TSTP Solution File: SYO361^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO361^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 17:33:34 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 100 ( 39 unt; 4 typ; 0 def)
% Number of atoms : 437 ( 224 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1772 ( 685 ~; 117 |; 6 &; 946 @)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 147 ( 147 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 417 ( 320 ^ 97 !; 0 ?; 417 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY4,type,
sK2_SY4: $i ).
thf(tp_sK3_SY7,type,
sK3_SY7: $i > $i > $o ).
thf(tp_sK4_Z,type,
sK4_Z: ( $i > $i > $o ) > $i ).
thf(1,conjecture,
! [X: $i,Y: $i] :
( ( X = Y )
<=> ! [R: $i > $i > $o] :
( ! [Z: $i] : ( R @ Z @ Z )
=> ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM47) ).
thf(2,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
<=> ! [R: $i > $i > $o] :
( ! [Z: $i] : ( R @ Z @ Z )
=> ( R @ X @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
<=> ! [R: $i > $i > $o] :
( ! [Z: $i] : ( R @ Z @ Z )
=> ( R @ X @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY4: $i] :
( ( sK1_X = SY4 )
<=> ! [SY5: $i > $i > $o] :
( ! [Z: $i] : ( SY5 @ Z @ Z )
=> ( SY5 @ sK1_X @ SY4 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sK1_X = sK2_SY4 )
<=> ! [SY7: $i > $i > $o] :
( ! [Z: $i] : ( SY7 @ Z @ Z )
=> ( SY7 @ sK1_X @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( sK1_X = sK2_SY4 )
=> ! [SY7: $i > $i > $o] :
( ! [Z: $i] : ( SY7 @ Z @ Z )
=> ( SY7 @ sK1_X @ sK2_SY4 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ! [SY7: $i > $i > $o] :
( ! [Z: $i] : ( SY7 @ Z @ Z )
=> ( SY7 @ sK1_X @ sK2_SY4 ) )
=> ( sK1_X = sK2_SY4 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ( ( sK1_X = sK2_SY4 )
=> ! [SY7: $i > $i > $o] :
( ! [Z: $i] : ( SY7 @ Z @ Z )
=> ( SY7 @ sK1_X @ sK2_SY4 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ! [SY7: $i > $i > $o] :
( ! [Z: $i] : ( SY7 @ Z @ Z )
=> ( SY7 @ sK1_X @ sK2_SY4 ) )
=> ( sK1_X = sK2_SY4 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ( sK1_X = sK2_SY4 )
& ! [SY9: $i] : ( sK3_SY7 @ SY9 @ SY9 )
& ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ! [SY7: $i > $i > $o] :
( ~ ( SY7 @ ( sK4_Z @ SY7 ) @ ( sK4_Z @ SY7 ) )
| ( SY7 @ sK1_X @ sK2_SY4 ) )
& ( sK1_X != sK2_SY4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ( sK1_X = sK2_SY4 )
& ! [SY9: $i] : ( sK3_SY7 @ SY9 @ SY9 )
& ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ( sK1_X != sK2_SY4 )
| ~ ~ ( ~ ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 )
| ~ ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ( sK1_X != sK2_SY4 )
| ~ ~ ( ~ ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 )
| ~ ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
( ( ( sK1_X != sK2_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 )
| ~ ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( sK1_X = sK2_SY4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( ~ ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 )
| ~ ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 )
| ~ ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
( ( ~ ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ! [SX0: $i] : ( sK3_SY7 @ SX0 @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( sK3_SY7 @ sK1_X @ sK2_SY4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i] :
( ( sK3_SY7 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( sK3_SY7 @ sK1_X @ sK2_SY4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,25,24]) ).
thf(27,plain,
( ( ! [SY7: $i > $i > $o] :
( ~ ( SY7 @ ( sK4_Z @ SY7 ) @ ( sK4_Z @ SY7 ) )
| ( SY7 @ sK1_X @ sK2_SY4 ) )
& ( sK1_X != sK2_SY4 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(28,plain,
( ( ~ ( ~ ! [SX0: $i > $i > $o] :
( ~ ( SX0 @ ( sK4_Z @ SX0 ) @ ( sK4_Z @ SX0 ) )
| ( SX0 @ sK1_X @ sK2_SY4 ) )
| ~ ( ( sK1_X != sK2_SY4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(29,plain,
( ( ~ ! [SX0: $i > $i > $o] :
( ~ ( SX0 @ ( sK4_Z @ SX0 ) @ ( sK4_Z @ SX0 ) )
| ( SX0 @ sK1_X @ sK2_SY4 ) )
| ~ ( ( sK1_X != sK2_SY4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
( ( ~ ! [SX0: $i > $i > $o] :
( ~ ( SX0 @ ( sK4_Z @ SX0 ) @ ( sK4_Z @ SX0 ) )
| ( SX0 @ sK1_X @ sK2_SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(31,plain,
( ( ~ ( ( sK1_X != sK2_SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ! [SX0: $i > $i > $o] :
( ~ ( SX0 @ ( sK4_Z @ SX0 ) @ ( sK4_Z @ SX0 ) )
| ( SX0 @ sK1_X @ sK2_SY4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ( sK1_X != sK2_SY4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV2: $i > $i > $o] :
( ( ~ ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
| ( SV2 @ sK1_X @ sK2_SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( sK1_X = sK2_SY4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) ) )
= $true )
| ( ( SV2 @ sK1_X @ sK2_SY4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false )
| ( ( SV2 @ sK1_X @ sK2_SY4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
( ( ( ( sK4_Z
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK4_Z
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( sK1_X = sK2_SY4 )
= $true ) ),
inference(replace_andrewsEQ,[status(thm)],[37:[bind(SV2,$thf( ^ [SV4: $i] : ^ [SV3: $i] : ( SV4 = SV3 ) ))]]) ).
