! [SV28: $i,SV12: $i,SV59: $i,SV42: $i,SV53: $i] :
( ( ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
= $false )
| ( ( visFreeVar @ SV12 @ SV28 )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(311,plain,
! [SV59: $i,SV42: $i,SV53: $i,SV28: $i,SV12: $i] :
( ( ( visFreeVar @ SV12 @ SV28 )
= $false )
| ( ( ( visFreeVar @ SV53 @ SV42 )
| ( visFreeVar @ SV53 @ SV59 ) )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(312,plain,
! [SV64: $i,SV31: $i,SV60: $i,SV15: $i,SV44: $i,SV67: $i,SV54: $i] :
( ( ( SV54 = SV67 )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV60
!= ( vvar @ SV31 ) )
= $true )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(313,plain,
! [SV65: $i,SV68: $i,SV61: $i,SV32: $i,SV45: $i,SV16: $i,SV55: $i] :
( ( ( SV55 = SV16 )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV61
!= ( vvar @ SV68 ) )
= $true )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(314,plain,
! [SV49: $i,SV69: $i,SV56: $i,SV37: $i,SV62: $i,SV7: $i,SV66: $i,SV23: $i] :
( ( ( SV23 = SV66 )
= $false )
| ( ( SV7 = SV62 )
= $false )
| ( ( SV37
!= ( vapp @ SV56 @ SV69 ) )
= $true )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(315,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) )
= $false )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(316,plain,
! [SV9: $i,SV63: $i,SV57: $i,SV50: $i,SV39: $i,SV25: $i] :
( ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( ~ ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) ) )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(317,plain,
! [SV59: $i,SV28: $i,SV12: $i,SV42: $i,SV53: $i] :
( ( ( visFreeVar @ SV53 @ SV42 )
= $false )
| ( ( visFreeVar @ SV12 @ SV28 )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(318,plain,
! [SV42: $i,SV28: $i,SV12: $i,SV59: $i,SV53: $i] :
( ( ( visFreeVar @ SV53 @ SV59 )
= $false )
| ( ( visFreeVar @ SV12 @ SV28 )
= $true )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(319,plain,
! [SV28: $i,SV12: $i,SV59: $i,SV42: $i,SV53: $i] :
( ( ( visFreeVar @ SV53 @ SV42 )
= $true )
| ( ( visFreeVar @ SV53 @ SV59 )
= $true )
| ( ( visFreeVar @ SV12 @ SV28 )
= $false )
| ( ( SV12 = SV53 )
= $false )
| ( ( SV28
= ( vapp @ SV42 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(320,plain,
! [SV64: $i,SV67: $i,SV54: $i,SV15: $i,SV44: $i,SV31: $i,SV60: $i] :
( ( ( SV60
= ( vvar @ SV31 ) )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV54 = SV67 )
= $false )
| ( ( ( SV15 != SV31 )
| ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(321,plain,
! [SV65: $i,SV16: $i,SV55: $i,SV32: $i,SV45: $i,SV68: $i,SV61: $i] :
( ( ( SV61
= ( vvar @ SV68 ) )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV55 = SV16 )
= $false )
| ( ( ~ ( ( SV32 != SV68 ) )
| ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(322,plain,
! [SV49: $i,SV66: $i,SV23: $i,SV62: $i,SV7: $i,SV69: $i,SV56: $i,SV37: $i] :
( ( ( SV37
= ( vapp @ SV56 @ SV69 ) )
= $false )
| ( ( SV7 = SV62 )
= $false )
| ( ( SV23 = SV66 )
= $false )
| ( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
| ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(323,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(324,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( SV50 != SV57 ) )
| ~ ( visFreeVar @ SV57 @ SV63 ) )
= $false )
| ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(325,plain,
! [SV67: $i,SV60: $i,SV54: $i,SV44: $i,SV64: $i,SV31: $i,SV15: $i] :
( ( ( SV15 != SV31 )
= $true )
| ( ( ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true )
| ( ( SV54 = SV67 )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV60
= ( vvar @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(326,plain,
! [SV16: $i,SV61: $i,SV55: $i,SV45: $i,SV65: $i,SV68: $i,SV32: $i] :
( ( ( ~ ( ( SV32 != SV68 ) ) )
= $true )
| ( ( ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true )
| ( ( SV55 = SV16 )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV61
= ( vvar @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(327,plain,
! [SV69: $i,SV56: $i,SV66: $i,SV62: $i,SV37: $i,SV23: $i,SV7: $i,SV49: $i] :
( ( ( SV49
!= ( vsubst @ SV7 @ SV23 @ SV37 ) )
= $true )
| ( ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) )
= $true )
| ( ( SV23 = SV66 )
= $false )
| ( ( SV7 = SV62 )
= $false )
| ( ( SV37
= ( vapp @ SV56 @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(328,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( SV50 != SV57 ) ) )
= $true )
| ( ( ~ ( visFreeVar @ SV57 @ SV63 ) )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(329,plain,
! [SV63: $i,SV9: $i,SV39: $i,SV25: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( SV50 != SV57 ) ) )
= $false )
| ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(330,plain,
! [SV9: $i,SV50: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i] :
( ( ( ~ ( visFreeVar @ SV57 @ SV63 ) )
= $false )
| ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(331,plain,
! [SV67: $i,SV60: $i,SV54: $i,SV44: $i,SV64: $i,SV31: $i,SV15: $i] :
( ( ( SV15 = SV31 )
= $false )
| ( ( ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
| ( SV64 = SV67 ) )
= $true )
