%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 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 11:02:33 AM UTC 2026
% Result : Theorem 7.12s 1.56s
% Output : CNFRefutation 7.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 196 ( 158 unt; 0 typ; 0 def)
% Number of atoms : 876 ( 295 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1776 ( 273 ~; 218 |; 18 &;1251 @)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 468 ( 0 ^; 464 !; 4 ?; 468 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_append,type,
append: $i > $i > $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_elemNat,type,
elemNat: $i > $i > $o ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_lengthNat,type,
lengthNat: $i > $i ).
thf(tp_leqNat,type,
leqNat: $i > $i > $o ).
thf(tp_nil,type,
nil: $i ).
thf(tp_proj1S,type,
proj1S: $i > $i ).
thf(tp_rev,type,
rev: $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_sorted,type,
sorted: $i > $o ).
thf(tp_tail,type,
tail: $i > $i ).
thf(tp_unique,type,
unique: $i > $o ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [Y: $i,Xs: $i] :
( ( rev @ ( cons @ Y @ Xs ) )
= ( append @ ( rev @ Xs ) @ ( cons @ Y @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(2,axiom,
( ( rev @ nil )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(3,axiom,
! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(4,axiom,
! [Y: $i] :
( ( append @ nil @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(5,axiom,
! [Y: $i,Xs: $i] :
( ( unique @ ( cons @ Y @ Xs ) )
<=> ( ~ ( elemNat @ Y @ Xs )
& ( unique @ Xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(6,axiom,
unique @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(7,axiom,
! [X: $i,Z: $i,Xs: $i] :
( ( elemNat @ X @ ( cons @ Z @ Xs ) )
<=> ( ( X = Z )
| ( elemNat @ X @ Xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(8,axiom,
! [X: $i] :
~ ( elemNat @ X @ nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(9,axiom,
! [Y: $i,Xs: $i] :
( ( lengthNat @ ( cons @ Y @ Xs ) )
= ( s @ ( lengthNat @ Xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(10,axiom,
( ( lengthNat @ nil )
= z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(11,axiom,
! [Y: $i,Y2: $i,Xs: $i] :
( ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
<=> ( ( leqNat @ Y @ Y2 )
& ( sorted @ ( cons @ Y2 @ Xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(12,axiom,
! [Y: $i] : ( sorted @ ( cons @ Y @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(13,axiom,
sorted @ nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(14,axiom,
! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(15,axiom,
! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(16,axiom,
! [Y: $i] : ( leqNat @ z @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(17,axiom,
! [X: $i] :
( z
!= ( s @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(18,axiom,
! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(19,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(20,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(21,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(22,conjecture,
? [Xs: $i] :
~ ( ( sorted @ ( rev @ Xs ) )
=> ( ( unique @ Xs )
=> ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_022) ).
thf(23,negated_conjecture,
( ( ? [Xs: $i] :
~ ( ( sorted @ ( rev @ Xs ) )
=> ( ( unique @ Xs )
=> ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( ? [Xs: $i] :
~ ( ( sorted @ ( rev @ Xs ) )
=> ( ( unique @ Xs )
=> ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [Y: $i,Xs: $i] :
( ( rev @ ( cons @ Y @ Xs ) )
= ( append @ ( rev @ Xs ) @ ( cons @ Y @ nil ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ( rev @ nil )
= nil )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [Y: $i,Xs: $i] :
( ( unique @ ( cons @ Y @ Xs ) )
<=> ( ~ ( elemNat @ Y @ Xs )
& ( unique @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( unique @ nil )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [X: $i,Z: $i,Xs: $i] :
( ( elemNat @ X @ ( cons @ Z @ Xs ) )
<=> ( ( X = Z )
