%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM128+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 : n009.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 0.72s 0.34s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 238 ( 127 unt; 0 typ; 0 def)
% Number of atoms : 1851 (1221 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 2939 ( 824 ~; 631 |; 42 &;1372 @)
% ( 0 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 1104 ( 0 ^;1104 !; 0 ?;1104 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Ve,type,
sK1_Ve: $i ).
thf(tp_sK2_SY60,type,
sK2_SY60: $i ).
thf(tp_sK3_SY63,type,
sK3_SY63: $i ).
thf(tp_sK4_SY65,type,
sK4_SY65: $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(34,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(35,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(36,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(37,axiom,
! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
thf(53,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,
! [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(56,axiom,
! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
thf(57,axiom,
! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
thf(59,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(60,axiom,
! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
thf(61,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(62,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(64,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(65,conjecture,
! [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(66,negated_conjecture,
( ( ! [Ve: $i,Ve1: $i,Vx: $i,Vfresh: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ( Vx != Vfresh ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[65]) ).
thf(67,plain,
( ( ! [Ve: $i,Ve1: $i,Vx: $i,Vfresh: $i] :
( ( Vfresh
= ( vgensym @ ( vapp @ ( vapp @ Ve @ Ve1 ) @ ( vvar @ Vx ) ) ) )
=> ( Vx != Vfresh ) ) )
= $false ),
inference(unfold_def,[status(thm)],[66]) ).
thf(68,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)],[34]) ).
thf(69,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)],[35]) ).
thf(70,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)],[36]) ).
thf(71,plain,
( ( ! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(72,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)],[53]) ).
thf(73,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)],[55]) ).
thf(74,plain,
( ( ! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(75,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(76,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(77,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(78,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(79,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)],[62]) ).
thf(80,plain,
( ( ! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(81,plain,
( ( ! [SY60: $i,SY61: $i,SY62: $i] :
( ( SY62
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ SY60 ) @ ( vvar @ SY61 ) ) ) )
=> ( SY61 != SY62 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(82,plain,
( ( ! [SY63: $i,SY64: $i] :
( ( SY64
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK2_SY60 ) @ ( vvar @ SY63 ) ) ) )
=> ( SY63 != SY64 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(83,plain,
( ( ! [SY65: $i] :
( ( SY65
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK2_SY60 ) @ ( vvar @ sK3_SY63 ) ) ) )
=> ( sK3_SY63 != SY65 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(84,plain,
( ( ( sK4_SY65
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK2_SY60 ) @ ( vvar @ sK3_SY63 ) ) ) )
=> ( sK3_SY63 != sK4_SY65 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(85,plain,
( ( sK4_SY65
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK2_SY60 ) @ ( vvar @ sK3_SY63 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(86,plain,
( ( sK3_SY63 != sK4_SY65 )
= $false ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(87,plain,
( ( ~ ( ( sK3_SY63 != sK4_SY65 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [VVar0: $i,VVar1: $i] :
( ( ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) )
=> ( VVar0 = VVar1 ) )
& ( ( VVar0 = VVar1 )
=> ( ( vvar @ VVar0 )
= ( vvar @ VVar1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(89,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)],[79]) ).
thf(90,plain,
( ( ! [VVar0: $i,VVar1: $i,VTyp0: $i,VExp0: $i] :
( ( vvar @ VVar0 )
!= ( vabs @ VVar1 @ VTyp0 @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(91,plain,
( ( ! [VVar0: $i,VExp0: $i,VExp1: $i] :
( ( vvar @ VVar0 )
!= ( vapp @ VExp0 @ VExp1 ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(92,plain,
( ( ! [VVar0: $i,VTyp0: $i,VExp0: $i,VExp1: $i,VExp2: $i] :
( ( vabs @ VVar0 @ VTyp0 @ VExp0 )
!= ( vapp @ VExp1 @ VExp2 ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(93,plain,
( ( ! [Vx: $i,VExp0: $i] :
( ( VExp0
= ( vvar @ Vx ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(94,plain,
( ( ! [Ve1: $i,Ve2: $i,VExp0: $i] :
( ( VExp0
= ( vapp @ Ve1 @ Ve2 ) )
=> ~ ( visValue @ VExp0 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(95,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)],[73]) ).
thf(96,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)],[72]) ).
thf(97,plain,
( ( ! [Vv: $i,Ve: $i] :
( ( ( vgensym @ Ve )
= Vv )
=> ~ ( visFreeVar @ Vv @ Ve ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(98,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)],[70]) ).
thf(99,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)],[69]) ).
thf(100,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)],[68]) ).
thf(101,plain,
( ( sK4_SY65
= ( vgensym @ ( vapp @ ( vapp @ sK1_Ve @ sK2_SY60 ) @ ( vvar @ sK3_SY63 ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(102,plain,
( ( ~ ( ( sK3_SY63 != sK4_SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( vvar @ SX0 )
!= ( vvar @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( vvar @ SX0 )
= ( vvar @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( vabs @ SX0 @ SX1 @ SX2 )
!= ( vapp @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(105,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)],[95]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( vvar @ SX0 ) )
| ~ ( visValue @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(107,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)],[99]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( vgensym @ SX1 )
!= SX0 )
| ~ ( visFreeVar @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( vvar @ SX0 )
!= ( vapp @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( vvar @ SX0 )
!= ( vabs @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(111,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)],[98]) ).