thf(39,plain,
( ( sK1_X = sK2_SY4 )
= $true ),
inference(sim,[status(thm)],[38]) ).
thf(42,plain,
! [SV7: $i > $i > $o] :
( ( ( ~ ( SV7
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV7 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV2,$thf( ^ [SV5: $i] : ^ [SV6: $i] : ~ ( SV7 @ SV5 @ SV6 ) ))]]) ).
thf(44,plain,
( ( ( ( sK4_Z
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( sK4_Z
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( sK1_X = sK2_SY4 )
= $true ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV2,$thf( ^ [SV13: $i] : ^ [SV12: $i] : ( SV13 = SV12 ) ))]]) ).
thf(45,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false )
| ( ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= ( ~ ( SV2 @ sK1_X @ sK2_SY4 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[37]) ).
thf(46,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
| ~ ( SV2 @ sK1_X @ sK2_SY4 ) )
| ~ ( ~ ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
| ~ ~ ( SV2 @ sK1_X @ sK2_SY4 ) ) )
= $false )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[45]) ).
thf(47,plain,
! [SV2: $i > $i > $o] :
( ( ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= ( ~ ( SV2 @ sK1_X @ sK2_SY4 ) ) )
= $false )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[45]) ).
thf(49,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
| ~ ~ ( SV2 @ sK1_X @ sK2_SY4 ) ) )
= $false )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
| ~ ~ ( SV2 @ sK1_X @ sK2_SY4 ) )
= $true )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) ) )
= $true )
| ( ( ~ ~ ( SV2 @ sK1_X @ sK2_SY4 ) )
= $true )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false )
| ( ( ~ ~ ( SV2 @ sK1_X @ sK2_SY4 ) )
= $true )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ sK1_X @ sK2_SY4 ) )
= $false )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ sK1_X @ sK2_SY4 )
= $true )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV38: $i > $i > $o] :
( ( ( ~ ~ ~ ~ ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extuni,[status(esa)],[47:[bind(SV2,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( ~ ( ~ ( ~ ( SV38 @ SX0 @ SX1 ) ) ) ) ) ))]]) ).
thf(60,plain,
! [SV33: $i > $i > $o] :
( ( ( ~ ~ ~ ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extuni,[status(esa)],[47:[bind(SV2,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( ~ ( ~ ( SV33 @ SX0 @ SX1 ) ) ) ) ))]]) ).
thf(63,plain,
! [SV28: $i > $i > $o] :
( ( ( ~ ~ ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV28 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extuni,[status(esa)],[47:[bind(SV2,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( ~ ( SV28 @ SX0 @ SX1 ) ) ) ))]]) ).
thf(64,plain,
! [SV23: $i > $i > $o] :
( ( ( ~ ~ ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV23 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extuni,[status(esa)],[47:[bind(SV2,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( SV23 @ SX0 @ SX1 ) ) ))]]) ).
thf(67,plain,
! [SV18: $i > $i > $o] :
( ( ( ~ ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV18 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extuni,[status(esa)],[47:[bind(SV2,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( SV18 @ SX0 @ SX1 ) ))]]) ).