| ( elemNat @ X @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ! [X: $i] :
~ ( elemNat @ X @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( ! [Y: $i,Xs: $i] :
( ( lengthNat @ ( cons @ Y @ Xs ) )
= ( s @ ( lengthNat @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ( lengthNat @ nil )
= z )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [Y: $i,Y2: $i,Xs: $i] :
( ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
<=> ( ( leqNat @ Y @ Y2 )
& ( sorted @ ( cons @ Y2 @ Xs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [Y: $i] : ( sorted @ ( cons @ Y @ nil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( sorted @ nil )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [Y: $i] : ( leqNat @ z @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ~ ? [Xs: $i] :
~ ( ( sorted @ ( rev @ Xs ) )
=> ( ( unique @ Xs )
=> ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [Xs: $i] :
( ~ ( sorted @ ( rev @ Xs ) )
| ~ ( unique @ Xs )
| ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(48,plain,
( ( ! [Y: $i,Xs: $i] :
( ( elemNat @ Y @ Xs )
| ~ ( unique @ Xs )
| ( unique @ ( cons @ Y @ Xs ) ) )
& ! [Y: $i,Xs: $i] :
( ~ ( unique @ ( cons @ Y @ Xs ) )
| ~ ( elemNat @ Y @ Xs ) )
& ! [Y: $i,Xs: $i] :
( ~ ( unique @ ( cons @ Y @ Xs ) )
| ( unique @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(49,plain,
( ( ! [X: $i] :
( ! [Z: $i,Xs: $i] :
( ~ ( elemNat @ X @ ( cons @ Z @ Xs ) )
| ( X = Z )
| ( elemNat @ X @ Xs ) )
& ! [Z: $i] :
( ( X != Z )
| ! [Xs: $i] : ( elemNat @ X @ ( cons @ Z @ Xs ) ) )
& ! [Z: $i,Xs: $i] :
( ~ ( elemNat @ X @ Xs )
| ( elemNat @ X @ ( cons @ Z @ Xs ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(50,plain,
( ( ! [Y: $i] :
( ! [Y2: $i,Xs: $i] :
( ~ ( leqNat @ Y @ Y2 )
| ~ ( sorted @ ( cons @ Y2 @ Xs ) )
| ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) ) )
& ! [Y2: $i] :
( ! [Xs: $i] :
~ ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
| ( leqNat @ Y @ Y2 ) )
& ! [Y2: $i,Xs: $i] :
( ~ ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
| ( sorted @ ( cons @ Y2 @ Xs ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(51,plain,
( ( ! [Z: $i,M: $i] :
( ~ ( leqNat @ ( s @ Z ) @ ( s @ M ) )
| ( leqNat @ Z @ M ) )
& ! [Z: $i,M: $i] :
( ~ ( leqNat @ Z @ M )
| ( leqNat @ ( s @ Z ) @ ( s @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(52,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(53,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(54,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(56,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(57,plain,
( ( ! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(58,plain,
( ( ! [X: $i] :
( z
!= ( s @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(59,plain,
( ( ! [Y: $i] : ( leqNat @ z @ Y ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(61,plain,
( ( ! [Z: $i,M: $i] :
( ~ ( leqNat @ ( s @ Z ) @ ( s @ M ) )
| ( leqNat @ Z @ M ) )
& ! [Z: $i,M: $i] :
( ~ ( leqNat @ Z @ M )
| ( leqNat @ ( s @ Z ) @ ( s @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(62,plain,
( ( sorted @ nil )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(63,plain,
( ( ! [Y: $i] : ( sorted @ ( cons @ Y @ nil ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(64,plain,
( ( ! [Y: $i] :
( ! [Y2: $i,Xs: $i] :
( ~ ( leqNat @ Y @ Y2 )
| ~ ( sorted @ ( cons @ Y2 @ Xs ) )
| ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) ) )
& ! [Y2: $i] :
( ! [Xs: $i] :
~ ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
| ( leqNat @ Y @ Y2 ) )
& ! [Y2: $i,Xs: $i] :
( ~ ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
| ( sorted @ ( cons @ Y2 @ Xs ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(65,plain,
( ( ( lengthNat @ nil )
= z )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(66,plain,
( ( ! [Y: $i,Xs: $i] :
( ( lengthNat @ ( cons @ Y @ Xs ) )
= ( s @ ( lengthNat @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(67,plain,
( ( ! [X: $i] :
~ ( elemNat @ X @ nil ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(68,plain,
( ( ! [X: $i] :
( ! [Z: $i,Xs: $i] :