thf(112,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)],[100]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX2
!= ( vapp @ SX0 @ SX1 ) )
| ~ ( visValue @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(114,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)],[96]) ).
thf(115,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)],[89]) ).
thf(116,plain,
( ( ~ ( ( sK3_SY63 != sK4_SY65 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(117,plain,
! [SV1: $i] :
( ( ! [SY66: $i] :
~ ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SY66 ) )
| ( SV1 = SY66 ) )
| ~ ( ( SV1 != SY66 )
| ( ( vvar @ SV1 )
= ( vvar @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV2: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i,SY70: $i] :
( ( vabs @ SV2 @ SY67 @ SY68 )
!= ( vapp @ SY69 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV3: $i] :
( ( ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ~ ( ( SV3 != SY73 )
| ( SY71
!= ( vvar @ SY72 ) ) )
| ~ ( ~ ( ( SY72 != SY73 )
| ( visFreeVar @ SV3 @ SY71 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SY71 )
| ( SY72 = SY73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV4: $i] :
( ( ! [SY74: $i] :
( ( SY74
!= ( vvar @ SV4 ) )
| ~ ( visValue @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV5: $i] :
( ( ! [SY75: $i,SY76: $i,SY77: $i,SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ( SY76 != SY75 )
| ( SY77 != SV5 ) )
| ( SY78
!= ( vvar @ SY80 ) ) )
| ~ ( ( SY75 != SY80 ) )
| ( SY79
!= ( vsubst @ SY76 @ SY77 @ SY78 ) )
| ( SY79
= ( vvar @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV6: $i] :
( ( ! [SY81: $i] :
( ( ( vgensym @ SY81 )
!= SV6 )
| ~ ( visFreeVar @ SV6 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV7: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ( vvar @ SV7 )
!= ( vapp @ SY82 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV8: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i] :
( ( vvar @ SV8 )
!= ( vabs @ SY84 @ SY85 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV9: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i,SY91: $i,SY92: $i] :
( ~ ~ ( ~ ~ ( ( SY88 != SV9 )
| ( SY89 != SY92 ) )
| ( SY90
!= ( vvar @ SY87 ) ) )
| ( SV9 != SY87 )
| ( SY91
!= ( vsubst @ SY88 @ SY89 @ SY90 ) )
| ( SY91 = SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV10: $i] :
( ( ! [SY93: $i,SY94: $i,SY95: $i,SY96: $i,SY97: $i,SY98: $i,SY99: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SY97 )
| ( SY93 != SY98 ) )
| ( SY94
!= ( vapp @ SY96 @ SY99 ) ) )
| ( SY95
!= ( vsubst @ SV10 @ SY93 @ SY94 ) )
| ( SY95
= ( vapp @ ( vsubst @ SY97 @ SY98 @ SY96 ) @ ( vsubst @ SY97 @ SY98 @ SY99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV11: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ( SY101
!= ( vapp @ SV11 @ SY100 ) )
| ~ ( visValue @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV12: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i,SY105: $i] :
( ~ ~ ( ( SV12 != SY104 )
| ( SY102
!= ( vapp @ SY103 @ SY105 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY104 @ SY103 )
| ( visFreeVar @ SY104 @ SY105 ) )
| ( visFreeVar @ SV12 @ SY102 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SY102 )
| ( visFreeVar @ SY104 @ SY103 )
| ( visFreeVar @ SY104 @ SY105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV13: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i] :
~ ( ~ ( ( ( vapp @ SV13 @ SY106 )
!= ( vapp @ SY107 @ SY108 ) )
| ~ ( ( SV13 != SY107 )
| ( SY106 != SY108 ) ) )
| ~ ( ~ ~ ( ( SV13 != SY107 )
| ( SY106 != SY108 ) )
| ( ( vapp @ SV13 @ SY106 )
= ( vapp @ SY107 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
( ( sK3_SY63 != sK4_SY65 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV14: $i,SV1: $i] :
( ( ~ ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SV14 ) )
| ( SV1 = SV14 ) )
| ~ ( ( SV1 != SV14 )
| ( ( vvar @ SV1 )
= ( vvar @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV15: $i,SV2: $i] :
( ( ! [SY109: $i,SY110: $i,SY111: $i] :
( ( vabs @ SV2 @ SV15 @ SY109 )
!= ( vapp @ SY110 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV16: $i,SV3: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ~ ( ( SV3 != SY113 )
| ( SV16
!= ( vvar @ SY112 ) ) )
| ~ ( ~ ( ( SY112 != SY113 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SY112 = SY113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV4: $i,SV17: $i] :
( ( ( SV17
!= ( vvar @ SV4 ) )
| ~ ( visValue @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV5: $i,SV18: $i] :
( ( ! [SY114: $i,SY115: $i,SY116: $i,SY117: $i,SY118: $i] :
( ~ ~ ( ~ ~ ( ( SY114 != SV18 )
| ( SY115 != SV5 ) )
| ( SY116
!= ( vvar @ SY118 ) ) )
| ~ ( ( SV18 != SY118 ) )
| ( SY117
!= ( vsubst @ SY114 @ SY115 @ SY116 ) )
| ( SY117
= ( vvar @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV6: $i,SV19: $i] :
( ( ( ( vgensym @ SV19 )
!= SV6 )
| ~ ( visFreeVar @ SV6 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY119: $i] :
( ( vvar @ SV7 )
!= ( vapp @ SV20 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ( vvar @ SV8 )
!= ( vabs @ SV21 @ SY120 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV22: $i,SV9: $i] :
( ( ! [SY122: $i,SY123: $i,SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ( SY122 != SV9 )
| ( SY123 != SY126 ) )
| ( SY124
!= ( vvar @ SV22 ) ) )
| ( SV9 != SV22 )
| ( SY125