thf(68,plain,
! [SV18: $i > $i > $o] :
( ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV18 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV23: $i > $i > $o] :
( ( ( ~ ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV23 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV28: $i > $i > $o] :
( ( ( ~ ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV28 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(75,plain,
! [SV33: $i > $i > $o] :
( ( ( ~ ~ ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(76,plain,
! [SV38: $i > $i > $o] :
( ( ( ~ ~ ~ ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(78,plain,
! [SV18: $i > $i > $o] :
( ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(81,plain,
! [SV23: $i > $i > $o] :
( ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV23 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV28: $i > $i > $o] :
( ( ( ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV28 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV33: $i > $i > $o] :
( ( ( ~ ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV38: $i > $i > $o] :
( ( ( ~ ~ ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV18: $i > $i > $o] :
( ( ( ~ ( SV18 @ sK1_X @ sK2_SY4 ) )
= $true )
| ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(91,plain,
! [SV23: $i > $i > $o] :
( ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ~ ( SV23 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV28: $i > $i > $o] :
( ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV28 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(95,plain,
! [SV33: $i > $i > $o] :
( ( ( ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV38: $i > $i > $o] :
( ( ( ~ ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(98,plain,
! [SV18: $i > $i > $o] :
( ( ( SV18 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV23: $i > $i > $o] :
( ( ( ~ ( SV23 @ sK1_X @ sK2_SY4 ) )
= $false )
| ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV28: $i > $i > $o] :
( ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ( SV28 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(105,plain,
! [SV33: $i > $i > $o] :
( ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) ) )
= $true )
| ( ( ~ ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV38: $i > $i > $o] :
( ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV23: $i > $i > $o] :
( ( ( SV23 @ sK1_X @ sK2_SY4 )
= $true )
| ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(110,plain,
! [SV28: $i > $i > $o] :
( ( ( ~ ( SV28 @ sK1_X @ sK2_SY4 ) )
= $true )
| ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(113,plain,
! [SV33: $i > $i > $o] :
( ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV38: $i > $i > $o] :
( ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(116,plain,
! [SV28: $i > $i > $o] :
( ( ( SV28 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV33: $i > $i > $o] :
( ( ( ~ ( SV33 @ sK1_X @ sK2_SY4 ) )
= $false )
| ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV38: $i > $i > $o] :
( ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV33: $i > $i > $o] :
( ( ( SV33 @ sK1_X @ sK2_SY4 )
= $true )
| ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV38: $i > $i > $o] :
( ( ( ~ ( SV38 @ sK1_X @ sK2_SY4 ) )
= $true )
| ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(126,plain,
! [SV38: $i > $i > $o] :
( ( ( SV38 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true )
| ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(128,plain,
! [SV7: $i > $i > $o] :
( ( ( SV7
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) ) )
= $true )
| ( ( ~ ( SV7 @ sK1_X @ sK2_SY4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(130,plain,
! [SV7: $i > $i > $o] :
( ( ( SV7 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV7
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV7 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
( ( sK1_X = sK2_SY4 )
= $true ),
inference(extuni,[status(esa)],[44]) ).
thf(133,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ sK1_X @ sK2_SY4 )
= $true )
| ( ( SV2 @ ( sK4_Z @ SV2 ) @ ( sK4_Z @ SV2 ) )
= $false ) ),
inference(sim,[status(thm)],[57]) ).
thf(134,plain,
! [SV18: $i > $i > $o] :
( ( ( SV18 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV18
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ( SV18 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(sim,[status(thm)],[98]) ).
thf(135,plain,
! [SV23: $i > $i > $o] :
( ( ( SV23 @ sK1_X @ sK2_SY4 )
= $true )
| ( ( SV23
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV23 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(sim,[status(thm)],[109]) ).
thf(136,plain,
! [SV28: $i > $i > $o] :
( ( ( SV28 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV28
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ( SV28 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(sim,[status(thm)],[116]) ).
thf(137,plain,
! [SV33: $i > $i > $o] :
( ( ( SV33 @ sK1_X @ sK2_SY4 )
= $true )
| ( ( SV33
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ( SV33 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(sim,[status(thm)],[123]) ).
thf(138,plain,
! [SV38: $i > $i > $o] :
( ( ( SV38 @ sK1_X @ sK2_SY4 )
= $false )
| ( ( SV38
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) )
@ ( sK4_Z
@ ^ [SX0: $i,SX1: $i] :
~ ~ ~ ~ ~ ( SV38 @ SX0 @ SX1 ) ) )
= $true ) ),
inference(sim,[status(thm)],[126]) ).
thf(139,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,138,137,136,135,134,133,132,130,39,37]) ).
thf(140,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[139,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO361^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 04:05:07 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.55
% 0.20/0.55 ********************************
% 0.20/0.55 * All subproblems solved! *
% 0.20/0.55 ********************************
% 0.20/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:139,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.20/0.55
% 0.20/0.55 %**** Beginning of derivation protocol ****
% 0.20/0.55 % SZS output start CNFRefutation
% See solution above
% 0.38/0.55
% 0.38/0.55 %**** End of derivation protocol ****
% 0.38/0.55 %**** no. of clauses in derivation: 96 ****
% 0.38/0.55 %**** clause counter: 139 ****
% 0.38/0.55
% 0.38/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:139,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------