( ~ ( elemNat @ X @ ( cons @ Z @ Xs ) )
| ( X = Z )
| ( elemNat @ X @ Xs ) )
& ! [Z: $i] :
( ( X != Z )
| ! [Xs: $i] : ( elemNat @ X @ ( cons @ Z @ Xs ) ) )
& ! [Z: $i,Xs: $i] :
( ~ ( elemNat @ X @ Xs )
| ( elemNat @ X @ ( cons @ Z @ Xs ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(69,plain,
( ( unique @ nil )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [Y: $i,Xs: $i] :
( ( elemNat @ Y @ Xs )
| ~ ( unique @ Xs )
| ( unique @ ( cons @ Y @ Xs ) ) )
& ! [Y: $i,Xs: $i] :
( ~ ( unique @ ( cons @ Y @ Xs ) )
| ~ ( elemNat @ Y @ Xs ) )
& ! [Y: $i,Xs: $i] :
( ~ ( unique @ ( cons @ Y @ Xs ) )
| ( unique @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(71,plain,
( ( ! [Y: $i] :
( ( append @ nil @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(72,plain,
( ( ! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(73,plain,
( ( ( rev @ nil )
= nil )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(74,plain,
( ( ! [Y: $i,Xs: $i] :
( ( rev @ ( cons @ Y @ Xs ) )
= ( append @ ( rev @ Xs ) @ ( cons @ Y @ nil ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(75,plain,
( ( ! [Xs: $i] :
( ~ ( sorted @ ( rev @ Xs ) )
| ~ ( unique @ Xs )
| ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(76,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ~ ( sorted @ ( cons @ SX1 @ SX2 ) )
| ( sorted @ ( cons @ SX0 @ ( cons @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( sorted @ ( cons @ SX0 @ ( cons @ SX1 @ SX2 ) ) )
| ( leqNat @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( sorted @ ( cons @ SX0 @ ( cons @ SX1 @ SX2 ) ) )
| ( sorted @ ( cons @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(77,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(78,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( elemNat @ SX0 @ ( cons @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( elemNat @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( elemNat @ SX0 @ ( cons @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( elemNat @ SX0 @ SX2 )
| ( elemNat @ SX0 @ ( cons @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(79,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( elemNat @ SX0 @ SX1 )
| ~ ( unique @ SX1 )
| ( unique @ ( cons @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(80,plain,
! [SV1: $i] :
( ( ! [SY31: $i] :
( ( head @ ( cons @ SV1 @ SY31 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(81,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ( tail @ ( cons @ SV2 @ SY32 ) )
= SY32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(82,plain,
! [SV3: $i] :
( ( ! [SY33: $i] :
( nil
!= ( cons @ SV3 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(83,plain,
! [SV4: $i] :
( ( ( proj1S @ ( s @ SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(84,plain,
! [SV5: $i] :
( ( z
!= ( s @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(85,plain,
! [SV6: $i] :
( ( leqNat @ z @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(86,plain,
! [SV7: $i] :
( ( ~ ( leqNat @ ( s @ SV7 ) @ z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(87,plain,
! [SV8: $i] :
( ( sorted @ ( cons @ SV8 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(88,plain,
! [SV9: $i] :
( ( ! [SY34: $i] :
( ( lengthNat @ ( cons @ SV9 @ SY34 ) )
= ( s @ ( lengthNat @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV10: $i] :
( ( ~ ( elemNat @ SV10 @ nil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV11: $i] :
( ( ( append @ nil @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV12: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ( append @ ( cons @ SY35 @ SY36 ) @ SV12 )
= ( cons @ SY35 @ ( append @ SY36 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(92,plain,
! [SV13: $i] :
( ( ! [SY37: $i] :
( ( rev @ ( cons @ SV13 @ SY37 ) )
= ( append @ ( rev @ SY37 ) @ ( cons @ SV13 @ nil ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(93,plain,
! [SV14: $i] :
( ( ~ ( sorted @ ( rev @ SV14 ) )
| ~ ( unique @ SV14 )
| ( leqNat @ ( lengthNat @ SV14 ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(94,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY38: $i,SY39: $i] :