!= ( vsubst @ SY122 @ SY123 @ SY124 ) )
| ( SY125 = SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV23: $i,SV10: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i,SY130: $i,SY131: $i,SY132: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SY130 )
| ( SV23 != SY131 ) )
| ( SY127
!= ( vapp @ SY129 @ SY132 ) ) )
| ( SY128
!= ( vsubst @ SV10 @ SV23 @ SY127 ) )
| ( SY128
= ( vapp @ ( vsubst @ SY130 @ SY131 @ SY129 ) @ ( vsubst @ SY130 @ SY131 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY133: $i] :
( ( SY133
!= ( vapp @ SV11 @ SV24 ) )
| ~ ( visValue @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY134: $i,SY135: $i,SY136: $i] :
( ~ ~ ( ( SV12 != SY135 )
| ( SV25
!= ( vapp @ SY134 @ SY136 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY135 @ SY134 )
| ( visFreeVar @ SY135 @ SY136 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SY135 @ SY134 )
| ( visFreeVar @ SY135 @ SY136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY137: $i,SY138: $i] :
~ ( ~ ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SY137 @ SY138 ) )
| ~ ( ( SV13 != SY137 )
| ( SV26 != SY138 ) ) )
| ~ ( ~ ~ ( ( SV13 != SY137 )
| ( SV26 != SY138 ) )
| ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SY137 @ SY138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(144,plain,
( ( sK3_SY63 = sK4_SY65 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(145,plain,
! [SV14: $i,SV1: $i] :
( ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SV14 ) )
| ( SV1 = SV14 ) )
| ~ ( ( SV1 != SV14 )
| ( ( vvar @ SV1 )
= ( vvar @ SV14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV27: $i,SV15: $i,SV2: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ( vabs @ SV2 @ SV15 @ SV27 )
!= ( vapp @ SY139 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV28: $i,SV16: $i,SV3: $i] :
( ( ! [SY141: $i] :
( ~ ~ ( ( SV3 != SY141 )
| ( SV16
!= ( vvar @ SV28 ) ) )
| ~ ( ~ ( ( SV28 != SY141 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SY141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV4: $i,SV17: $i] :
( ( ( SV17
!= ( vvar @ SV4 ) )
= $true )
| ( ( ~ ( visValue @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV5: $i,SV18: $i,SV29: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i,SY145: $i] :
( ~ ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SY142 != SV5 ) )
| ( SY143
!= ( vvar @ SY145 ) ) )
| ~ ( ( SV18 != SY145 ) )
| ( SY144
!= ( vsubst @ SV29 @ SY142 @ SY143 ) )
| ( SY144
= ( vvar @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV6: $i,SV19: $i] :
( ( ( ( vgensym @ SV19 )
!= SV6 )
= $true )
| ( ( ~ ( visFreeVar @ SV6 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV30: $i,SV20: $i,SV7: $i] :
( ( ( vvar @ SV7 )
!= ( vapp @ SV20 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV31: $i,SV21: $i,SV8: $i] :
( ( ! [SY146: $i] :
( ( vvar @ SV8 )
!= ( vabs @ SV21 @ SV31 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV22: $i,SV9: $i,SV32: $i] :
( ( ! [SY147: $i,SY148: $i,SY149: $i,SY150: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SY147 != SY150 ) )
| ( SY148
!= ( vvar @ SV22 ) ) )
| ( SV9 != SV22 )
| ( SY149
!= ( vsubst @ SV32 @ SY147 @ SY148 ) )
| ( SY149 = SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV33: $i,SV23: $i,SV10: $i] :
( ( ! [SY151: $i,SY152: $i,SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SY153 )
| ( SV23 != SY154 ) )
| ( SV33
!= ( vapp @ SY152 @ SY155 ) ) )
| ( SY151
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SY151
= ( vapp @ ( vsubst @ SY153 @ SY154 @ SY152 ) @ ( vsubst @ SY153 @ SY154 @ SY155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV24: $i,SV11: $i,SV34: $i] :
( ( ( SV34
!= ( vapp @ SV11 @ SV24 ) )
| ~ ( visValue @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV35: $i,SV25: $i,SV12: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ~ ~ ( ( SV12 != SY156 )
| ( SV25
!= ( vapp @ SV35 @ SY157 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SY156 @ SV35 )
| ( visFreeVar @ SY156 @ SY157 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SY156 @ SV35 )
| ( visFreeVar @ SY156 @ SY157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV36: $i,SV26: $i,SV13: $i] :
( ( ! [SY158: $i] :
~ ( ~ ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SV36 @ SY158 ) )
| ~ ( ( SV13 != SV36 )
| ( SV26 != SY158 ) ) )
| ~ ( ~ ~ ( ( SV13 != SV36 )
| ( SV26 != SY158 ) )
| ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SY158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV14: $i,SV1: $i] :
( ( ~ ( ( ( vvar @ SV1 )
!= ( vvar @ SV14 ) )
| ( SV1 = SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(159,plain,
! [SV14: $i,SV1: $i] :
( ( ~ ( ( SV1 != SV14 )
| ( ( vvar @ SV1 )
= ( vvar @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(160,plain,
! [SV37: $i,SV27: $i,SV15: $i,SV2: $i] :
( ( ! [SY159: $i] :
( ( vabs @ SV2 @ SV15 @ SV27 )
!= ( vapp @ SV37 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV28: $i,SV16: $i,SV38: $i,SV3: $i] :
( ( ~ ~ ( ( SV3 != SV38 )
| ( SV16
!= ( vvar @ SV28 ) ) )
| ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(162,plain,
! [SV4: $i,SV17: $i] :
( ( ( SV17
= ( vvar @ SV4 ) )
= $false )
| ( ( ~ ( visValue @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ! [SY160: $i,SY161: $i,SY162: $i] :
( ~ ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SY160
!= ( vvar @ SY162 ) ) )
| ~ ( ( SV18 != SY162 ) )