| ( ( SV54 = SV67 )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV60
= ( vvar @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(332,plain,
! [SV16: $i,SV61: $i,SV55: $i,SV45: $i,SV65: $i,SV68: $i,SV32: $i] :
( ( ( SV32 != SV68 )
= $false )
| ( ( ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true )
| ( ( SV55 = SV16 )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV61
= ( vvar @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(333,plain,
! [SV69: $i,SV56: $i,SV66: $i,SV62: $i,SV37: $i,SV23: $i,SV7: $i,SV49: $i] :
( ( ( SV49
= ( vsubst @ SV7 @ SV23 @ SV37 ) )
= $false )
| ( ( SV49
= ( vapp @ ( vsubst @ SV62 @ SV66 @ SV56 ) @ ( vsubst @ SV62 @ SV66 @ SV69 ) ) )
= $true )
| ( ( SV23 = SV66 )
= $false )
| ( ( SV7 = SV62 )
= $false )
| ( ( SV37
= ( vapp @ SV56 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(334,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( SV50 != SV57 )
= $false )
| ( ( ~ ( visFreeVar @ SV57 @ SV63 ) )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(335,plain,
! [SV63: $i,SV9: $i,SV39: $i,SV25: $i,SV57: $i,SV50: $i] :
( ( ( SV50 != SV57 )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(336,plain,
! [SV9: $i,SV50: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i] :
( ( ( visFreeVar @ SV57 @ SV63 )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(337,plain,
! [SV31: $i,SV15: $i,SV67: $i,SV60: $i,SV54: $i,SV44: $i,SV64: $i] :
( ( ( SV64
!= ( vsubst @ SV44 @ SV54 @ SV60 ) )
= $true )
| ( ( SV64 = SV67 )
= $true )
| ( ( SV15 = SV31 )
= $false )
| ( ( SV54 = SV67 )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV60
= ( vvar @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(338,plain,
! [SV16: $i,SV61: $i,SV55: $i,SV45: $i,SV65: $i,SV68: $i,SV32: $i] :
( ( ( SV32 = SV68 )
= $true )
| ( ( ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
| ( SV65
= ( vvar @ SV68 ) ) )
= $true )
| ( ( SV55 = SV16 )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV61
= ( vvar @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(339,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV63: $i,SV57: $i,SV50: $i] :
( ( ( SV50 = SV57 )
= $true )
| ( ( ~ ( visFreeVar @ SV57 @ SV63 ) )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(340,plain,
! [SV63: $i,SV9: $i,SV39: $i,SV25: $i,SV57: $i,SV50: $i] :
( ( ( SV50 = SV57 )
= $false )
| ( ( visFreeVar @ SV25 @ SV39 )
= $false )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(341,plain,
! [SV31: $i,SV15: $i,SV67: $i,SV60: $i,SV54: $i,SV44: $i,SV64: $i] :
( ( ( SV64
= ( vsubst @ SV44 @ SV54 @ SV60 ) )
= $false )
| ( ( SV64 = SV67 )
= $true )
| ( ( SV15 = SV31 )
= $false )
| ( ( SV54 = SV67 )
= $false )
| ( ( SV44 = SV15 )
= $false )
| ( ( SV60
= ( vvar @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(342,plain,
! [SV16: $i,SV32: $i,SV68: $i,SV61: $i,SV55: $i,SV45: $i,SV65: $i] :
( ( ( SV65
!= ( vsubst @ SV45 @ SV55 @ SV61 ) )
= $true )
| ( ( SV65
= ( vvar @ SV68 ) )
= $true )
| ( ( SV32 = SV68 )
= $true )
| ( ( SV55 = SV16 )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV61
= ( vvar @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(343,plain,
! [SV9: $i,SV39: $i,SV25: $i,SV50: $i,SV63: $i,SV57: $i] :
( ( ( visFreeVar @ SV57 @ SV63 )
= $false )
| ( ( SV50 = SV57 )
= $true )
| ( ( visFreeVar @ SV25 @ SV39 )
= $true )
| ( ( SV25 = SV57 )
= $false )
| ( ( SV39
= ( vabs @ SV50 @ SV9 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(344,plain,
! [SV16: $i,SV32: $i,SV68: $i,SV61: $i,SV55: $i,SV45: $i,SV65: $i] :
( ( ( SV65
= ( vsubst @ SV45 @ SV55 @ SV61 ) )
= $false )
| ( ( SV65
= ( vvar @ SV68 ) )
= $true )
| ( ( SV32 = SV68 )
= $true )
| ( ( SV55 = SV16 )
= $false )
| ( ( SV45 = SV32 )
= $false )
| ( ( SV61
= ( vvar @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(345,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[108,344,343,341,340,336,333,319,318,317,299,298,280,271,270,267,226,222,221,216,214,204,200,195,176,109]) ).
thf(346,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM129+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n018.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 18:40:07 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.90/0.51
% 1.90/0.51 No.of.Axioms: 16
% 1.90/0.51
% 1.90/0.51 Length.of.Defs: 0
% 1.90/0.51
% 1.90/0.51 Contains.Choice.Funs: false
% 1.90/0.51 .............
% 1.90/0.51
% 1.90/0.51 ********************************
% 1.90/0.51 * All subproblems solved! *
% 1.90/0.51 ********************************
% 1.90/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,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:345,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.90/0.51
% 1.90/0.51 %**** Beginning of derivation protocol ****
% 1.90/0.51 % SZS output start CNFRefutation
% See solution above
% 1.90/0.52
% 1.90/0.52 %**** End of derivation protocol ****
% 1.90/0.52 %**** no. of clauses in derivation: 297 ****
% 1.90/0.52 %**** clause counter: 345 ****
% 1.90/0.52
% 1.90/0.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,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:345,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------