( ~ ( leqNat @ SV15 @ SY38 )
| ~ ( sorted @ ( cons @ SY38 @ SY39 ) )
| ( sorted @ ( cons @ SV15 @ ( cons @ SY38 @ SY39 ) ) ) )
| ~ ~ ( ~ ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(96,plain,
! [SV16: $i] :
( ( ~ ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( elemNat @ SV16 @ ( cons @ SY44 @ SY45 ) )
| ( SV16 = SY44 )
| ( elemNat @ SV16 @ SY45 ) )
| ~ ~ ( ~ ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(97,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( elemNat @ SX0 @ SX1 )
| ~ ( unique @ SX1 )
| ( unique @ ( cons @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(98,plain,
! [SV17: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV17 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(99,plain,
! [SV18: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV18 ) )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(100,plain,
! [SV19: $i,SV3: $i] :
( ( nil
!= ( cons @ SV3 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(101,plain,
! [SV5: $i] :
( ( z
= ( s @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV7: $i] :
( ( leqNat @ ( s @ SV7 ) @ z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV20: $i,SV9: $i] :
( ( ( lengthNat @ ( cons @ SV9 @ SV20 ) )
= ( s @ ( lengthNat @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV10: $i] :
( ( elemNat @ SV10 @ nil )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV12: $i,SV21: $i] :
( ( ! [SY50: $i] :
( ( append @ ( cons @ SV21 @ SY50 ) @ SV12 )
= ( cons @ SV21 @ ( append @ SY50 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV22: $i,SV13: $i] :
( ( ( rev @ ( cons @ SV13 @ SV22 ) )
= ( append @ ( rev @ SV22 ) @ ( cons @ SV13 @ nil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV14: $i] :
( ( ( ~ ( sorted @ ( rev @ SV14 ) ) )
= $true )
| ( ( ~ ( unique @ SV14 )
| ( leqNat @ ( lengthNat @ SV14 ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV15: $i] :
( ( ~ ! [SY38: $i,SY39: $i] :
( ~ ( leqNat @ SV15 @ SY38 )
| ~ ( sorted @ ( cons @ SY38 @ SY39 ) )
| ( sorted @ ( cons @ SV15 @ ( cons @ SY38 @ SY39 ) ) ) )
| ~ ~ ( ~ ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(110,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(111,plain,
! [SV16: $i] :
( ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( elemNat @ SV16 @ ( cons @ SY44 @ SY45 ) )
| ( SV16 = SY44 )
| ( elemNat @ SV16 @ SY45 ) )
| ~ ~ ( ~ ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(112,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( elemNat @ SX0 @ SX1 )
| ~ ( unique @ SX1 )
| ( unique @ ( cons @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(113,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(114,plain,
! [SV19: $i,SV3: $i] :
( ( nil
= ( cons @ SV3 @ SV19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(115,plain,
! [SV12: $i,SV23: $i,SV21: $i] :
( ( ( append @ ( cons @ SV21 @ SV23 ) @ SV12 )
= ( cons @ SV21 @ ( append @ SV23 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV14: $i] :
( ( ( sorted @ ( rev @ SV14 ) )
= $false )
| ( ( ~ ( unique @ SV14 )
| ( leqNat @ ( lengthNat @ SV14 ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV15: $i] :
( ( ~ ! [SY38: $i,SY39: $i] :
( ~ ( leqNat @ SV15 @ SY38 )
| ~ ( sorted @ ( cons @ SY38 @ SY39 ) )
| ( sorted @ ( cons @ SV15 @ ( cons @ SY38 @ SY39 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(118,plain,
! [SV15: $i] :
( ( ~ ~ ( ~ ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) )
| ( leqNat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leqNat @ SX0 @ SX1 )
| ( leqNat @ ( s @ SX0 ) @ ( s @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(121,plain,
! [SV16: $i] :
( ( ~ ! [SY44: $i,SY45: $i] :
( ~ ( elemNat @ SV16 @ ( cons @ SY44 @ SY45 ) )
| ( SV16 = SY44 )
| ( elemNat @ SV16 @ SY45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( elemNat @ SX0 @ SX1 )
| ~ ( unique @ SX1 )
| ( unique @ ( cons @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(124,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(125,plain,
! [SV14: $i] :
( ( ( ~ ( unique @ SV14 ) )