| ( SY161
!= ( vsubst @ SV29 @ SV39 @ SY160 ) )
| ( SY161
= ( vvar @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV6: $i,SV19: $i] :
( ( ( ( vgensym @ SV19 )
= SV6 )
= $false )
| ( ( ~ ( visFreeVar @ SV6 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV30: $i,SV20: $i,SV7: $i] :
( ( ( vvar @ SV7 )
= ( vapp @ SV20 @ SV30 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(166,plain,
! [SV40: $i,SV31: $i,SV21: $i,SV8: $i] :
( ( ( vvar @ SV8 )
!= ( vabs @ SV21 @ SV31 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV22: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ! [SY163: $i,SY164: $i,SY165: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SY165 ) )
| ( SY163
!= ( vvar @ SV22 ) ) )
| ( SV9 != SV22 )
| ( SY164
!= ( vsubst @ SV32 @ SV41 @ SY163 ) )
| ( SY164 = SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(168,plain,
! [SV42: $i,SV33: $i,SV23: $i,SV10: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i,SY169: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SY167 )
| ( SV23 != SY168 ) )
| ( SV33
!= ( vapp @ SY166 @ SY169 ) ) )
| ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SY167 @ SY168 @ SY166 ) @ ( vsubst @ SY167 @ SY168 @ SY169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV24: $i,SV11: $i,SV34: $i] :
( ( ( SV34
!= ( vapp @ SV11 @ SV24 ) )
= $true )
| ( ( ~ ( visValue @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ! [SY170: $i] :
( ~ ~ ( ( SV12 != SV43 )
| ( SV25
!= ( vapp @ SV35 @ SY170 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SY170 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SY170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(171,plain,
! [SV44: $i,SV36: $i,SV26: $i,SV13: $i] :
( ( ~ ( ~ ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SV36 @ SV44 ) )
| ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
| ~ ( ~ ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) )
| ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(172,plain,
! [SV14: $i,SV1: $i] :
( ( ( ( vvar @ SV1 )
!= ( vvar @ SV14 ) )
| ( SV1 = SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(173,plain,
! [SV14: $i,SV1: $i] :
( ( ( SV1 != SV14 )
| ( ( vvar @ SV1 )
= ( vvar @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(174,plain,
! [SV45: $i,SV37: $i,SV27: $i,SV15: $i,SV2: $i] :
( ( ( vabs @ SV2 @ SV15 @ SV27 )
!= ( vapp @ SV37 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(175,plain,
! [SV28: $i,SV16: $i,SV38: $i,SV3: $i] :
( ( ( ~ ~ ( ( SV3 != SV38 )
| ( SV16
!= ( vvar @ SV28 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(176,plain,
! [SV4: $i,SV17: $i] :
( ( ( visValue @ SV17 )
= $false )
| ( ( SV17
= ( vvar @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(177,plain,
! [SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SV46
!= ( vvar @ SY172 ) ) )
| ~ ( ( SV18 != SY172 ) )
| ( SY171
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SY171
= ( vvar @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(178,plain,
! [SV19: $i,SV6: $i] :
( ( ( visFreeVar @ SV6 @ SV19 )
= $false )
| ( ( ( vgensym @ SV19 )
= SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(179,plain,
! [SV40: $i,SV31: $i,SV21: $i,SV8: $i] :
( ( ( vvar @ SV8 )
= ( vabs @ SV21 @ SV31 @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV22: $i,SV47: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SY174 ) )
| ( SV47
!= ( vvar @ SV22 ) ) )
| ( SV9 != SV22 )
| ( SY173
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SY173 = SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV42: $i,SV48: $i,SV33: $i,SV23: $i,SV10: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SY175 )
| ( SV23 != SY176 ) )
| ( SV33
!= ( vapp @ SV48 @ SY177 ) ) )
| ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SY175 @ SY176 @ SV48 ) @ ( vsubst @ SY175 @ SY176 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV24: $i,SV11: $i,SV34: $i] :
( ( ( SV34
= ( vapp @ SV11 @ SV24 ) )
= $false )
| ( ( ~ ( visValue @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV49: $i,SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ~ ~ ( ( SV12 != SV43 )
| ( SV25
!= ( vapp @ SV35 @ SV49 ) ) )
| ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(184,plain,
! [SV44: $i,SV36: $i,SV26: $i,SV13: $i] :
( ( ~ ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SV36 @ SV44 ) )
| ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
| ~ ( ~ ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) )
| ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV14: $i,SV1: $i] :
( ( ( ( vvar @ SV1 )
!= ( vvar @ SV14 ) )
= $true )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV14: $i,SV1: $i] :
( ( ( SV1 != SV14 )
= $true )
| ( ( ( vvar @ SV1 )
= ( vvar @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(187,plain,
! [SV45: $i,SV37: $i,SV27: $i,SV15: $i,SV2: $i] :
( ( ( vabs @ SV2 @ SV15 @ SV27 )
= ( vapp @ SV37 @ SV45 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV28: $i,SV16: $i,SV38: $i,SV3: $i] :
( ( ( ~ ( ( SV3 != SV38 )
| ( SV16
!= ( vvar @ SV28 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV50: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ! [SY178: $i] :
( ~ ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SV46
!= ( vvar @ SY178 ) ) )
| ~ ( ( SV18 != SY178 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ! [SY179: $i] :
( ~ ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SY179 ) )
| ( SV47
!= ( vvar @ SV22 ) ) )
| ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(191,plain,
! [SV42: $i,SV48: $i,SV33: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ! [SY180: $i,SY181: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SY180 ) )
| ( SV33
!= ( vapp @ SV48 @ SY181 ) ) )
| ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SY180 @ SV48 ) @ ( vsubst @ SV52 @ SY180 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV24: $i,SV11: $i,SV34: $i] :
( ( ( visValue @ SV34 )
= $false )
| ( ( SV34
= ( vapp @ SV11 @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(193,plain,
! [SV49: $i,SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12 != SV43 )
| ( SV25
!= ( vapp @ SV35 @ SV49 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV44: $i,SV36: $i,SV26: $i,SV13: $i] :
( ( ~ ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SV36 @ SV44 ) )
| ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(195,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) )
| ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(196,plain,
! [SV14: $i,SV1: $i] :
( ( ( ( vvar @ SV1 )
= ( vvar @ SV14 ) )
= $false )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV14: $i,SV1: $i] :
( ( ( SV1 = SV14 )
= $false )
| ( ( ( vvar @ SV1 )
= ( vvar @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV28: $i,SV16: $i,SV38: $i,SV3: $i] :
( ( ( ( SV3 != SV38 )
| ( SV16
!= ( vvar @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(199,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ~ ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SV46
!= ( vvar @ SV53 ) ) )
| ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(200,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ~ ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SV54 ) )
| ( SV47
!= ( vvar @ SV22 ) ) )
| ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(201,plain,
! [SV42: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ! [SY182: $i] :
( ~ ~ ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) )
| ( SV33
!= ( vapp @ SV48 @ SY182 ) ) )
| ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SY182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(202,plain,
! [SV49: $i,SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV43 )
| ( SV25
!= ( vapp @ SV35 @ SV49 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV44: $i,SV36: $i,SV26: $i,SV13: $i] :
( ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SV36 @ SV44 ) )
| ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(204,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ~ ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) )
| ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(205,plain,
! [SV28: $i,SV16: $i,SV38: $i,SV3: $i] :
( ( ( SV3 != SV38 )
= $true )
| ( ( SV16
!= ( vvar @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(206,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SV46
!= ( vvar @ SV53 ) ) ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(207,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SV54 ) )
| ( SV47
!= ( vvar @ SV22 ) ) ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(208,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) )
| ( SV33
!= ( vapp @ SV48 @ SV56 ) ) )
| ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(209,plain,
! [SV49: $i,SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ( ( SV12 != SV43 )
| ( SV25
!= ( vapp @ SV35 @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(210,plain,
! [SV44: $i,SV36: $i,SV26: $i,SV13: $i] :
( ( ( ( vapp @ SV13 @ SV26 )
!= ( vapp @ SV36 @ SV44 ) )
= $true )
| ( ( ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(211,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
= $true )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(212,plain,
! [SV28: $i,SV16: $i,SV38: $i,SV3: $i] :
( ( ( SV3 = SV38 )
= $false )
| ( ( SV16
!= ( vvar @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(213,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SV46
!= ( vvar @ SV53 ) ) ) )
= $false )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(214,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( ~ ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SV54 ) )
| ( SV47
!= ( vvar @ SV22 ) ) ) )
= $false )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(215,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) )
| ( SV33
!= ( vapp @ SV48 @ SV56 ) ) ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(216,plain,
! [SV49: $i,SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ( SV12 != SV43 )
= $true )
| ( ( SV25
!= ( vapp @ SV35 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(217,plain,
! [SV44: $i,SV36: $i,SV26: $i,SV13: $i] :
( ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $false )
| ( ( ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(218,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( ~ ( ( SV13 != SV36 )
| ( SV26 != SV44 ) ) )
= $false )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(219,plain,
! [SV38: $i,SV3: $i,SV28: $i,SV16: $i] :
( ( ( SV16
= ( vvar @ SV28 ) )
= $false )
| ( ( SV3 = SV38 )
= $false )
| ( ( ~ ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(220,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
| ( SV46