= $true )
| ( ( leqNat @ ( lengthNat @ SV14 ) @ ( s @ ( s @ ( s @ z ) ) ) )
= $true )
| ( ( sorted @ ( rev @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV15: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( leqNat @ SV15 @ SY38 )
| ~ ( sorted @ ( cons @ SY38 @ SY39 ) )
| ( sorted @ ( cons @ SV15 @ ( cons @ SY38 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV24: $i] :
( ( ! [SY51: $i] :
( ~ ( leqNat @ ( s @ SV24 ) @ ( s @ SY51 ) )
| ( leqNat @ SV24 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV25: $i] :
( ( ! [SY52: $i] :
( ~ ( leqNat @ SV25 @ SY52 )
| ( leqNat @ ( s @ SV25 ) @ ( s @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV16: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( elemNat @ SV16 @ ( cons @ SY44 @ SY45 ) )
| ( SV16 = SY44 )
| ( elemNat @ SV16 @ SY45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(131,plain,
! [SV16: $i] :
( ( ~ ( ~ ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV26: $i] :
( ( ! [SY53: $i] :
( ( elemNat @ SV26 @ SY53 )
| ~ ( unique @ SY53 )
| ( unique @ ( cons @ SV26 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(133,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(134,plain,
! [SV14: $i] :
( ( ( unique @ SV14 )
= $false )
| ( ( leqNat @ ( lengthNat @ SV14 ) @ ( s @ ( s @ ( s @ z ) ) ) )
= $true )
| ( ( sorted @ ( rev @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY54: $i] :
( ~ ( leqNat @ SV15 @ SV27 )
| ~ ( sorted @ ( cons @ SV27 @ SY54 ) )
| ( sorted @ ( cons @ SV15 @ ( cons @ SV27 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV15: $i] :
( ( ~ ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(137,plain,
! [SV28: $i,SV24: $i] :
( ( ~ ( leqNat @ ( s @ SV24 ) @ ( s @ SV28 ) )
| ( leqNat @ SV24 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(138,plain,
! [SV29: $i,SV25: $i] :
( ( ~ ( leqNat @ SV25 @ SV29 )
| ( leqNat @ ( s @ SV25 ) @ ( s @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY55: $i] :
( ~ ( elemNat @ SV16 @ ( cons @ SV30 @ SY55 ) )
| ( SV16 = SV30 )
| ( elemNat @ SV16 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV16: $i] :
( ( ~ ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) )
| ~ ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV31: $i,SV26: $i] :
( ( ( elemNat @ SV26 @ SV31 )
| ~ ( unique @ SV31 )
| ( unique @ ( cons @ SV26 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(142,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(143,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(144,plain,
! [SV32: $i,SV27: $i,SV15: $i] :
( ( ~ ( leqNat @ SV15 @ SV27 )
| ~ ( sorted @ ( cons @ SV27 @ SV32 ) )
| ( sorted @ ( cons @ SV15 @ ( cons @ SV27 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV15: $i] :
( ( ~ ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(146,plain,
! [SV15: $i] :
( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(147,plain,
! [SV28: $i,SV24: $i] :
( ( ( ~ ( leqNat @ ( s @ SV24 ) @ ( s @ SV28 ) ) )
= $true )
| ( ( leqNat @ SV24 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV29: $i,SV25: $i] :
( ( ( ~ ( leqNat @ SV25 @ SV29 ) )
= $true )
| ( ( leqNat @ ( s @ SV25 ) @ ( s @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV33: $i,SV30: $i,SV16: $i] :
( ( ~ ( elemNat @ SV16 @ ( cons @ SV30 @ SV33 ) )
| ( SV16 = SV30 )
| ( elemNat @ SV16 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV16: $i] :
( ( ~ ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(151,plain,
! [SV16: $i] :
( ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(152,plain,
! [SV31: $i,SV26: $i] :
( ( ( ( elemNat @ SV26 @ SV31 )
| ~ ( unique @ SV31 ) )
= $true )
| ( ( unique @ ( cons @ SV26 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ~ ( elemNat @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( unique @ ( cons @ SX0 @ SX1 ) )
| ( unique @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(155,plain,
! [SV32: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( leqNat @ SV15 @ SV27 )
| ~ ( sorted @ ( cons @ SV27 @ SV32 ) ) )
= $true )