!= ( vvar @ SV53 ) ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(221,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SV54 ) )
| ( SV47
!= ( vvar @ SV22 ) ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(222,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) )
| ( SV33
!= ( vapp @ SV48 @ SV56 ) ) ) )
= $false )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV49: $i,SV35: $i,SV25: $i,SV43: $i,SV12: $i] :
( ( ( SV12 = SV43 )
= $false )
| ( ( SV25
!= ( vapp @ SV35 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(224,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( ( SV13 != SV36 )
| ( SV26 != SV44 ) )
= $false )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( ( SV13 != SV36 )
| ( SV26 != SV44 ) )
= $true )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(226,plain,
! [SV16: $i,SV3: $i,SV38: $i,SV28: $i] :
( ( ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
| ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) )
= $false )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(227,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( ~ ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) ) )
= $true )
| ( ( SV46
!= ( vvar @ SV53 ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( ~ ~ ( ( SV32 != SV9 )
| ( SV41 != SV54 ) ) )
= $true )
| ( ( SV47
!= ( vvar @ SV22 ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(229,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) )
| ( SV33
!= ( vapp @ SV48 @ SV56 ) ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(230,plain,
! [SV43: $i,SV12: $i,SV49: $i,SV35: $i,SV25: $i] :
( ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false )
| ( ( SV12 = SV43 )
= $false )
| ( ( ~ ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(231,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( SV13 != SV36 )
= $false )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(232,plain,
! [SV36: $i,SV13: $i,SV44: $i,SV26: $i] :
( ( ( SV26 != SV44 )
= $false )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(233,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( SV13 != SV36 )
= $true )
| ( ( SV26 != SV44 )
= $true )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(234,plain,
! [SV16: $i,SV3: $i,SV38: $i,SV28: $i] :
( ( ( ~ ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) ) )
= $false )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(235,plain,
! [SV38: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) ) )
= $false )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(236,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( ~ ( ( SV29 != SV18 )
| ( SV39 != SV5 ) ) )
= $false )
| ( ( SV46
!= ( vvar @ SV53 ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(237,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( ~ ( ( SV32 != SV9 )
| ( SV41 != SV54 ) ) )
= $false )
| ( ( SV47
!= ( vvar @ SV22 ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(238,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( ~ ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) ) )
= $true )
| ( ( SV33
!= ( vapp @ SV48 @ SV56 ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(239,plain,
! [SV25: $i,SV12: $i,SV49: $i,SV35: $i,SV43: $i] :
( ( ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
| ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) )
= $false )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(240,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( SV13 = SV36 )
= $true )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(241,plain,
! [SV36: $i,SV13: $i,SV44: $i,SV26: $i] :
( ( ( SV26 = SV44 )
= $true )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(242,plain,
! [SV44: $i,SV26: $i,SV36: $i,SV13: $i] :
( ( ( SV13 = SV36 )
= $false )
| ( ( SV26 != SV44 )
= $true )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(243,plain,
! [SV16: $i,SV3: $i,SV38: $i,SV28: $i] :
( ( ( ( SV28 != SV38 )
| ( visFreeVar @ SV3 @ SV16 ) )
= $true )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(244,plain,
! [SV38: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ( ~ ( visFreeVar @ SV3 @ SV16 )
| ( SV28 = SV38 ) )
= $true )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(245,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( ( SV29 != SV18 )
| ( SV39 != SV5 ) )
= $true )
| ( ( SV46
!= ( vvar @ SV53 ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(246,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( ( SV32 != SV9 )
| ( SV41 != SV54 ) )
= $true )
| ( ( SV47
!= ( vvar @ SV22 ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(247,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != SV52 )
| ( SV23 != SV55 ) ) )
= $false )
| ( ( SV33
!= ( vapp @ SV48 @ SV56 ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(248,plain,
! [SV25: $i,SV12: $i,SV49: $i,SV35: $i,SV43: $i] :
( ( ( ~ ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) ) )
= $false )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(249,plain,
! [SV49: $i,SV35: $i,SV43: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) )
= $false )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(250,plain,
! [SV36: $i,SV13: $i,SV44: $i,SV26: $i] :
( ( ( SV26 = SV44 )
= $false )
| ( ( SV13 = SV36 )
= $false )
| ( ( ( vapp @ SV13 @ SV26 )
= ( vapp @ SV36 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(251,plain,
! [SV16: $i,SV3: $i,SV38: $i,SV28: $i] :
( ( ( SV28 != SV38 )
= $true )
| ( ( visFreeVar @ SV3 @ SV16 )
= $true )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV38: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ( ~ ( visFreeVar @ SV3 @ SV16 ) )
= $true )
| ( ( SV28 = SV38 )
= $true )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(253,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( SV29 != SV18 )
= $true )
| ( ( SV39 != SV5 )
= $true )
| ( ( SV46
!= ( vvar @ SV53 ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( SV32 != SV9 )
= $true )
| ( ( SV41 != SV54 )
= $true )
| ( ( SV47
!= ( vvar @ SV22 ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(255,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( ( SV10 != SV52 )
| ( SV23 != SV55 ) )
= $true )
| ( ( SV33
!= ( vapp @ SV48 @ SV56 ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(256,plain,
! [SV25: $i,SV12: $i,SV49: $i,SV35: $i,SV43: $i] :
( ( ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
| ( visFreeVar @ SV12 @ SV25 ) )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(257,plain,
! [SV49: $i,SV35: $i,SV43: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( visFreeVar @ SV12 @ SV25 )
| ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(258,plain,
! [SV16: $i,SV3: $i,SV38: $i,SV28: $i] :
( ( ( SV28 = SV38 )
= $false )
| ( ( visFreeVar @ SV3 @ SV16 )
= $true )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(259,plain,
! [SV38: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ( visFreeVar @ SV3 @ SV16 )
= $false )
| ( ( SV28 = SV38 )
= $true )
| ( ( SV3 = SV38 )
= $false )
| ( ( SV16
= ( vvar @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(260,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i] :
( ( ( SV29 = SV18 )
= $false )
| ( ( SV39 != SV5 )
= $true )
| ( ( SV46
!= ( vvar @ SV53 ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(261,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i] :
( ( ( SV32 = SV9 )
= $false )
| ( ( SV41 != SV54 )
= $true )
| ( ( SV47
!= ( vvar @ SV22 ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(262,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( SV10 != SV52 )
= $true )
| ( ( SV23 != SV55 )
= $true )
| ( ( SV33
!= ( vapp @ SV48 @ SV56 ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(263,plain,
! [SV25: $i,SV12: $i,SV49: $i,SV35: $i,SV43: $i] :
( ( ( ~ ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) ) )
= $true )
| ( ( visFreeVar @ SV12 @ SV25 )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(264,plain,
! [SV49: $i,SV35: $i,SV43: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( visFreeVar @ SV12 @ SV25 ) )
= $true )
| ( ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(265,plain,
! [SV50: $i,SV53: $i,SV46: $i,SV18: $i,SV29: $i,SV5: $i,SV39: $i] :
( ( ( SV39 = SV5 )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV46
!= ( vvar @ SV53 ) )
= $true )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(266,plain,
! [SV51: $i,SV22: $i,SV47: $i,SV9: $i,SV32: $i,SV54: $i,SV41: $i] :
( ( ( SV41 = SV54 )
= $false )
| ( ( SV32 = SV9 )
= $false )
| ( ( SV47
!= ( vvar @ SV22 ) )
= $true )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(267,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i] :
( ( ( SV10 = SV52 )
= $false )
| ( ( SV23 != SV55 )
= $true )
| ( ( SV33
!= ( vapp @ SV48 @ SV56 ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(268,plain,
! [SV25: $i,SV12: $i,SV49: $i,SV35: $i,SV43: $i] :
( ( ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
= $false )
| ( ( visFreeVar @ SV12 @ SV25 )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(269,plain,
! [SV49: $i,SV35: $i,SV43: $i,SV25: $i,SV12: $i] :
( ( ( visFreeVar @ SV12 @ SV25 )
= $false )
| ( ( ( visFreeVar @ SV43 @ SV35 )
| ( visFreeVar @ SV43 @ SV49 ) )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(270,plain,
! [SV50: $i,SV5: $i,SV39: $i,SV18: $i,SV29: $i,SV53: $i,SV46: $i] :
( ( ( SV46
= ( vvar @ SV53 ) )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV39 = SV5 )
= $false )
| ( ( ~ ( ( SV18 != SV53 ) )
| ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(271,plain,
! [SV51: $i,SV54: $i,SV41: $i,SV9: $i,SV32: $i,SV22: $i,SV47: $i] :
( ( ( SV47
= ( vvar @ SV22 ) )
= $false )
| ( ( SV32 = SV9 )
= $false )
| ( ( SV41 = SV54 )
= $false )
| ( ( ( SV9 != SV22 )
| ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(272,plain,
! [SV42: $i,SV56: $i,SV48: $i,SV33: $i,SV52: $i,SV10: $i,SV55: $i,SV23: $i] :
( ( ( SV23 = SV55 )
= $false )
| ( ( SV10 = SV52 )
= $false )
| ( ( SV33
!= ( vapp @ SV48 @ SV56 ) )
= $true )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(273,plain,
! [SV49: $i,SV25: $i,SV12: $i,SV35: $i,SV43: $i] :
( ( ( visFreeVar @ SV43 @ SV35 )
= $false )
| ( ( visFreeVar @ SV12 @ SV25 )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(274,plain,
! [SV35: $i,SV25: $i,SV12: $i,SV49: $i,SV43: $i] :
( ( ( visFreeVar @ SV43 @ SV49 )
= $false )
| ( ( visFreeVar @ SV12 @ SV25 )
= $true )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(275,plain,
! [SV25: $i,SV12: $i,SV49: $i,SV35: $i,SV43: $i] :
( ( ( visFreeVar @ SV43 @ SV35 )
= $true )
| ( ( visFreeVar @ SV43 @ SV49 )
= $true )
| ( ( visFreeVar @ SV12 @ SV25 )
= $false )
| ( ( SV12 = SV43 )
= $false )
| ( ( SV25
= ( vapp @ SV35 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(276,plain,
! [SV5: $i,SV46: $i,SV39: $i,SV29: $i,SV50: $i,SV53: $i,SV18: $i] :