| ( ( sorted @ ( cons @ SV15 @ ( cons @ SV27 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV15: $i] :
( ( ! [SY40: $i] :
( ! [SY41: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SY40 @ SY41 ) ) )
| ( leqNat @ SV15 @ SY40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(157,plain,
! [SV15: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SY42 @ SY43 ) ) )
| ( sorted @ ( cons @ SY42 @ SY43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(158,plain,
! [SV28: $i,SV24: $i] :
( ( ( leqNat @ ( s @ SV24 ) @ ( s @ SV28 ) )
= $false )
| ( ( leqNat @ SV24 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV29: $i,SV25: $i] :
( ( ( leqNat @ SV25 @ SV29 )
= $false )
| ( ( leqNat @ ( s @ SV25 ) @ ( s @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV33: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( elemNat @ SV16 @ ( cons @ SV30 @ SV33 ) ) )
= $true )
| ( ( ( SV16 = SV30 )
| ( elemNat @ SV16 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV16: $i] :
( ( ! [SY46: $i] :
( ( SV16 != SY46 )
| ! [SY47: $i] : ( elemNat @ SV16 @ ( cons @ SY46 @ SY47 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(162,plain,
! [SV16: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ( elemNat @ SV16 @ SY49 )
| ( elemNat @ SV16 @ ( cons @ SY48 @ SY49 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(163,plain,
! [SV31: $i,SV26: $i] :
( ( ( elemNat @ SV26 @ SV31 )
= $true )
| ( ( ~ ( unique @ SV31 ) )
= $true )
| ( ( unique @ ( cons @ SV26 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV34: $i] :
( ( ! [SY56: $i] :
( ~ ( unique @ ( cons @ SV34 @ SY56 ) )
| ~ ( elemNat @ SV34 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV35: $i] :
( ( ! [SY57: $i] :
( ~ ( unique @ ( cons @ SV35 @ SY57 ) )
| ( unique @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(166,plain,
! [SV32: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( leqNat @ SV15 @ SV27 ) )
= $true )
| ( ( ~ ( sorted @ ( cons @ SV27 @ SV32 ) ) )
= $true )
| ( ( sorted @ ( cons @ SV15 @ ( cons @ SV27 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(167,plain,
! [SV36: $i,SV15: $i] :
( ( ! [SY58: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SV36 @ SY58 ) ) )
| ( leqNat @ SV15 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(168,plain,
! [SV37: $i,SV15: $i] :
( ( ! [SY59: $i] :
( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SV37 @ SY59 ) ) )
| ( sorted @ ( cons @ SV37 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV33: $i,SV30: $i,SV16: $i] :
( ( ( elemNat @ SV16 @ ( cons @ SV30 @ SV33 ) )
= $false )
| ( ( ( SV16 = SV30 )
| ( elemNat @ SV16 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV38: $i,SV16: $i] :
( ( ( SV16 != SV38 )
| ! [SY60: $i] : ( elemNat @ SV16 @ ( cons @ SV38 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV39: $i,SV16: $i] :
( ( ! [SY61: $i] :
( ~ ( elemNat @ SV16 @ SY61 )
| ( elemNat @ SV16 @ ( cons @ SV39 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV26: $i,SV31: $i] :
( ( ( unique @ SV31 )
= $false )
| ( ( elemNat @ SV26 @ SV31 )
= $true )
| ( ( unique @ ( cons @ SV26 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV40: $i,SV34: $i] :
( ( ~ ( unique @ ( cons @ SV34 @ SV40 ) )
| ~ ( elemNat @ SV34 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV41: $i,SV35: $i] :
( ( ~ ( unique @ ( cons @ SV35 @ SV41 ) )
| ( unique @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV32: $i,SV27: $i,SV15: $i] :
( ( ( leqNat @ SV15 @ SV27 )
= $false )
| ( ( ~ ( sorted @ ( cons @ SV27 @ SV32 ) ) )
= $true )
| ( ( sorted @ ( cons @ SV15 @ ( cons @ SV27 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV36: $i,SV15: $i] :
( ( ( ! [SY58: $i] :
~ ( sorted @ ( cons @ SV15 @ ( cons @ SV36 @ SY58 ) ) ) )
= $true )
| ( ( leqNat @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV42: $i,SV37: $i,SV15: $i] :
( ( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SV37 @ SV42 ) ) )
| ( sorted @ ( cons @ SV37 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV33: $i,SV30: $i,SV16: $i] :
( ( ( SV16 = SV30 )
= $true )
| ( ( elemNat @ SV16 @ SV33 )
= $true )