( ( ( ~ ( ( SV18 != SV53 ) ) )
= $true )
| ( ( ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true )
| ( ( SV39 = SV5 )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV46
= ( vvar @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(277,plain,
! [SV54: $i,SV47: $i,SV41: $i,SV32: $i,SV51: $i,SV22: $i,SV9: $i] :
( ( ( SV9 != SV22 )
= $true )
| ( ( ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true )
| ( ( SV41 = SV54 )
= $false )
| ( ( SV32 = SV9 )
= $false )
| ( ( SV47
= ( vvar @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(278,plain,
! [SV42: $i,SV55: $i,SV23: $i,SV52: $i,SV10: $i,SV56: $i,SV48: $i,SV33: $i] :
( ( ( SV33
= ( vapp @ SV48 @ SV56 ) )
= $false )
| ( ( SV10 = SV52 )
= $false )
| ( ( SV23 = SV55 )
= $false )
| ( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
| ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(279,plain,
! [SV5: $i,SV46: $i,SV39: $i,SV29: $i,SV50: $i,SV53: $i,SV18: $i] :
( ( ( SV18 != SV53 )
= $false )
| ( ( ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true )
| ( ( SV39 = SV5 )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV46
= ( vvar @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(280,plain,
! [SV54: $i,SV47: $i,SV41: $i,SV32: $i,SV51: $i,SV22: $i,SV9: $i] :
( ( ( SV9 = SV22 )
= $false )
| ( ( ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
| ( SV51 = SV54 ) )
= $true )
| ( ( SV41 = SV54 )
= $false )
| ( ( SV32 = SV9 )
= $false )
| ( ( SV47
= ( vvar @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(281,plain,
! [SV56: $i,SV48: $i,SV55: $i,SV52: $i,SV33: $i,SV23: $i,SV10: $i,SV42: $i] :
( ( ( SV42
!= ( vsubst @ SV10 @ SV23 @ SV33 ) )
= $true )
| ( ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) )
= $true )
| ( ( SV23 = SV55 )
= $false )
| ( ( SV10 = SV52 )
= $false )
| ( ( SV33
= ( vapp @ SV48 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(282,plain,
! [SV5: $i,SV46: $i,SV39: $i,SV29: $i,SV50: $i,SV53: $i,SV18: $i] :
( ( ( SV18 = SV53 )
= $true )
| ( ( ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
| ( SV50
= ( vvar @ SV53 ) ) )
= $true )
| ( ( SV39 = SV5 )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV46
= ( vvar @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(283,plain,
! [SV22: $i,SV9: $i,SV54: $i,SV47: $i,SV41: $i,SV32: $i,SV51: $i] :
( ( ( SV51
!= ( vsubst @ SV32 @ SV41 @ SV47 ) )
= $true )
| ( ( SV51 = SV54 )
= $true )
| ( ( SV9 = SV22 )
= $false )
| ( ( SV41 = SV54 )
= $false )
| ( ( SV32 = SV9 )
= $false )
| ( ( SV47
= ( vvar @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(284,plain,
! [SV56: $i,SV48: $i,SV55: $i,SV52: $i,SV33: $i,SV23: $i,SV10: $i,SV42: $i] :
( ( ( SV42
= ( vsubst @ SV10 @ SV23 @ SV33 ) )
= $false )
| ( ( SV42
= ( vapp @ ( vsubst @ SV52 @ SV55 @ SV48 ) @ ( vsubst @ SV52 @ SV55 @ SV56 ) ) )
= $true )
| ( ( SV23 = SV55 )
= $false )
| ( ( SV10 = SV52 )
= $false )
| ( ( SV33
= ( vapp @ SV48 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(285,plain,
! [SV5: $i,SV18: $i,SV53: $i,SV46: $i,SV39: $i,SV29: $i,SV50: $i] :
( ( ( SV50
!= ( vsubst @ SV29 @ SV39 @ SV46 ) )
= $true )
| ( ( SV50
= ( vvar @ SV53 ) )
= $true )
| ( ( SV18 = SV53 )
= $true )
| ( ( SV39 = SV5 )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV46
= ( vvar @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(286,plain,
! [SV22: $i,SV9: $i,SV54: $i,SV47: $i,SV41: $i,SV32: $i,SV51: $i] :
( ( ( SV51
= ( vsubst @ SV32 @ SV41 @ SV47 ) )
= $false )
| ( ( SV51 = SV54 )
= $true )
| ( ( SV9 = SV22 )
= $false )
| ( ( SV41 = SV54 )
= $false )
| ( ( SV32 = SV9 )
= $false )
| ( ( SV47
= ( vvar @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(287,plain,
! [SV5: $i,SV18: $i,SV53: $i,SV46: $i,SV39: $i,SV29: $i,SV50: $i] :
( ( ( SV50
= ( vsubst @ SV29 @ SV39 @ SV46 ) )
= $false )
| ( ( SV50
= ( vvar @ SV53 ) )
= $true )
| ( ( SV18 = SV53 )
= $true )
| ( ( SV39 = SV5 )
= $false )
| ( ( SV29 = SV18 )
= $false )
| ( ( SV46
= ( vvar @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(288,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[101,287,286,284,275,274,273,259,258,250,241,240,197,196,192,187,179,178,176,165,144]) ).
thf(289,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM128+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
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 18:37:47 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.72/0.34
% 0.72/0.34 No.of.Axioms: 13
% 0.72/0.34
% 0.72/0.34 Length.of.Defs: 0
% 0.72/0.34
% 0.72/0.34 Contains.Choice.Funs: false
% 0.72/0.34 ..........
% 0.72/0.34
% 0.72/0.34 ********************************
% 0.72/0.34 * All subproblems solved! *
% 0.72/0.34 ********************************
% 0.72/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:14,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:288,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.72/0.34
% 0.72/0.34 %**** Beginning of derivation protocol ****
% 0.72/0.34 % SZS output start CNFRefutation
% See solution above
% 0.72/0.34
% 0.72/0.34 %**** End of derivation protocol ****
% 0.72/0.34 %**** no. of clauses in derivation: 238 ****
% 0.72/0.34 %**** clause counter: 288 ****
% 0.72/0.34
% 0.72/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:14,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:288,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------