| ( ( elemNat @ SV16 @ ( cons @ SV30 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(179,plain,
! [SV38: $i,SV16: $i] :
( ( ( SV16 != SV38 )
= $true )
| ( ( ! [SY60: $i] : ( elemNat @ SV16 @ ( cons @ SV38 @ SY60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV39: $i,SV43: $i,SV16: $i] :
( ( ~ ( elemNat @ SV16 @ SV43 )
| ( elemNat @ SV16 @ ( cons @ SV39 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV40: $i,SV34: $i] :
( ( ( ~ ( unique @ ( cons @ SV34 @ SV40 ) ) )
= $true )
| ( ( ~ ( elemNat @ SV34 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV41: $i,SV35: $i] :
( ( ( ~ ( unique @ ( cons @ SV35 @ SV41 ) ) )
= $true )
| ( ( unique @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV15: $i,SV32: $i,SV27: $i] :
( ( ( sorted @ ( cons @ SV27 @ SV32 ) )
= $false )
| ( ( leqNat @ SV15 @ SV27 )
= $false )
| ( ( sorted @ ( cons @ SV15 @ ( cons @ SV27 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV44: $i,SV36: $i,SV15: $i] :
( ( ( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SV36 @ SV44 ) ) ) )
= $true )
| ( ( leqNat @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV42: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( sorted @ ( cons @ SV15 @ ( cons @ SV37 @ SV42 ) ) ) )
= $true )
| ( ( sorted @ ( cons @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV38: $i,SV16: $i] :
( ( ( SV16 = SV38 )
= $false )
| ( ( ! [SY60: $i] : ( elemNat @ SV16 @ ( cons @ SV38 @ SY60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(187,plain,
! [SV39: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( elemNat @ SV16 @ SV43 ) )
= $true )
| ( ( elemNat @ SV16 @ ( cons @ SV39 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(188,plain,
! [SV40: $i,SV34: $i] :
( ( ( unique @ ( cons @ SV34 @ SV40 ) )
= $false )
| ( ( ~ ( elemNat @ SV34 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(189,plain,
! [SV41: $i,SV35: $i] :
( ( ( unique @ ( cons @ SV35 @ SV41 ) )
= $false )
| ( ( unique @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(190,plain,
! [SV44: $i,SV36: $i,SV15: $i] :
( ( ( sorted @ ( cons @ SV15 @ ( cons @ SV36 @ SV44 ) ) )
= $false )
| ( ( leqNat @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(191,plain,
! [SV42: $i,SV37: $i,SV15: $i] :
( ( ( sorted @ ( cons @ SV15 @ ( cons @ SV37 @ SV42 ) ) )
= $false )
| ( ( sorted @ ( cons @ SV37 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(192,plain,
! [SV45: $i,SV38: $i,SV16: $i] :
( ( ( elemNat @ SV16 @ ( cons @ SV38 @ SV45 ) )
= $true )
| ( ( SV16 = SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(193,plain,
! [SV39: $i,SV43: $i,SV16: $i] :
( ( ( elemNat @ SV16 @ SV43 )
= $false )
| ( ( elemNat @ SV16 @ ( cons @ SV39 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(194,plain,
! [SV40: $i,SV34: $i] :
( ( ( elemNat @ SV34 @ SV40 )
= $false )
| ( ( unique @ ( cons @ SV34 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(195,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,194,193,192,191,190,189,183,178,172,159,158,134,115,114,106,104,103,102,101,99,98,90,87,85,83,73,69,65]) ).
thf(196,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX203+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:11:17 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.12/1.56
% 7.12/1.56 No.of.Axioms: 21
% 7.12/1.56
% 7.12/1.56 Length.of.Defs: 0
% 7.12/1.56
% 7.12/1.56 Contains.Choice.Funs: false
% 7.12/1.56 ......
% 7.12/1.56
% 7.12/1.56 ********************************
% 7.12/1.56 * All subproblems solved! *
% 7.12/1.56 ********************************
% 7.12/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:195,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.12/1.56
% 7.12/1.56 %**** Beginning of derivation protocol ****
% 7.12/1.56 % SZS output start CNFRefutation
% See solution above
% 7.12/1.56
% 7.12/1.56 %**** End of derivation protocol ****
% 7.12/1.56 %**** no. of clauses in derivation: 196 ****
% 7.12/1.56 %**** clause counter: 195 ****
% 7.12/1.56
% 7.12/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:195,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------